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History of the British canal system The British canal system of water transport played a vital role in the United Kingdom's Industrial Revolution at a time when roads were only just emerging from the medieval mud and long trains of packhorses were the only means of "mass" transit by road of raw materials and finished products (it was no accident that amongst the first canal promoters were the pottery manufacturers of Staffordshire). The UK was the first country to acquire a nationwide canal network. - 1 Overview - 2 Early history - 3 The Industrial Revolution - 4 Standard locks - 5 Geography - 6 Operations - 7 Gradual decline - 8 Restoration - 9 See also - 10 References - 11 External links The canal system grew rapidly at first, and became an almost completely connected network covering the South, Midlands, and parts of the North of England and Wales. There were canals in Scotland, but they were not connected to the English canals or, generally, to each other (the main exception being the Monkland Canal, the Union Canal and the Forth and Clyde Canal which connected the River Clyde and Glasgow to the River Forth and Edinburgh). As building techniques improved, older canals were improved by straightening, embankments, cuttings, tunnels, aqueducts, inclined planes, and boat lifts, which together snipped many miles and locks, and therefore hours and cost, from journeys. However, there was often fierce opposition to the building The modern canal network came into being because the Industrial Revolution (which began in Britain during the mid-18th century) demanded an economic and reliable way to transport goods and commodities in large quantities. Some 29 river navigation improvements took place in the 16th and 17th centuries starting with the Thames locks and the River Wey Navigation. The biggest growth was in the so-called "narrow" canals which extended water transport to the emerging industrial areas of the Staffordshire potteries and Birmingham as well as a network of canals joining Yorkshire and Lancashire and extending to London. The 19th century saw some major new canals such as the Caledonian Canal and the Manchester Ship Canal. By the second half of the 19th century, many canals were increasingly becoming owned by railway companies or competing with them, and many were in decline, with decreases in mile-ton charges to try to remain competitive. After this, the less successful canals (particularly narrow-locked canals, whose boats could only carry about thirty tons) failed quickly. The 20th century brought competition from road haulage, and only the strongest canals survived until the Second World War. After the war, there was a rapid decline in trade on all the remaining canals, and by the mid 1960s only a token traffic was left, even on the widest and most industrial waterways. In the 1960s the infant canal leisure industry was only just sufficient to prevent the closure of the remaining canals, but then the pressure to maintain canals for leisure purposes increased. From the 1970s, increasing numbers of closed canals were restored by enthusiast volunteers. The success of these projects has led to the funding and use of contractors to complete large restoration projects and complex civil engineering projects such as the restoration of the Victorian Anderton Boat Lift and the new Falkirk Wheel rotating lift. Restoration projects by volunteer-led groups continue. There is now a substantial network of interconnecting, fully navigable canals across the country. In places, serious plans are in progress by the Environment Agency and British Waterways Board, later the Canal & River Trust, for building new canals to expand the network, link isolated sections, and create new leisure opportunities for navigating "canal rings", for example the Fens Waterways Link and the Bedford and Milton Keynes Waterway. The first British canals were built in Roman times as irrigation or land drainage canals or short connecting spurs between navigable rivers, such as the Foss Dyke, Car Dyke and Bourne-Morton Canal; all in Lincolnshire. See Roman Britain and list of Roman canals. A spate of building projects, such as castles, monasteries and churches, led to the improvement of rivers for the transportation of building materials. Various Acts of Parliament were passed regulating transportation of goods, tolls and horse towpaths for various rivers. These included the rivers Severn, Witham, Trent and Yorkshire Ouse. The first Act for navigational improvement in England was in 1425, for improvement of the river Lea, a major tributary of the River Thames. Post-medieval transport systems In the post-medieval period, some natural waterways were "canalised" or improved for boat traffic in the 16th century. The first Act of Parliament was obtained by the City of Canterbury in 1515, to extend navigation on the River Stour in Kent, followed by the River Exe in 1539, which led to the construction in 1566 of a new channel, the Exeter Canal. Simple flash locks were provided to regulate the flow of water and allow loaded boats to pass through shallow waters by admitting a rush of water, but these were not purpose-built canals as we understand them today. The transport system that existed before the canals were built consisted of coastal shipping and horses and carts struggling along mostly unsurfaced mud roads (although there were some surfaced turnpike roads). There was also a small amount of traffic carried along navigable rivers. In the 17th century, as early industry started to expand, this transport situation was highly unsatisfactory. The restrictions of coastal shipping and river transport were obvious, and horses and carts could only carry one or two tons of cargo at a time. The poor state of most of the roads meant that they could often become unusable after heavy rain. Because of the small loads that could be carried, supplies of essential commodities such as coal and iron ore were limited, and this kept prices high and restricted economic growth. One horse-drawn canal barge could carry about thirty tonnes at a time, faster than road transport and at half the cost. Some 29 river navigation improvements took place in the 16th and 17th centuries. In 1605, the government of King James I established the Oxford-Burcot Commission, which began to improve the system of locks and weirs on the River Thames, which were opened between Oxford and Abingdon by 1635. In 1635 Sir Richard Weston was appointed to develop the River Wey Navigation, making Guildford accessible by 1653. In 1670 the Stamford Canal opened, indistinguishable from 18th century examples with a dedicated cut and double-door locks. In 1699 legislation was passed to permit the Aire & Calder Navigation which was opened 1703, and the Trent Navigation which was built by George Hayne and opened in 1712. Subsequently, the Kennet built by John Hore opened in 1723, the Mersey and Irwell opened in 1725, and the Bristol Avon in 1727. John Smeaton was the engineer of the Calder & Hebble which opened in 1758, and a series of eight pound locks was built to replace flash locks on the River Thames between Maidenhead and Reading, beginning in 1772. The net effect of these was to bring most of England, with the notable exceptions of Birmingham and Staffordshire, within 15 miles (24 km) of a waterway. The Industrial Revolution The modern canal system was mainly a product of the 18th and early 19th centuries. It came into being because the Industrial Revolution (which began in Britain during the mid-18th century) demanded an economic and reliable way to transport goods and commodities in large quantities. By the early 18th century, river navigations such as the Aire and Calder Navigation were becoming quite sophisticated, with pound locks and longer and longer "cuts" (some with intermediate locks) to avoid circuitous or difficult stretches of rivers. Eventually, the experience of building long multi-level cuts with their own locks gave rise to the idea of building a "pure" canal, a waterway designed on the basis of where goods needed to go, not where a river happened to be. The claim for the first pure canal in Great Britain is debated between "Sankey" and "Bridgewater" supporters. The first true canal in the United Kingdom was the Newry Canal in Northern Ireland constructed by Thomas Steers in 1741. The Sankey Brook Navigation, which connected St Helens with the River Mersey, is often claimed as the first modern "purely artificial" canal, because although it was originally a scheme to make the Sankey Brook navigable, it included an entirely new artificial channel that was effectively a canal along the Sankey Brook valley. However, "Bridgewater" supporters point out that the last quarter-mile (400 m) of the navigation is indeed a canalised stretch of the Brook, and that it was the Bridgewater Canal (less obviously associated with an existing river) that captured the popular imagination and inspired further canals. The Bridgewater Canal In the mid-18th century the 3rd Duke of Bridgewater, who owned a number of coal mines in northern England, wanted a reliable way to transport his coal to the rapidly industrialising city of Manchester. He commissioned the engineer James Brindley to build a canal to do just that. Brindley's design included an aqueduct carrying the canal over the River Irwell. This was an engineering wonder which immediately attracted tourists. The construction of this canal was funded entirely by the Duke and it was called the Bridgewater Canal. It opened in 1761 and was the longest canal constructed in Britain to that date. Horse drawn canal transport The new canals proved highly successful. The boats on the canals were horse-drawn with a towpath alongside the canal for the horse to walk along. This horse-drawn system proved to be highly economical and became standard across the British canal network. Commercial horse-drawn canal boats could be seen on the UK's canals until as late as the 1950s, although by then diesel powered boats, often towing a second unpowered boat, had become standard. The canal boats could carry thirty tons at a time with only one horse pulling - more than ten times the amount of cargo per horse that was possible with a cart. Because of this huge increase in supply, the Bridgewater Canal reduced the price of coal in Manchester by nearly two-thirds within just a year of its opening. The Bridgewater Canal was also a huge financial success: it repaid the cost of its construction within just a few years. The Golden Age This success proved the viability of canal transport, and soon industrialists in many other parts of the country wanted canals. After the Bridgewater Canal, the early canals were built by groups of private individuals with an interest in improving communications. In Staffordshire the famous potter Josiah Wedgwood saw an opportunity to bring bulky cargoes of clay to his factory doors, and to transport his fragile finished goods to market in Manchester, Birmingham or further afield by water, minimising breakages. Within just a few years of the Bridgewater's opening, an embryonic national canal network came into being, with the construction of canals such as the Oxford Canal and the Trent & Mersey Canal. The new canal system was both cause and effect of the rapid industrialisation of the Midlands and the north. The period between the 1770s and the 1830s is often referred to as the "Golden Age" of British canals. For each canal, an Act of Parliament was necessary to authorise construction, and as people saw the high incomes achieved from canal tolls, canal proposals came to be put forward by investors interested in profiting from dividends, at least as much as by people whose businesses would profit from cheaper transport of raw materials and finished goods. In a further development, there was often out-and-out speculation, in which people would try to buy shares in a newly floated company simply to sell them on for an immediate profit, regardless of whether the canal was ever profitable, or even built. During this period of "canal mania", huge sums were invested in canal building, and although many schemes came to nothing, the canal system rapidly expanded to nearly 4,000 miles (over 6,400 kilometres) in length. Many rival canal companies were formed and competition was rampant. Perhaps the best example was Worcester Bar in Birmingham, a point where the Worcester and Birmingham Canal and the Birmingham Canal Navigations Main Line were only 7 feet (2.1 m) apart. For many years, a dispute about tolls meant that goods travelling through Birmingham had to be portaged from boats in one canal to boats in the other. For the first era of canals until toll cuts to combat railway competition family boating did not exist.[clarification needed] Crews were all male and their families lived in cottages on the bank. The practice of all male crews for steamers continued until after the First World War. Wives and children came aboard as extra labour and to save rental costs during the latter part of the 19th century. About this time boat decoration of "Roses and Castles" began to appear. During this period, whole families lived aboard the boats. They were often marginalised from land-based society. The church of St Thomas the Martyr, Oxford, under the curacy of John Jones, acquired in 1839 an innovative "Boatman's Floating Chapel", a houseboat to serve the families working on the river and the canals. This boat was St Thomas' first chapel of ease; it was donated by H. Ward, a local coal merchant, and used until it sank in 1868. It was replaced by a chapel dedicated to St Nicholas, which remained in use until 1892. For reasons of economy and the constraints of 18th-century engineering technology, the early canals were built to a narrow width. The standard for the dimensions of narrow canal locks was set by Brindley with his first canal locks, those on the Trent and Mersey Canal in 1776. These locks were 72 feet 7 inches (22.12 m) long by 7 feet 6 inches (2.29 m) wide. The narrow width was perhaps set by the fact that he was only able to build Harecastle Tunnel to accommodate 7 feet (2.1 m) wide boats. His next locks were wider. He built locks 72 feet 7 inches (22.12 m) long by 15 feet (4.6 m) wide when he extended the Bridgewater Canal to Runcorn, where the canal's only locks lowered boats to the River Mersey. The narrow locks on the Trent and Mersey limited the width (beam) of the boats (which came to be called narrowboats), and thus limited the quantity of the cargo they could carry to around thirty tonnes. This decision would in later years make the canal network economically uncompetitive for freight transport, and by the mid 20th century it was no longer possible to work a thirty-tonne load economically. Brindley believed it would be possible to use canals to link the four great rivers of England: the Mersey, Trent, Severn and Thames. The Trent and Mersey Canal was the first part of this ambitious network, but although he and his assistants surveyed the whole potential system, he did not live to see it completed - coal was finally transported from the Midlands to the Thames at Oxford in January 1790, eighteen years after his death. Development of the network was left to other engineers, notably Thomas Telford, whose Ellesmere Canal helped link the Severn and the Mersey. The bulk of the canal system was built in the industrial Midlands and the north of England, where navigable rivers most needed extending and connecting, and heavy cargoes of manufactured goods, raw materials or coal most needed carrying. Most of the traffic on the canal network was internal. However, the network linked with coastal port cities such as London, Liverpool, and Bristol, where cargo could be exchanged with seagoing ships for import and export. The West Midlands and the North West of England The great manufacturing cities of Manchester and Birmingham were major economic drivers for the 'canal mania' which reached its peak in 1793, and both benefited from a network of canals, most of which survive. In the industrial conurbation of Birmingham and the Black Country, a dense network of nearly 160 miles (260 km) of canals, dubbed the Birmingham Canal Navigations (BCN) was constructed to serve the network of industries. Manchester had a canal connection to the nearby port of Liverpool via the Leeds and Liverpool Canal. However, in the nineteenth century, Manchester's merchants became dissatisfied with the poor service and high charges offered by the Liverpool docks, and the near-monopoly of the railways. They decided to bypass the Liverpool monopoly on coastal trade by converting a section of the Irwell into the Manchester Ship Canal, which opened in 1894, turning Manchester into an inland port in its own right. Birmingham's canals linked to the national network in several directions. To the north, several trunk cross-country canals, linking Birmingham to Manchester were constructed, including the Trent and Mersey and Shropshire Union Canal. The Coventry Canal, the Oxford Canal, and what is now the Grand Union Canal linked southwards to London. And to the south-west, the Worcester & Birmingham and Staffordshire & Worcestershire canals linked to the River Severn. Yorkshire and the East of England The industrial revolution saw Yorkshire towns and cities such as Leeds, Sheffield, Bradford and Huddersfield develop large textile and coal mining industries, which required an efficient transport system. As early as the late 17th century, the Aire and Calder and Calder and Hebble navigations had been canalised, allowing navigation from Leeds to the Humber Estuary, whereas the River Don Navigation connected Sheffield to the Humber. Later in the 18th century, the Leeds and Liverpool Canal was constructed, creating an east-west link, giving access to the port at Liverpool allowing export of finished goods. The Rochdale and Huddersfield Broad and Narrow canals connected to Manchester. The East Midlands cities of Nottingham and Leicester were connected to the national network via the canalised River Trent and River Soar, whilst Leicester had a connection to London via the Grand Union Canal. London and the South East By contrast, London was a port, served by already-navigable rivers like the Thames and the River Lea, (which was canalised). It needed canals only to take goods in and out from seagoing ships, where such rivers were unavailable. As early as 1790 London was linked to the national network via the River Thames and the Oxford Canal. A more direct route between London and the national canal network; the Grand Junction Canal opened in 1805. South Wales and South West England The South West of England had several east-west cross-country canals, which connected the River Thames to the River Severn and the River Avon, allowing the cities of Bristol and Bath to be connected to London: These were Thames and Severn Canal which linked to the Stroudwater Navigation, the Kennet and Avon Canal and the Wilts and Berks Canal, which linked to these three rivers; all of these linked into the national canal system via the Oxford Canal and the River Severn (via the Worcester & Birmingham and Staffordshire & Worcestershire canals). All of these east-west canals fell derelict in the early 20th century, and only the Kennet and Avon is today navigable, having been restored. A few self-contained canals, not connected to the national system, were built in Devon and Cornwall, such as the Bude Canal and the St. Columb Canal. The same was true for South Wales, with several isolated canals running along the South Wales Valleys. These included the Swansea Canal, the Neath and Tennant Canal, the Glamorganshire Canal and the Monmouthshire & Brecon Canal. Nearly all of these canals were constructed to serve local industries, and fell derelict when faced with competition from other modes of transport. Within Scotland, the Forth and Clyde Canal and the Union Canal connected the major cities in the industrial Central Belt; they also provide a short cut for boats to cross between the west and the east without a sea voyage. The Caledonian Canal provided a similar function in the Highlands of Scotland. The Crinan Canal avoided the need for a long diversion around the Kintyre peninsula, and the Glasgow, Paisley and Johnstone Canal was intended to link these three places directly to the west coast of Scotland, but never reached beyond Johnstone. The Monkland Canal was conceived in 1769 by tobacco merchants and other entrepreneurs as a way of bringing cheap coal into Glasgow from the coalfields of the Monklands area. On the majority of British canals, the canal-owning companies did not own or run a fleet of boats since this was usually prohibited by the Acts of Parliament setting them up to prevent monopolies developing. Instead, they charged private operators tolls to use the canal. These tolls were also usually regulated by the Acts. From these tolls they would try, with varying degrees of success, to maintain the canal, pay back initial loans and pay dividends to their shareholders. In winter special icebreaker boats with reinforced hulls would be used to break the ice. The boats used on canals were usually derived from local coasting or river craft, but on the narrow canals the 7-foot-wide (2.1 m) narrowboat was the standard. Their 72-foot (22 m) length came from the boats used on the Mersey estuary, with their width of 7 feet (2.1 m) chosen as half that of existing boats, and adopted to make canals cheaper to build. All boats on the canals were horsedrawn. Packet boats carried packages up to 112 pounds (51 kg) in weight as well as passengers at relatively high speed day and night. To compete with railways, the flyboat was introduced, cargo-carrying boats working day and night. These boats were crewed by three men, who operated a watch system whereby two men worked while the other slept. Horses were changed regularly. When steam boats were introduced in the late nineteenth century, crews were enlarged to four. The boats were owned and operated by individual carriers, or by carrying companies who would pay the captain a wage depending on the distance travelled, and the amount of cargo. From about 1840 railways began to threaten canals, as they could not only carry more than the canals but could transport people and goods far more quickly than the walking pace of the canal boats. Most of the investment that had previously gone into canal building was diverted into railway building. Canal companies were unable to compete against the speed of the new railways, and in order to survive, they had to slash their prices. This put an end to the huge profits that canal companies had enjoyed before the coming of the railways, and also had an effect on the boatmen who faced a drop in wages. Flyboat working virtually ceased, as it could not compete with the railways on speed and the boatmen found they could only afford to keep their families by taking them with them on the boats. This became standard practice across the canal system, with in many cases families with several children living in tiny boat cabins, creating a considerable community of boat people. Though this community ostensibly had much in common with Gypsies both communities strongly resisted any such comparison, and surviving boat people feel deeply insulted if described as 'water gypsies'. By the 1850s the railway system had become well established and the amount of cargo carried on the canals had fallen by nearly two-thirds, lost mostly to railway competition. In many cases struggling canal companies were bought out by railway companies. Sometimes this was a tactical move by railway companies to gain ground in their competitors' territory, but sometimes canal companies were bought out, either to close them down and remove competition or to build a railway on the line of the canal. A notable example of this is the Croydon Canal. Larger canal companies survived independently and were able to continue to make profits. The canals survived through the 19th century largely by occupying the niches in the transport market that the railways had missed, or by supplying local markets such as the coal-hungry factories and mills of the big cities. Overall, the canals adapted to the appearance of railways and in 1900 the canal network differed little from its extent in 1830. Limited modernisation to broad canals During the 19th century in much of continental Europe the canal systems of many countries such as France, Germany and the Netherlands were drastically modernised and widened to take much larger boats, often able to transport up to two thousand tonnes, compared to the thirty to one hundred tonnes that was possible on the much narrower British canals. As it is economic to transport freight by canal only if this is done in bulk, the widening ensured that in many of these countries, canal freight transport is still economically viable. This canal modernisation never occurred on a large scale in the UK, mainly because of the power of the railway companies who owned most of the canals and saw no reason to invest in a competing, and from their point of view obsolete, form of transport. In view of this attitude, there was little point in the non-railway owned canals modernising, since they controlled only parts of the system. The only significant exception to this was the modernisation carried out on the Grand Union Canal in the 1930s. Thus almost uniquely in Europe, many of the UK's canals remain as they have been since the 18th and 19th century: mostly operated with narrowboats less than 7 feet (2.1 m) wide and 70 feet (21 m) long (although in parts of the country slightly larger canals were constructed, called 'broad' or 'wide' canals, which could take boats that were 14 feet (4.3 m) wide and 70 feet (21 m) long). A major exception to this stagnation was the Manchester Ship Canal, newly built in the 1890s using the existing River Irwell and River Mersey, to take ocean-going ships into the centre of Manchester via its neighbour Salford. 20th century nationalisation The canal network gradually declined. During the early 20th century, especially in the 1920s and 1930s, many canals, mostly in rural areas, were abandoned due to falling traffic, caused mainly by competition from road transport. However, the main network saw brief surges in use during the First and Second World Wars and still carried a substantial amount of freight until the early 1950s. The final blow was delivered by technological change. Most of the canal system and inland waterways were nationalised in 1948, along with the railways, under the British Transport Commission, whose subsidiary Docks and Inland Waterways Executive managed them into the 1950s. A report in 1955 by the British Transport Commission placed the canals in the UK into three categories according to their economic prospects; waterways to be developed, waterways to be retained, and waterways having insufficient commercial prospects to justify their retention for navigation. During the 1950s and 1960s freight transport on the canals declined rapidly in the face of mass road transport, and several more canals were abandoned during this period. Most of the traffic on the canals by this time was in coal delivered to waterside factories which had no other convenient access. In the 1950s and 60s, these factories either switched to using other fuels, often because of the Clean Air Act of 1956, or closed completely. The last regular long distance narrow boat carrying contract, to a jam factory near London, ended in 1971, although lime juice continued to be carried between Brentford and Boxmoor until 1981, substantial tonnages of aggregates were carried by narrow boat subsequently on the Grand Union (River Soar) until 1996 and more recently between Denham and West Drayton. Under the Transport Act of 1962, the canals were transferred in 1963 to the British Waterways Board (BWB), which later became British Waterways, and the railways to the British Railways Board (BRB). In the same year a remarkably harsh winter saw many boats frozen into their moorings, and unable to move for weeks at a time. This was one of the reasons given for the decision by BWB to formally cease most of its narrow boat carrying on the canals - with boats and traffics transferred to a private operator, Willow Wren Canal Transport services. By this time the canal network had shrunk to just two thousand miles (3,000 kilometres), half the size it was at its peak in the early 19th century. However, the basic network was still intact; many of the closures were of duplicate routes or branches. Transport Act 1968 The Transport Act 1968 classified the nationalised waterways as: - Commercial - Waterways that could still support commercial traffic; - Cruising - Waterways that had a potential for leisure use, such as cruising, fishing and recreational use; - Remainder - Waterways for which no potential commercial or leisure use could be seen. British Waterways Board was required, under the Act, to keep Commercial Waterways, mainly in the north-east, fit for commercial use; and Cruising Waterways fit for cruising. However, these obligations were subject to the caveat of being by the most economical means. There was no requirement to maintain Remainder waterways or keep them in a navigable condition; they were to be treated in the most economic way possible, which could mean abandonment. British Waterways could also change the classification of an existing waterway. Parts, or all, of a Remainder Waterway canal, could also be transferred to local authorities, etc.; and this transfer could, as happened, allow roads and motorways to be built over them, mitigating the need to provide (expensive) accommodation bridges or aqueducts. The act also allowed local authorities to contribute to the upkeep of Remainder Waterways. Though commercial use of the UK's canals declined after the Second World War, recreational use gradually increased as people had more leisure time and disposable income. The establishment in 1946 of a group called the Inland Waterways Association by L. T. C. Rolt and Robert Aickman has helped revive interest in the UK's canals to the point where they are a major leisure destination. Since the formation of the Basingstoke Canal Purchasing Committee in March 1949, waterway restoration organisations have returned many hundreds of miles of abandoned and remainder canals to use, and work is still ongoing to save many more. Many restoration projects have been led by local canal societies or trusts, who were initially formed to fight the closure of a remainder waterway or to save an abandoned canal from further decay. They now work with local authorities and landowners to develop restoration plans and secure funding. The physical work is sometimes done by contractors, sometimes by volunteers. In 1970 the Waterway Recovery Group was formed to co-ordinate volunteer efforts on canals and river navigation's throughout the United Kingdom. British Waterways began to see the economic and social potential of canalside development, and moved from hostility towards restoration, through neutrality, towards a supportive stance. Whilst British Waterways was broadly supportive of restoration, its official policy was that it would not take on the support of newly restored navigations unless they came with a sufficient dowry to pay for their ongoing upkeep. In effect, this meant either reclassifying the Remainder Waterway as a Cruising Waterway or entering into an agreement for another body to maintain the waterway. There has also been a movement to redevelop canals in inner city areas, such as Birmingham, Manchester, Salford and Sheffield, which have both numerous waterways and urban blight. In these cities, waterways redevelopment provides a focus for successful commercial/residential developments such as Gas Street Basin in Birmingham, Castlefield Basin and Salford Quays in Manchester, Victoria Quays in Sheffield. However, these developments are sometimes controversial. In 2005 environmentalists complained that housing developments on London's waterways threatened the vitality of the canal system. Today the major majority of canals in England and Wales are managed by the Canal & River Trust which, unlike its predecessor British Waterways, tries to have a more positive view on canal restoration and in some cases actively supports ongoing restoration projects such as the restoration projects on the Manchester Bolton & Bury Canal and the Grantham Canal. - Canals of the United Kingdom for a list of the UK's canals - Canals of Ireland of a list of canals throughout Ireland - Tooley's Boatyard - Reader's Digest Library of Modern Knowledge. London: Readers Digest. 1978. p. 990. - "Canal Acts - UK Parliament". Parliament.uk. 2010-04-21. Retrieved 2017-02-12. - Skempton, quoted in Burton, (1995). Chapter 2: The River Navigations - Hadfield, Charles (1981). The Canal Age (Second ed.). David & Charles. ISBN 0-7153-8079-6. - See http://www.britishwaterways.co.uk/ - Rolt, Inland Waterways - Burton, (1995). Chapter 2: The River Navigations - History of the Lee Navigation (1190-1790) - London Canal Museum - Fred. S. Thacker The Thames Highway: Volume I General History 1920 - republished 1968 David & Charles - Dictionary of National Biography - Sir Richard Weston - History of Burton from 'British History Online' - Fred. S. Thacker The Thames Highway: Volume II Locks and Weirs 1920 - republished 1968 David & Charles - L.T.C. Rolt (1969). Navigable Waterways. Longmans, London. - Burton, (1995). Chapter 3: Building the Canals - Hadfield, Charles (1966). The Canals of the West Midlands. David & Charles. ISBN 0-7153-4660-1. - Hibbert, Christopher & Edward (1988). The Encyclopaedia of Oxford. Macmillan. ISBN 0-333-39917-X. - Boughey, Joseph. (1998) Hadfield's British Canals, Sutton Publishing Ltd, ISBN 0-7509-1840-3 - Russell, Ronald. (1983) Lost Canals & Waterways of Britain, Sphere Books Ltd, ISBN 0-7221-7562-0 - Palmer (chairman) 1955, pp. 68–70. - "Transport Act 1968". - Squires (2008), p.24 - Squires (2008), p.71 - Guardian article on London waterways developments - Blair, John (ed.) (2007). Waterways and Canal-building in Medieval England. Oxford: Oxford University Press. ISBN 978-0-19-921715-1. - Broadbridge, S.R. (1974). The Birmingham Canal Navigations. Volume 1: 1768-1846. Newton Abbot: David & Charles. ISBN 0-7153-6381-6. - Volume 2 was never published. - Burton, Anthony (1995). The Great Days of the Canals. London: Tiger Books International. ISBN 1-85501-695-8. - Burton, Anthony (1983). The Waterways of Britain: A Guide to the Canals and Rivers of England, Scotland and Wales. London: Willow Books, William Collins and Sons & Co Ltd. ISBN 0-00-218047-2. - Hadfield, Charles (1966). The Canals of the West Midlands. Newton Abbot: David & Charles. ISBN 0-7153-4660-1. - Hadfield, Charles (1981). The Canal Age (Second ed.). David & Charles. ISBN 0-7153-8079-6. - Lindsay, Jean (1968). The Canals of Scotland. Newton Abbot: David & Charles. ISBN 0-7153-4240-1. - Malet, Hugh (1961/1990). Bridgewater: The Canal Duke 1736-1803, 3rd rev ed, paperback. Nelson, UK: Henton Publishing Co. ISBN 0-86067-136-4. - Paget-Tomlinson, E. (2006) The Illustrated History of Canal & River Navigations: Landmark Publishing Ltd ISBN 1-84306-207-0 - Palmer (chairman), Robert (1955). "Canals and Inland Waterways, Report of the Board of Survey". British Transport Commission. - "Reader's Digest Library of Modern Knowledge". London: Reader's Digest. 1978.. - Rolt, L.T.C. (1944). Narrow Boat. London: Eyre Methuen. ISBN 0-413-22000-1. - Rolt, L.T.C. (1950). The Inland waterways of England. London: George Allen and Unwin Ltd. ISBN 0-04-386003-6. - Roger Squires (2008). Britain's restored canals. Landmark Publishing. ISBN 978-1-84306-331-5. - Thompson, Hubert Gordon (1904). The Canal System of England. London: T. Fisher Unwin.
In a purely economic sense, inflation refers to a general increase in price levels due to an increase in the quantity of money; the growth of the money stock increases faster than the level of productivity in the economy. The exact nature of price increases is the subject of much economic debate, but the word inflation narrowly refers to a monetary phenomenon in this context. Using these specific parameters, the term deflation is used to describe productivity increasing faster than the money stock. This leads to a general decrease in prices and the cost of living, which many economists paradoxically interpret to be harmful. The arguments against deflation trace back to John Maynard Keynes’ paradox of thrift. Due to this belief, most central banks pursue a slightly inflationary monetary policy to safeguard against deflation. - Central banks today primarily use inflation targeting in order to keep economic growth steady and prices stable. - With a 2-3% inflation target, when prices in an economy deviate the central bank can enact monetary policy to try and restore that target. - If inflation heats up, raising interest rates or restricting the money supply are both contractionary monetary policies designed to lower inflation. Most modern central banks target the rate of inflation in a country as their primary metric for monetary policy. If prices rise faster than their target, central banks tighten monetary policy by increasing interest rates or other hawkish policies. Higher interest rates make borrowing more expensive, curtailing both consumption and investment, both of which rely heavily on credit. Likewise, if inflation falls and economic output declines, the central bank will lower interest rates and make borrowing cheaper, along with several other possible expansionary policy tools. As a strategy, inflation targeting views the primary goal of the central bank as maintaining price stability. All of the tools of monetary policy that a central bank has, including open market operations and discount lending, can be employed in a general strategy of inflation targeting. Inflation targeting can be contrasted to strategies of central banks aimed at other measures of economic performance as their primary goals, such as targeting currency exchange rates, the unemployment rate, or the rate of nominal Gross Domestic Product (GDP) growth. How Central Banks Influence the Money Supply Contemporary governments and central banks rarely ever print and distribute physical money to influence the money supply, instead relying on other controls such as interest rates for interbank lending. There are several reasons for this, but the two largest are: 1) new financial instruments, electronic account balances and other changes in the way individuals hold money make basic monetary controls less predictable; and 2) history has produced more than a handful of money-printing disasters that have led to hyperinflation and mass recession. The U.S. Federal Reserve switched from controlling actual monetary aggregates, or number of bills in circulation, to implementing changes in key interest rates, which has sometimes been called the “price of money.” Interest rate adjustments impact the levels of borrowing, saving, and spending in an economy. When interest rates rise, for example, savers can earn more on their demand deposit accounts and are more likely to delay present consumption for future consumption. Conversely, it is more expensive to borrow money, which discourages lending. Since lending in a modern fractional reserve banking system actually creates “new” money, discouraging lending slows the rate of monetary growth and inflation. The opposite is true if interest rates are lowered; saving is less attractive, borrowing is cheaper, and spending is likely to increase, etc. Increasing and Decreasing Demand In short, central banks manipulate interest rates to either increase or decrease the present demand for goods and services, the levels of economic productivity, the impact of the banking money multiplier and inflation. However, many of the impacts of monetary policy are delayed and difficult to evaluate. Additionally, economic participants are becoming increasingly sensitive to monetary policy signals and their expectations about the future. There are some ways in which the Federal Reserve controls the money stock; it participates in what is called “open market operations,” by which federal banks purchase and sell government bonds. Buying bonds injects new dollars into the economy, while selling bonds drains dollars out of circulation. So-called quantitative easing (QE) measures are extensions of these operations. Additionally, the Federal Reserve can change the reserve requirements at other banks, limiting or expanding the impact of money multipliers. Economists continue to debate the usefulness of monetary policy, but it remains the most direct tool of central banks to combat or create inflation.
Newton's Laws of Motion are: Newton's Laws are all contained in a more general principle called conservation of momentum. Momentum is mass times velocity, and in a system that is not disturbed from outside, the total momentum stays constant. Thus: Suppose you are standing on very slick ice. You weigh 50 kg. You fire a 10 gram (.01 kg) bullet at 500 m/sec. Its momentum is .01 x 500 = 5 (the units are kg-m/sec, if you're curious). To keep the total momentum of the original system zero, you have to acquire -5 momentum. Since you weigh 50 kg, your velocity will be -5/50 or -0.1 m/sec. You will start sliding backward on the ice at 10 centimeters per second. This is why a rifle has a kick. As an aside, what matters are instantaneous changes. Once the bullet leaves the gun, it's no longer part of your system, and what happens to it doesn't affect you. You don't feel a momentum change when the bullet strikes its target. Likewise, when friction eventually slows your slide on the ice, that doesn't affect the bullet. Okay, go back to what you were doing. Rockets and jets work according to Newton's Third Law. They fire mass out at high speed and acquire velocity in the opposite direction. Thus, we can dispel one common myth about rockets and jets: they do not need something to push against. A rocket does not take off because it is pushing against the ground, nor does a jet fly because it is pushing against the air. They move because they are expelling exhaust gases at high speeds. If you like, the rocket or jet is pushing mass away, and the mass is pushing back (equal and opposite reaction.) Rockets and jets expel mass by burning fuel. A rocket differs from a jet in that a jet gets the oxygen for combustion from the atmosphere, and a rocket carries oxygen in some form with it. Thus rockets can function outside the Earth's atmosphere; jets can't. When a rocket or jet takes off, it has to carry all its remaining fuel with it. Most of the mass of the Space Shuttle is fuel, and most of that is used to get the remaining fuel off the ground. The miles-per-gallon fuel efficiency of the Space Shuttle in its first foot off the ground is pretty terrible! Satellites travel elliptical paths with the center of the Earth at one focus (A below - Kepler's First Law, again). Anything shot from the surface of the Earth, a baseball, say, or a cannonball, travels an elliptical path, but the ellipse soon intersects the surface of the Earth again (we often say it's a parabola, and it is to very high precision, but technically it's the outer end of a very long ellipse.) Ballistic missiles do the same thing except their ellipses intersect the surface of the Earth thousands of kilometers away. Nothing shot directly from the surface of the Earth can go into orbit; it will either fall back to Earth again or, if it's moving fast enough, escape completely. Incidentally, if we could somehow magically let the object pass through the earth's interior, it would not travel in an ellipse. One of the cool things about gravity is that, for a spherical object, the gravity is the same as if all the mass were at a single point in the center. That's if you're outside the planet. If you're inside the planet, the mass above you has no gravitational effect. Only the mass between you and the center counts. If the earth were perfectly uniform, gravity would decrease linearly toward the center and would be zero at the center - all the mass of the earth around you would be pulling in all directions equally. In the real earth, because mass is concentrated in the core, gravity actually increases with depth and is a few per cent higher at the core boundary than on the surface. However, on the real earth, if we throw something up, it follows an elliptical path until it intersects the surface again. Objects stay in orbit because of a balance between inertia, that would cause them to keep moving in a straight line, and gravity, that would pull them down. Isaac Newton conceived of artificial satellites (B below). He pointed out that a cannon on a high enough mountain and firing ever faster cannonballs could fire them to greater and greater distances. If fired with a great enough velocity, the curvature of the cannonball's path would be equal to that of the Earth and the cannonball would circle the Earth. To get into orbit, you have to climb Newton's mountain first (C). Rockets are launched into orbit by launching them vertically to get them above the atmosphere, then accelerating them horizontally to reach orbital velocity. It takes 29,000 km/hour to do this in low Earth orbit. You get 1670 km/hour of this for free thanks to the Earth's rotation. That's why most satellites are launched eastward. Assuming you're far enough out of the earth's atmosphere, you do not have to use fuel to stay in orbit. Satellites follow Kepler's laws and have elliptical orbits with the center of the earth at the focus. It is impossible to have a satellite orbit over only part of the earth, or to remain fixed above one spot, unless it's on the equator. Even then, the satellite doesn't stand still, it revolves around the earth as fast as the earth rotates. Generally we don't have any particular reason to launch a satellite opposite the earth's rotation, so we take advantage of the earth's rotation to save energy. Orbits in the same direction as the earth's rotation are called prograde and those opposing it are retrograde. Orbits over the poles are sometimes slightly retrograde to allow the satellite to track across the earth in certain ways. Very retrograde orbits are really uncommon. The angle the plane of the satellite's orbit makes with the earth's equator is called its inclination. Satellites with zero inclination orbit directly along the equator. Satellites with other inclinations can travel as far north and south of the equator as their inclination. A satellite with an inclination of 40 degrees can reach as far as 40 degrees north or south of the equator. A satellite with an orbit of 90 degrees can travel over the poles and is said to be in a polar orbit. Satellites in polar orbits can view the entire earth. An inclination greater than 90 degrees means the orbit is retrograde. If you launch from a location not on the equator, obviously your satellite will reach that latitude, so the orbital inclination must be at least as great as your latitude. If you want to put a satellite into equatorial orbit, you can launch it and then use fuel to change the orbit once in space, or you can use the fuel on earth and go to the equator. That way you can launch less fuel and more satellite. French Guyana and Kenya are both launch sites for equatorial satellites. Since what goes up sometimes comes down in the wrong places, the U.S. launches its satellites from the coasts, where accidents won't drop debris onto populated areas. High inclination satellites are usually launched south from Vandenburg Air Force Base in California, where there is clear ocean all the way to Antarctica. Russia launches eastward over sparsely populated Siberia. China has no choice but to launch over populated areas. All the things that cause planetary orbits to change over time act on satellites, except much faster. In particular the plane of the orbit precesses rapidly because of the gravity of the Sun and Moon. We can use precession to our advantage. One way is to match the precession rate to the earth's motion around the Sun, so that on every pass, the earth is illuminated the same. This is a sun-synchronous orbit and is commonly used in earth observation satellites. Fortunately, sun-synchronous orbits are nearly polar, so the satellite can observe almost the entire earth. We can also design the orbit so that passes repeat precisely over the earth at regular intervals. A satellite just above the atmosphere takes about 90 minutes to circle the earth. The Moon takes a month. Somewhere in between, there must be an altitude where satellites take exactly 24 hours to circle the earth. That happens at an altitude of 22,000 miles. Such an orbit is called geosynchronous. A satellite with an inclination would appear to drift north and south over the course of a day, but a satellite with zero inclination would appear to remain stationary in the sky. Such an orbit is called geostationary. In reality, the satellite is moving, but the earth is rotating at the same rate. Your satellite dish is pointing at a satellite 22,000 miles (36,000 km) in space. One downside of a geosynchronous orbit is that, at the equinoxes, the Sun is on the celestial equator, so there is a short interval where geosynchronous satellites pass in front of the Sun. During those windows, radio emissions from the Sun interfere with reception of signals from the satellite. Old geostationary satellites have to go somewhere to die, lest they clutter the narrow band along the equator where geostationary satellites can orbit. Rather than drop them back to earth, they are nudged into a slightly higher orbit called a graveyard orbit. Another downside of geosynchronous satellites is that they are below the horizon beyond about 60 degrees latitude. Since much of Russia is at high latitudes, they cannot use standard geosynchronous orbits. A satellite series called Molniya (lightning) employed a very elliptical 12-hour orbit, going out to about 25,000 miles (40,000 km). Thanks to Kepler's Second Law, the satellite appears nearly stationary in the sky for a long time. Other communications satellites and some spy satellites use similar orbits, which are now called Molniya orbits. During one 12-hour orbit the satellite hangs for a long time over Russia, but during the next 12-hour orbit it hangs over North America. This has obvious advantages for both U.S. and Russian spy satellites. The earth's equatorial bulge would cause the near and far points of the orbit to move over time, but for an orbital inclination of 63.4 degrees the drift rate is zero, so that inclination is used. GPS (Geopositioning system) satellites are placed in orbits with two special characteristics. First, they are circular 12-hour orbits, meaning the satellites orbit at an altitude of 20,000 km. Second, the satellite follows the same track over the earth's surface on every orbit. To do that, the plane of the orbit has to remain constant in orientation relative to the stars. This happens if the orbit has an inclination of 55 degrees. There are six sets of GPS satellites, orbiting 60 degrees apart Created 20 May 1997, Last Update 12 May 2014 Not an official UW Green Bay site
About This Chapter GED Math: Geometry - Chapter Summary This chapter focuses on the material you'll want to have down when tackling the geometry portion of the GED math exam. You'll review examples of geometrical operations while familiarizing yourself with related formulas and terms. Topics discussed in this chapter include: - Perimeter and area - Finding the area and circumference of a circle - Determining the volume of shapes - Formulas for measuring surface area - Combined figures - Reading and interpreting scale drawings The practice quizzes that come with each lesson allow you to measure your comprehension of the content step-by-step. These quizzes are available to be taken as many times as you feel necessary and they can also be printed as worksheets to study with offline. And at the end of the chapter, you'll have the chance to test yourself on a more overall plane by means of a practice final exam. 1. The Pythagorean Theorem: Practice and Application The Pythagorean theorem is one of the most famous geometric theorems. Written by the Greek mathematician Pythagoras, this theorem makes it possible to find a missing side length of a right triangle. Learn more about the famous theorem here and test your understanding with a quiz. 2. What is Perimeter? - Definition & Formula In mathematics, the perimeter is the distance around a two-dimensional shape. The formula for finding the perimeter of certain shapes will be discussed in this lesson, and there will be some examples to help you understand how to calculate the perimeter. 3. What is Area in Math? - Definition & Formula Area is the size of a two-dimensional surface. This lesson will define area, give some of the most common formulas, and give examples of those formulas. A quiz at the end of the lesson will allow you to work out some area problems on your own. 4. Circles: Area and Circumference Understanding how to calculate the area and circumference of circles plays a vital role in some of our everyday functions. They serve as the foundation for operating with three-dimensional figures. Learn more about the area and circumference of circles in this lesson. 5. Volumes of Shapes: Definition & Examples Volume is defined as the 3-dimensional space enclosed by a boundary. In this lesson we will define volume, give some of the most common formulas and then work some example problems to become familiar with the formulas. There will be a quiz at the end of the lesson for practice. 6. What is Surface Area? - Definition & Formulas In this lesson, you use general and specific formulas to learn how to find the surface area of three-dimensional shapes, such as cubes, prisms, spheres, cones and cylinders. 7. Combined Figures: Perimeter, Area, and Volume Watch this video lesson to learn how you can break up the shapes in a combined figure to easily find the perimeter, area, and volume of the whole figure. 8. How to Read and Interpret Scale Drawings Watch this video lesson to learn how scale drawings and legends are used on maps and blueprints. Learn skills that will serve you well when traveling and when looking at the blueprints of a car. Earning College Credit Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level. To learn more, visit our Earning Credit Page Transferring credit to the school of your choice Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you. Other chapters within the GED Math: Quantitative, Arithmetic & Algebraic Problem Solving course - About the GED: Mathematical Reasoning - GED Question Types - GED Math: Number Sense & Problem Solving - GED Math: Decimals & Fractions - GED Math: Ratio, Proportion & Percent - GED Math: Data, Probability & Statistics - GED Math: Algebra Basics, Expressions & Polynomials - GED Math: Equations, Inequalities & Functions - GED Math: Problem Solving Flashcards
Japanese History/The Taisho Period The Taishō period (大正時代 Taishō jidai?, "period of great righteousness"), or Taishō era, is a period in the history of Japan dating from July 30, 1912 to December 25, 1926, coinciding with the reign of the Taishō Emperor. The health of the new emperor was weak, which prompted the shift in political power from the old oligarchic group of elder statesmen (or genrō) to the Diet of Japan and the democratic parties. Thus, the era is considered the time of the liberal movement known as the "Taishō democracy" in Japan; it is usually distinguished from the preceding chaotic Meiji period and the following militarism-driven first part of the Shōwa period. On July 30, 1912, the Meiji Emperor died and Crown Prince Yoshihito became the new emperor of Japan and succeeded to the throne, beginning the Taishō period. The end of the Meiji period was marked by huge government domestic and overseas investments and defense programs, nearly exhausted credit, and a lack of foreign reserves to pay debts. The influence of western culture experienced in the Meiji period continued. Kobayashi Kiyochika adopted western painting styles while continuing to work in ukiyo-e. Okakura Kakuzō kept an interest in traditional Japanese painting. Mori Ōgai and Natsume Sōseki studied in the West and introduced a more modern view of human life. The events flowing from the Meiji Restoration in 1868 had seen not only the fulfillment of many domestic and foreign economic and political objectives—without Japan suffering the colonial fate of other Asian nations—but also a new intellectual ferment, in a time when there was worldwide interest in socialism and an urban proletariat was developing. Universal male suffrage, social welfare, workers' rights, and nonviolent protests were ideals of the early leftist movement. Government suppression of leftist activities, however, led to more radical leftist action and even more suppression, resulting in the dissolution of the Japan Socialist Party (日本社会党 Nihon Shakaitō) only a year after its 1906 founding and the general failure of the socialist movement. The beginning of the Taishō period was marked by the Taishō political crisis in 1912–13 that interrupted the earlier politics of compromise. When Saionji Kinmochi tried to cut the military budget, the army minister resigned, bringing down the Rikken Seiyūkai cabinet. Both Yamagata Aritomo and Saionji refused to resume office, and the genrō were unable to find a solution. Public outrage over the military manipulation of the cabinet and the recall of Katsura Tarō for a third term led to still more demands for an end to genrō politics. Despite old guard opposition, the conservative forces formed a party of their own in 1913, the Rikken Dōshikai, a party that won a majority in the House over the Seiyūkai in late 1914. On February 12, 1913 Yamamoto Gonnohyōe succeeded Katsura as prime minister. In April 1914, Ōkuma Shigenobu replaced Yamamoto. World War I and hegemony in China Seizing the opportunity of Berlin's distraction with the European War (which would become World War I) and wanting to expand its sphere of influence in China, Japan declared war on Germany on August 23, 1914, and quickly occupied German-leased territories in China's Shandong Province and the Mariana, Caroline, and Marshall islands in the Pacific Ocean. On November 7, Jiaozhou surrendered to Japan. With its Western allies heavily involved in the war in Europe, Japan sought further to consolidate its position in China by presenting the Twenty-One Demands (Japanese: 対華二十一ヶ条要求; Chinese: 二十一条) to China in January 1915. Besides expanding its control over German holdings, Manchuria and Inner Mongolia, Japan also sought joint ownership of a major mining and metallurgical complex in central China, prohibitions on China's ceding or leasing any coastal areas to a third power, and miscellaneous other political, economic and military controls, which, if achieved, would have reduced China to a Japanese protectorate. In the face of slow negotiations with the Chinese government, widespread anti-Japanese sentiments in China and international condemnation forced Japan to withdraw the final group of demands and treaties were signed in May 1915. Japan's hegemony in northern China and other parts of Asia was facilitated through other international agreements. One with Russia in 1916 helped further secure Japan's influence in Manchuria and Inner Mongolia, and agreements with France, Britain, and the United States in 1917 recognized Japan's territorial gains in China and the Pacific. The Nishihara Loans (named after Nishihara Kamezo, Tokyo's representative in Beijing) of 1917 and 1918, while aiding the Chinese government, put China still deeper into Japan's debt. Toward the end of the war, Japan increasingly filled orders for its European allies' needed war material, thus helping to diversify the country's industry, increase its exports, and transform Japan from a debtor to a creditor nation for the first time. Japan's power in Asia grew with the demise of the tsarist regime in Russia and the disorder of the 1917 Bolshevik Revolution in Siberia. Wanting to seize the opportunity, the Japanese army planned to occupy Siberia as far west as Lake Baikal. To do so, Japan had to negotiate an agreement with China allowing the transit of Japanese troops through Chinese territory. Although the force was scaled back to avoid antagonizing the United States, more than 70,000 Japanese troops joined the much smaller units of the Allied Expeditionary Force sent to Siberia in 1918. World War I permitted Japan, which fought on the side of the victorious Allies, to expand its influence in Asia and its territorial holdings in the Pacific. Acting virtually independently of the civil government, the Imperial Japanese Navy seized Germany's Micronesian colonies. On October 9, 1916, Terauchi Masatake took over as prime minister from Ōkuma Shigenobu. On November 2, 1917, the Lansing-Ishii Agreement noted the recognition of Japan's interests in China and pledges of keeping an "Open Door Policy" (門戸開放政策). In July 1918, the Siberian Expedition was launched with the deployment of 75,000 Japanese troops. In August 1918, rice riots erupted in towns and cities throughout Japan. Japan after World War I: Taishō Democracy The postwar era brought Japan unprecedented prosperity. Japan went to the peace conference at Versailles in 1919 as one of the great military and industrial powers of the world and received official recognition as one of the "Big Five" of the new international order. Tokyo was granted a permanent seat on the Council of the League of Nations and the peace treaty confirmed the transfer to Japan of Germany's rights in Shandong, a provision that led to anti-Japanese riots and a mass political movement throughout China. Similarly, Germany's former Pacific islands were put under a Japanese mandate. Japan was also involved in the post-war Allied intervention in Russia and was the last Allied power to withdraw (doing so in 1925). Despite its small role in World War I (and the Western powers' rejection of its bid for a racial equality clause in the peace treaty), Japan emerged as a major actor in international politics at the close of the war. The two-party political system that had been developing in Japan since the turn of the century finally came of age after World War I, giving rise to the nickname for the period, "Taishō Democracy." In 1918, Hara Takashi, a protege of Saionji and a major influence in the prewar Seiyūkai cabinets, had become the first commoner to serve as prime minister. He took advantage of long-standing relationships he had throughout the government, won the support of the surviving genrō and the House of Peers, and brought into his cabinet as army minister Tanaka Giichi, who had a greater appreciation of favorable civil-military relations than his predecessors. Nevertheless, major problems confronted Hara: inflation, the need to adjust the Japanese economy to postwar circumstances, the influx of foreign ideas, and an emerging labor movement. Prewar solutions were applied by the cabinet to these postwar problems, and little was done to reform the government. Hara worked to ensure a Seiyūkai majority through time-tested methods, such as new election laws and electoral redistricting, and embarked on major government-funded public works programs. The public grew disillusioned with the growing national debt and the new election laws, which retained the old minimum tax qualifications for voters. Calls were raised for universal suffrage and the dismantling of the old political party network. Students, university professors, and journalists, bolstered by labor unions and inspired by a variety of democratic, socialist, communist, anarchist and other Western schools of thought, mounted large but orderly public demonstrations in favor of universal male suffrage in 1919 and 1920. New elections brought still another Seiyūkai majority, but barely so. In the political milieu of the day, there was a proliferation of new parties, including socialist and communist parties. In the midst of this political ferment, Hara was assassinated by a disenchanted railroad worker in 1921. Hara was followed by a succession of nonparty prime ministers and coalition cabinets. Fear of a broader electorate, left-wing power and the growing social change engendered by the influx of Western popular culture together led to the passage of the Peace Preservation Law in 1925, which forbade any change in the political structure or the abolition of private property. Unstable coalitions and divisiveness in the Diet led the Kenseikai (憲政会 Constitutional Government Association) and the Seiyū Hontō (政友本党 True Seiyūkai) to merge as the Rikken Minseitō (立憲民政党 Constitutional Democratic Party) in 1927. The Rikken Minseitō platform was committed to the parliamentary system, democratic politics and world peace. Thereafter, until 1932, the Seiyūkai and the Rikken Minseitō alternated in power. Despite the political realignments and hope for more orderly government, domestic economic crises plagued whichever party held power. Fiscal austerity programs and appeals for public support of such conservative government policies as the Peace Preservation Law—including reminders of the moral obligation to make sacrifices for the emperor and the state—were attempted as solutions. Although the worldwide depression of the late 1920s and early 1930s had minimal effects on Japan—indeed, Japanese exports grew substantially during this period—there was a sense of rising discontent that was heightened with the assault upon Rikken Minseitō prime minister Osachi Hamaguchi in 1930. Though Hamaguchi survived the attack and tried to continue in office despite the severity of his wounds, he was forced to resign the following year and died not long afterwards. Communism and the response The victory of the Bolsheviks in Russia in 1917 and their hopes for a world revolution led to the establishment of the Comintern. The Comintern realized the importance of Japan in achieving successful revolution in East Asia and actively worked to form the Japanese Communist Party, which was founded in July 1922. The announced goals of the Japanese Communist Party in 1923 were an end to feudalism, abolition of the monarchy, recognition of the Soviet Union and withdrawal of Japanese troops from Siberia, Sakhalin, China, Korea and Taiwan. A brutal suppression of the party followed. Radicals responded with an assassination attempt on Prince Regent Hirohito. The 1925 Peace Preservation Law was a direct response to the "dangerous thoughts" perpetrated by communist elements in Japan. The liberalization of election laws with the General Election Law in 1925, benefited communist candidates, even though the Japan Communist Party itself was banned. A new Peace Preservation Law in 1928, however, further impeded communist efforts by banning the parties they had infiltrated. The police apparatus of the day was ubiquitous and quite thorough in attempting to control the socialist movement. By 1926, the Japan Communist Party had been forced underground, by the summer of 1929 the party leadership had been virtually destroyed, and by 1933 the party had largely disintegrated. Pan asianism was characteristic of right-wing politics and conservative militarism since the inception of the Meiji Restoration, contributing greatly to the pro-war politics of the 1870s. Disenchanted former samurai had established pan asianistic societies and intelligence-gathering organizations, such as the Gen'yōsha (玄洋社, founded in 1881) and its later offshoot, the Kokuryūkai (黒竜会 Black Dragon Society or Amur River Society, founded in 1901). These groups became active in domestic and foreign politics, helped foment prowar sentiments, and supported Pan asianist causes through the end of World War II. Taishō foreign policy Emerging Chinese nationalism, the victory of the communists in Russia and the growing presence of the United States in East Asia all worked against Japan's postwar foreign policy interests. The four-year Siberian expedition and activities in China, combined with big domestic spending programs, had depleted Japan's wartime earnings. Only through more competitive business practices, supported by further economic development and industrial modernization, all accommodated by the growth of the zaibatsu, could Japan hope to become dominant in Asia. The United States, long a source of many imported goods and loans needed for development, was seen as becoming a major impediment to this goal because of its policies of containing Japanese imperialism. An international turning point in military diplomacy was the Washington Conference of 1921–22, which produced a series of agreements that effected a new order in the Pacific region. Japan's economic problems made a naval buildup nearly impossible and, realizing the need to compete with the United States on an economic rather than a military basis, rapprochement became inevitable. Japan adopted a more neutral attitude toward the civil war in China, dropped efforts to expand its hegemony into China proper, and joined the United States, Britain and France in encouraging Chinese self-development. In the Four Power Treaty on Insular Possessions signed on December 13, 1921, Japan, the United States, Britain and France agreed to recognize the status quo in the Pacific, and Japan and Britain agreed to terminate formally their Treaty of Alliance. The Five Power Naval Disarmament Treaty agreed to on February 6, 1922 established an international capital ship ratio for the United States, Britain, Japan, France, and Italy (5, 5, 3, 1.75, and 1.75, respectively) and limited the size and armaments of capital ships already built or under construction. In a move that gave the Japanese Imperial Navy greater freedom in the Pacific, Washington and London agreed not to build any new military bases between Singapore and Hawaii. The goal of the Nine Power Treaty also signed on February 6, 1922, by Belgium, China, the Netherlands and Portugal, along with the original five powers, was the prevention of war in the Pacific. The signatories agreed to respect China's independence and integrity, not to interfere in Chinese attempts to establish a stable government, to refrain from seeking special privileges in China or threatening the positions of other nations there, to support a policy of equal opportunity for commerce and industry of all nations in China, and to reexamine extraterritoriality and tariff autonomy policies. Japan also agreed to withdraw its troops from Shandong, relinquishing all but purely economic rights there, and to evacuate its troops from Siberia. The End of the Taishō Democracy Overall, during the 1920s, Japan changed its direction toward a democratic system of government. However, parliamentary government was not rooted deeply enough to withstand the economic and political pressures of the 1930s, during which military leaders became increasingly influential. These shifts in power were made possible by the ambiguity and imprecision of the Meiji constitution, particularly as regarded the position of the Emperor in relation to the constitution. After this period of democracy Japan's government was to become a form of military dictatorship. - 1912: The Taishō Emperor assumes the throne (July 30). General Katsura Tarō becomes prime minister for a third term (December 21). - 1913: Katsura is forced to resign, and Admiral Yamamoto Gonnohyōe becomes prime minister (February 20). - 1914: Ōkuma Shigenobu becomes prime minister for a second term (April 16). Japan declares war on Germany, joining the Allies side (August 23). - 1915: Japan sends the Twenty-One Demands to China (January 18). - 1916: Terauchi Masatake becomes prime minister (October 9). - 1917: Lansing-Ishii Agreement goes into effect (November 2). - 1918: Siberian expedition launched (July). Hara Takashi becomes prime minister (September 29). - 1919: March 1st Movement begins against colonial rule in Korea (March 1). - 1920: Japan helps found the League of Nations. - 1921: Hara is assassinated and Takahashi Korekiyo becomes prime minister (November 4). Hirohito becomes regent (November 29). Four Power Treaty is signed (December 13). - 1922: Five Power Naval Disarmament Treaty is signed (February 6). Admiral Katō Tomosaburō becomes prime minister (June 12). Japan withdraws troops from Siberia (August 28). - 1923: The Great Kantō earthquake devastates Tokyo (September 1). Yamamoto becomes prime minister for a second term (September 2). - 1924: Kiyoura Keigo becomes prime minister (January 7). Prince Hirohito (the future Emperor Shōwa) marries Kuni no miya Nagako Nyoō (the future Empress Kōjun) (January 26). Katō Takaaki becomes prime minister (June 11). - 1925: General Election Law was passed, all men above age 25 gained the right to vote (May 5). Besides, Peace Preservation Law is passed. Princess Shigeko, Hirohito's first daughter, is born (December 9). - 1926: Emperor Taishō dies; Hirohito becomes emperor (December 25).
Anemia (uh-NEE-me-uh) is a condition in which your blood has a lower than normal number of red blood cells. Anemia also can occur if your red blood cells don't contain enough hemoglobin (HEE-muh-glow-bin). Hemoglobin is an iron-rich protein that gives blood its red color. This protein helps red blood cells carry oxygen from the lungs to the rest of the body. If you have anemia, your body doesn't get enough oxygen-rich blood. As a result, you may feel tired or weak. You also may have other symptoms, such as shortness of breath, dizziness, or headaches. Severe or long-lasting anemia can damage your heart, brain, and other organs in your body. Very severe anemia may even cause death. Blood is made up of many parts, including red blood cells, white blood cells, platelets (PLATE-lets), and plasma (the fluid portion of blood). Red blood cells are disc-shaped and look like doughnuts without holes in the center. They carry oxygen and remove carbon dioxide (a waste product) from your body. These cells are made in the bone marrow—a sponge-like tissue inside the bones. White blood cells and platelets (PLATE-lets) also are made in the bone marrow. White blood cells help fight infection. Platelets stick together to seal small cuts or breaks on the blood vessel walls and stop bleeding. With some types of anemia, you may have low numbers of all three types of blood cells. Anemia has three main causes: blood loss, lack of red blood cell production, or high rates of red blood cell destruction. These causes might be the result of diseases, conditions, or other factors. Many types of anemia can be mild, short term, and easily treated. You can even prevent some types with a healthy diet. Other types can be treated with dietary supplements. However, certain types of anemia can be severe, long lasting, and even life threatening if not diagnosed and treated. If you have signs or symptoms of anemia, see your doctor to find out whether you have the condition. Treatment will depend on the cause of the anemia and how severe it is. There are many types of anemia with specific causes and traits. Some of these include: The three main causes of anemia are: For some people, the condition is caused by more than one of these factors. Blood loss is the most common cause of anemia, especially iron-deficiency anemia. Blood loss can be short term or persist over time. Heavy menstrual periods or bleeding in the digestive or urinary tract can cause blood loss. Surgery, trauma, or cancer also can cause blood loss. If a lot of blood is lost, the body may lose enough red blood cells to cause anemia. Both acquired and inherited conditions and factors can prevent your body from making enough red blood cells. "Acquired" means you aren't born with the condition, but you develop it. "Inherited" means your parents passed the gene for the condition on to you. Acquired conditions and factors that can lead to anemia include poor diet, abnormal hormone levels, some chronic (ongoing) diseases, and pregnancy. Aplastic anemia also can prevent your body from making enough red blood cells. This condition can be acquired or inherited. A diet that lacks iron, folic acid (folate), or vitamin B12 can prevent your body from making enough red blood cells. Your body also needs small amounts of vitamin C, riboflavin, and copper to make red blood cells. Conditions that make it hard for your body to absorb nutrients also can prevent your body from making enough red blood cells. Your body needs the hormone erythropoietin (eh-rith-ro-POY-eh-tin) to make red blood cells. This hormone stimulates the bone marrow to make these cells. A low level of this hormone can lead to anemia. Chronic diseases, like kidney disease and cancer, can make it hard for your body to make enough red blood cells. Some cancer treatments may damage the bone marrow or damage the red blood cells' ability to carry oxygen. If the bone marrow is damaged, it can't make red blood cells fast enough to replace the ones that die or are destroyed. People who have HIV/AIDS may develop anemia due to infections or medicines used to treat their diseases. Anemia can occur during pregnancy due to low levels of iron and folic acid and changes in the blood. During the first 6 months of pregnancy, the fluid portion of a woman's blood (the plasma) increases faster than the number of red blood cells. This dilutes the blood and can lead to anemia. Some infants are born without the ability to make enough red blood cells. This condition is called aplastic anemia. Infants and children who have aplastic anemia often need blood transfusions to increase the number of red blood cells in their blood. Acquired conditions or factors, such as certain medicines, toxins, and infectious diseases, also can cause aplastic anemia. Both acquired and inherited conditions and factors can cause your body to destroy too many red blood cells. One example of an acquired condition is an enlarged or diseased spleen. The spleen is an organ that removes wornout red blood cells from the body. If the spleen is enlarged or diseased, it may remove more red blood cells than normal, causing anemia. Examples of inherited conditions that can cause your body to destroy too many red blood cells include sickle cell anemia, thalassemias, and lack of certain enzymes. These conditions create defects in the red blood cells that cause them to die faster than healthy red blood cells. Hemolytic anemia is another example of a condition in which your body destroys too many red blood cells. Inherited or acquired conditions or factors can cause hemolytic anemia. Examples include immune disorders, infections, certain medicines, or reactions to blood transfusions. Anemia is a common condition. It occurs in all age, racial, and ethnic groups. Both men and women can have anemia. However, women of childbearing age are at higher risk for the condition because of blood loss from menstruation. Anemia can develop during pregnancy due to low levels of iron and folic acid (folate) and changes in the blood. During the first 6 months of pregnancy, the fluid portion of a woman's blood (the plasma) increases faster than the number of red blood cells. This dilutes the blood and can lead to anemia. During the first year of life, some babies are at risk for anemia because of iron deficiency. At-risk infants include those who are born too early and infants who are fed breast milk only or formula that isn't fortified with iron. These infants can develop iron deficiency by 6 months of age. Infants between 1 and 2 years of age also are at risk for anemia. They may not get enough iron in their diets, especially if they drink a lot of cow's milk. Cow's milk is low in the iron needed for growth. Drinking too much cow's milk may keep an infant or toddler from eating enough iron-rich foods or absorbing enough iron from foods. Older adults also are at increased risk for anemia. Researchers continue to study how the condition affects older adults. Many of these people have other medical conditions as well. Factors that raise your risk for anemia include: The most common symptom of anemia is fatigue (feeling tired or weak). If you have anemia, you may find it hard to find the energy to do normal activities. Other signs and symptoms of anemia include: These signs and symptoms can occur because your heart has to work harder to pump oxygen-rich blood through your body. Mild to moderate anemia may cause very mild symptoms or none at all. Some people who have anemia may have arrhythmias (ah-RITH-me-ahs). Arrhythmias are problems with the rate or rhythm of the heartbeat. Over time, arrhythmias can damage your heart and possibly lead to heart failure. Anemia also can damage other organs in your body because your blood can't get enough oxygen to them. Anemia can weaken people who have cancer or HIV/AIDS. This can make their treatments not work as well. Anemia also can cause many other health problems. People who have kidney disease and anemia are more likely to have heart problems. With some types of anemia, too little fluid intake or too much loss of fluid in the blood and body can occur. Severe loss of fluid can be life threatening. Your doctor will diagnose anemia based on your medical and family histories, a physical exam, and results from tests and procedures. Because anemia doesn't always cause symptoms, your doctor may find out you have it while checking for another condition. Your doctor may ask whether you have any of the common signs or symptoms of anemia. He or she also may ask whether you've had an illness or condition that could cause anemia. Let your doctor know about any medicines you take, what you typically eat (your diet), and whether you have family members who have anemia or a history of it. Your doctor will do a physical exam to find out how severe your anemia is and to check for possible causes. He or she may: Your doctor also may do a pelvic or rectal exam to check for common sources of blood loss. You may have various blood tests and other tests or procedures to find out what type of anemia you have and how severe it is. Often, the first test used to diagnose anemia is a complete blood count (CBC). The CBC measures many parts of your blood. The test checks your hemoglobin and hematocrit (hee-MAT-oh-crit) levels. Hemoglobin is the iron-rich protein in red blood cells that carries oxygen to the body. Hematocrit is a measure of how much space red blood cells take up in your blood. A low level of hemoglobin or hematocrit is a sign of anemia. The normal range of these levels might be lower in certain racial and ethnic populations. Your doctor can explain your test results to you. The CBC also checks the number of red blood cells, white blood cells, and platelets in your blood. Abnormal results might be a sign of anemia, another blood disorder, an infection, or another condition. Finally, the CBC looks at mean corpuscular (kor-PUS-kyu-lar) volume (MCV). MCV is a measure of the average size of your red blood cells and a clue as to the cause of your anemia. In iron-deficiency anemia, for example, red blood cells usually are smaller than normal. If the CBC results show that you have anemia, you may need other tests, such as: Because anemia has many causes, you also might be tested for conditions such as kidney failure, lead poisoning (in children), and vitamin deficiencies (lack of vitamins, such as B12 and folic acid). If your doctor thinks that you have anemia due to internal bleeding, he or she may suggest several tests to look for the source of the bleeding. A test to check the stool for blood might be done in your doctor's office or at home. Your doctor can give you a kit to help you get a sample at home. He or she will tell you to bring the sample back to the office or send it to a laboratory. If blood is found in the stool, you may have other tests to find the source of the bleeding. One such test is endoscopy (en-DOS-ko-pe). For this test, a tube with a tiny camera is used to view the lining of the digestive tract. Your doctor also may want to do bone marrow tests. These tests show whether your bone marrow is healthy and making enough blood cells. Treatment for anemia depends on the type, cause, and severity of the condition. Treatments may include dietary changes or supplements, medicines, procedures, or surgery to treat blood loss. The goal of treatment is to increase the amount of oxygen that your blood can carry. This is done by raising the red blood cell count and/or hemoglobin level. (Hemoglobin is the iron-rich protein in red blood cells that carries oxygen to the body.) Another goal is to treat the underlying cause of the anemia. Low levels of vitamins or iron in the body can cause some types of anemia. These low levels might be the result of a poor diet or certain diseases or conditions. To raise your vitamin or iron level, your doctor may ask you to change your diet or take vitamin or iron supplements. Common vitamin supplements are vitamin B12 and folic acid (folate). Vitamin C sometimes is given to help the body absorb iron. Your body needs iron to make hemoglobin. Your body can more easily absorb iron from meats than from vegetables or other foods. To treat your anemia, your doctor may suggest eating more meat—especially red meat (such as beef or liver), as well as chicken, turkey, pork, fish, and shellfish. Nonmeat foods that are good sources of iron include: You can look at the Nutrition Facts label on packaged foods to find out how much iron the items contain. The amount is given as a percentage of the total amount of iron you need every day. Iron also is available as a supplement. It's usually combined with multivitamins and other minerals that help your body absorb iron. Doctors may recommend iron supplements for premature infants, infants and young children who drink a lot of cow's milk, and infants who are fed breast milk only or formula that isn't fortified with iron. Large amounts of iron can be harmful, so take iron supplements only as your doctor prescribes. Low levels of vitamin B12 can lead to pernicious anemia. This type of anemia often is treated with vitamin B12 supplements. Good food sources of vitamin B12 include: Folic acid (folate) is a form of vitamin B that's found in foods. Your body needs folic acid to make and maintain new cells. Folic acid also is very important for pregnant women. It helps them avoid anemia and promotes healthy growth of the fetus. Good sources of folic acid include: Vitamin C helps the body absorb iron. Good sources of vitamin C are vegetables and fruits, especially citrus fruits. Citrus fruits include oranges, grapefruits, tangerines, and similar fruits. Fresh and frozen fruits, vegetables, and juices usually have more vitamin C than canned ones. If you're taking medicines, ask your doctor or pharmacist whether you can eat grapefruit or drink grapefruit juice. This fruit can affect the strength of a few medicines and how well they work. Other fruits rich in vitamin C include kiwi fruit, strawberries, and cantaloupes. Vegetables rich in vitamin C include broccoli, peppers, Brussels sprouts, tomatoes, cabbage, potatoes, and leafy green vegetables like turnip greens and spinach. Your doctor may prescribe medicines to help your body make more red blood cells or to treat an underlying cause of anemia. Some of these medicines include: If your anemia is severe, your doctor may recommend a medical procedure. Procedures include blood transfusions and blood and marrow stem cell transplants. A blood transfusion is a safe, common procedure in which blood is given to you through an intravenous (IV) line in one of your blood vessels. Transfusions require careful matching of donated blood with the recipient's blood. For more information, go to the Health Topics Blood Transfusion article. A blood and marrow stem cell transplant replaces your faulty stem cells with healthy ones from another person (a donor). Stem cells are made in the bone marrow. They develop into red and white blood cells and platelets. During the transplant, which is like a blood transfusion, you get donated stem cells through a tube placed in a vein in your chest. Once the stem cells are in your body, they travel to your bone marrow and begin making new blood cells. For more information, go to the Health Topics Blood and Marrow Stem Cell Transplant article. If you have serious or life-threatening bleeding that's causing anemia, you may need surgery. For example, you may need surgery to control ongoing bleeding due to a stomach ulcer or colon cancer. If your body is destroying red blood cells at a high rate, you may need to have your spleen removed. The spleen is an organ that removes wornout red blood cells from the body. An enlarged or diseased spleen may remove more red blood cells than normal, causing anemia. You might be able to prevent repeat episodes of some types of anemia, especially those caused by lack of iron or vitamins. Dietary changes or supplements can prevent these types of anemia from occurring again. Treating anemia's underlying cause may prevent the condition (or prevent repeat episodes). For example, if medicine is causing your anemia, your doctor may prescribe another type of medicine. To prevent anemia from getting worse, tell your doctor about all of your signs and symptoms. Talk with your doctor about the tests you may need and follow your treatment plan. You can't prevent some types of inherited anemia, such as sickle cell anemia. If you have an inherited anemia, talk with your doctor about treatment and ongoing care. Often, you can treat and control anemia. If you have signs or symptoms of anemia, seek prompt diagnosis and treatment. Treatment may increase your energy and activity levels, improve your quality of life, and help you live longer. With proper treatment, many types of anemia are mild and short term. However, anemia can be severe, long lasting, or even fatal when it's caused by an inherited or chronic disease or trauma. Infants and young children have a greater need for iron because of their rapid growth. Not enough iron can lead to anemia. Premature and low-birth-weight babies often are watched closely for anemia. Talk with your child's doctor if you're feeding your infant breast milk only or formula that isn't fortified with iron, especially after the child is 6 months old. Your child's doctor may recommend iron supplements. Children who drink a lot of cow's milk also are at risk for anemia. Cow's milk is low in the iron needed for growth. Most of the iron your child needs comes from food. Talk with your child's doctor about a healthy diet and good sources of iron, vitamins B12 and C, and folic acid (folate). Only give your child iron supplements if the doctor prescribes them. You should carefully follow instructions on how to give your child these supplements. If your child has anemia, his or her doctor may ask whether the child has been exposed to lead. Lead poisoning in children has been linked to iron-deficiency anemia. Teenagers also are at risk for anemia, especially iron-deficiency anemia, because of their growth spurts. Routine screenings for anemia often are started in the teen years. Older children and teens who have certain types of severe anemia might be at higher risk for injuries or infections. Talk with your child's doctor about whether your child needs to avoid high-risk activities, such as contact sports. Girls begin to menstruate and lose iron with each monthly period. Some girls and women are at higher risk for anemia due to excessive blood loss from menstruation or other causes, low iron intake, or a history of anemia. These girls and women may need regular screenings and followup for anemia. Anemia can occur during pregnancy due to a lack of iron and folic acid and changes in the blood. During the first 6 months of pregnancy, the fluid portion of a woman's blood (the plasma) increases faster than the number of red blood cells. This dilutes the blood and can lead to anemia. Severe anemia raises the risk of having a premature or low-birth-weight baby. Thus, pregnant women should be screened for anemia during their first prenatal visits. They also need routine followup as part of prenatal care. Women often are tested for anemia after delivery (postpartum), especially if they had: Chronic diseases, lack of iron, and/or generally poor nutrition often cause anemia in older adults. Also, in older adults, anemia often occurs with other medical problems. Thus, the signs and symptoms of anemia might not be as clear or they might be overlooked. Contact your doctor if you have any signs or symptoms of anemia. If you're diagnosed with anemia, your doctor may: The National Heart, Lung, and Blood Institute (NHLBI) is strongly committed to supporting research aimed at preventing and treating heart, lung, and blood diseases and conditions and sleep disorders. Researchers have learned a lot about anemia and other blood diseases and conditions over the years. This knowledge has led to advances in medical care. Many questions remain about blood diseases and conditions, including anemia. The NHLBI continues to support research aimed at learning more about these illnesses. For example, NHLBI-supported research on anemia includes studies that explore: Much of this research depends on the willingness of volunteers to take part in clinical trials. Clinical trials test new ways to prevent, diagnose, or treat various diseases and conditions. For example, new treatments for a disease or condition (such as medicines, medical devices, surgeries, or procedures) are tested in volunteers who have the illness. Testing shows whether a treatment is safe and effective in humans before it is made available for widespread use. By taking part in a clinical trial, you may gain access to new treatments before they're widely available. You also will have the support of a team of health care providers, who will likely monitor your health closely. Even if you don't directly benefit from the results of a clinical trial, the information gathered can help others and add to scientific knowledge. If you volunteer for a clinical trial, the research will be explained to you in detail. You'll learn about treatments and tests you may receive, and the benefits and risks they may pose. You'll also be given a chance to ask questions about the research. This process is called informed consent. If you agree to take part in the trial, you'll be asked to sign an informed consent form. This form is not a contract. You have the right to withdraw from a study at any time, for any reason. Also, you have the right to learn about new risks or findings that emerge during the trial. For more information about clinical trials related to anemia, talk with your doctor. You also can visit the following Web sites to learn more about clinical research and to search for clinical trials: For more information about clinical trials for children, visit the NHLBI's Children and Clinical Studies Web page. The NHLBI updates Health Topics articles on a biennial cycle based on a thorough review of research findings and new literature. The articles also are updated as needed if important new research is published. The date on each Health Topics article reflects when the content was originally posted or last revised.
The computer is also time-efficient when performing integer multiplication by powers of 2. Therefore, it is an efficient method for scan-converting straight lines. To accomplish this, the algorithm always increments either x or y by one unit depending on the slope of line. The increment in the other variable is determined by examining the distance between the actual line location and the nearest pixel. \|Published (Last):\|\|4 March 2006\| \|PDF File Size:\|\|12.40 Mb\| \|ePub File Size:\|\|15.31 Mb\| \|Price:\|\|Free* [*Free Regsitration Required]\| This algorithm was developed by Jack E. Bresenham in at IBM. And then show you the complete line drawing function. Before we begin on this topic, a revision of the concepts developed earlier like scan conversion methods and rasterization may be helpful. Once we finish this aspect, we will proceed towards exposition of items listed in the synopsis. One thing to note here is that it is impossible to draw the true line that we want because of the pixel spacing. The true line is indicated in bright color, and its approximation is indicated in black pixels. In this example the starting point of the line is located exactly at 0, 0 and the ending point of the line is located exactly at 9, 6. Now let discuss the way in which this algorithm works. First it decides which axis is the major axis and which is the minor axis. The major axis is longer than the minor axis. On this picture illustrated above the major axis is the X axis. Each iteration progresses the current value of the major axis starting from the original position , by exactly one pixel. Then it decides which pixel on the minor axis is appropriate for the current pixel of the major axis. Now how can you approximate the right pixel on the minor axis that matches the pixel on the major axis? Now you take a closer look at the picture. The center of each pixel is marked with a dot. The algorithm takes the coordinates of that dot and compares it to the true line. If the span from the center of the pixel to the true line is less or equal to 0. That span is more generally known as the error term. You might think of using floating variables but you can see that the whole algorithm is done in straight integer math with no multiplication or division in the main loops no fixed point math either. Now how is it possible? Basically, during each iteration through the main drawing loop the error term is tossed around to identify the right pixel as close as possible to the true line. Why do you scale the deltas? Finally the scaled values must be subtracted by either dx or dy the original, non-scaled delta values depending on what the major axis is either x or y. Line Generation Algorithm Multiplication by 2 can be implemented by left-shift. This version limited to slopes in the first octant,. This is an all-integer function, employs left shift for multiplication and eliminates redundant operations by tricky use of the eps variable. A real implementation should do this. Bresenham’s Circle Drawing Algorithm
A map projection is a systematic transformation of the latitudes and longitudes of locations from the surface of a sphere or an ellipsoid into locations on a plane. Maps cannot be created without map projections. All map projections necessarily distort the surface in some fashion. Depending on the purpose of the map, some distortions are acceptable and others are not; therefore, different map projections exist in order to preserve some properties of the sphere-like body at the expense of other properties. There is no limit to the number of possible map projections.:1 More generally, the surfaces of planetary bodies can be mapped even if they are too irregular to be modeled well with a sphere or ellipsoid; see below. Even more generally, projections are a subject of several pure mathematical fields, including differential geometry, projective geometry, and manifolds. However, "map projection" refers specifically to a cartographic projection. Maps can be more useful than globes in many situations: they are more compact and easier to store; they readily accommodate an enormous range of scales; they are viewed easily on computer displays; they can facilitate measuring properties of the region being mapped; they can show larger portions of the Earth's surface at once; and they are cheaper to produce and transport. These useful traits of maps motivate the development of map projections. However, Carl Friedrich Gauss's Theorema Egregium proved that a sphere's surface cannot be represented on a plane without distortion. The same applies to other reference surfaces used as models for the Earth, such as oblate spheroids, ellipsoids and geoids. Since any map projection is a representation of one of those surfaces on a plane, all map projections distort. Every distinct map projection distorts in a distinct way. The study of map projections is the characterization of these distortions. Projection is not limited to perspective projections, such as those resulting from casting a shadow on a screen, or the rectilinear image produced by a pinhole camera on a flat film plate. Rather, any mathematical function transforming coordinates from the curved surface to the plane is a projection. Few projections in actual use are perspective. For simplicity, most of this article assumes that the surface to be mapped is that of a sphere. In reality, the Earth and other large celestial bodies are generally better modeled as oblate spheroids, whereas small objects such as asteroids often have irregular shapes. These other surfaces can be mapped as well. Therefore, more generally, a map projection is any method of "flattening" a continuous curved surface onto a plane. Metric properties of mapsEdit Many properties can be measured on the Earth's surface independent of its geography. Some of these properties are: Map projections can be constructed to preserve at least one of these properties, though only in a limited way for most. Each projection preserves, compromises, or approximates basic metric properties in different ways. The purpose of the map determines which projection should form the base for the map. Because many purposes exist for maps, a diversity of projections have been created to suit those purposes. Another consideration in the configuration of a projection is its compatibility with data sets to be used on the map. Data sets are geographic information; their collection depends on the chosen datum (model) of the Earth. Different datums assign slightly different coordinates to the same location, so in large scale maps, such as those from national mapping systems, it is important to match the datum to the projection. The slight differences in coordinate assignation between different datums is not a concern for world maps or other vast territories, where such differences get shrunk to imperceptibility. The classical way of showing the distortion inherent in a projection is to use Tissot's indicatrix. For a given point, using the scale factor h along the meridian, the scale factor k along the parallel, and the angle θ′ between them, Nicolas Tissot described how to construct an ellipse that characterizes the amount and orientation of the components of distortion.:147–149 By spacing the ellipses regularly along the meridians and parallels, the network of indicatrices shows how distortion varies across the map. Construction of a map projectionEdit The creation of a map projection involves two steps: - Selection of a model for the shape of the Earth or planetary body (usually choosing between a sphere or ellipsoid). Because the Earth's actual shape is irregular, information is lost in this step. - Transformation of geographic coordinates (longitude and latitude) to Cartesian (x,y) or polar plane coordinates. In large-scale maps, Cartesian coordinates normally have a simple relation to eastings and northings defined as a grid superimposed on the projection. In small-scale maps, eastings and northings are not meaningful, and grids are not superimposed. Some of the simplest map projections are literal projections, as obtained by placing a light source at some definite point relative to the globe and projecting its features onto a specified surface. This is not the case for most projections, which are defined only in terms of mathematical formulae that have no direct geometric interpretation. However, picturing the light source-globe model can be helpful in understanding the basic concept of a map projection Choosing a projection surfaceEdit A surface that can be unfolded or unrolled into a plane or sheet without stretching, tearing or shrinking is called a developable surface. The cylinder, cone and the plane are all developable surfaces. The sphere and ellipsoid do not have developable surfaces, so any projection of them onto a plane will have to distort the image. (To compare, one cannot flatten an orange peel without tearing and warping it.) One way of describing a projection is first to project from the Earth's surface to a developable surface such as a cylinder or cone, and then to unroll the surface into a plane. While the first step inevitably distorts some properties of the globe, the developable surface can then be unfolded without further distortion. Aspect of the projectionEdit Once a choice is made between projecting onto a cylinder, cone, or plane, the aspect of the shape must be specified. The aspect describes how the developable surface is placed relative to the globe: it may be normal (such that the surface's axis of symmetry coincides with the Earth's axis), transverse (at right angles to the Earth's axis) or oblique (any angle in between). The developable surface may also be either tangent or secant to the sphere or ellipsoid. Tangent means the surface touches but does not slice through the globe; secant means the surface does slice through the globe. Moving the developable surface away from contact with the globe never preserves or optimizes metric properties, so that possibility is not discussed further here. Tangent and secant lines (standard lines) are represented undistorted. If these lines are a parallel of latitude, as in conical projections, it is called a standard parallel. The central meridian is the meridian to which the globe is rotated before projecting. The central meridian (usually written λ0) and a parallel of origin (usually written φ0) are often used to define the origin of the map projection. A globe is the only way to represent the earth with constant scale throughout the entire map in all directions. A map cannot achieve that property for any area, no matter how small. It can, however, achieve constant scale along specific lines. Some possible properties are: - The scale depends on location, but not on direction. This is equivalent to preservation of angles, the defining characteristic of a conformal map. - Scale is constant along any parallel in the direction of the parallel. This applies for any cylindrical or pseudocylindrical projection in normal aspect. - Combination of the above: the scale depends on latitude only, not on longitude or direction. This applies for the Mercator projection in normal aspect. - Scale is constant along all straight lines radiating from a particular geographic location. This is the defining characteristic of an equidistant projection such as the Azimuthal equidistant projection. There are also projections (Maurer's Two-point equidistant projection, Close) where true distances from two points are preserved.:234 Choosing a model for the shape of the bodyEdit Projection construction is also affected by how the shape of the Earth or planetary body is approximated. In the following section on projection categories, the earth is taken as a sphere in order to simplify the discussion. However, the Earth's actual shape is closer to an oblate ellipsoid. Whether spherical or ellipsoidal, the principles discussed hold without loss of generality. Selecting a model for a shape of the Earth involves choosing between the advantages and disadvantages of a sphere versus an ellipsoid. Spherical models are useful for small-scale maps such as world atlases and globes, since the error at that scale is not usually noticeable or important enough to justify using the more complicated ellipsoid. The ellipsoidal model is commonly used to construct topographic maps and for other large- and medium-scale maps that need to accurately depict the land surface. Auxiliary latitudes are often employed in projecting the ellipsoid. A third model is the geoid, a more complex and accurate representation of Earth's shape coincident with what mean sea level would be if there were no winds, tides, or land. Compared to the best fitting ellipsoid, a geoidal model would change the characterization of important properties such as distance, conformality and equivalence. Therefore, in geoidal projections that preserve such properties, the mapped graticule would deviate from a mapped ellipsoid's graticule. Normally the geoid is not used as an Earth model for projections, however, because Earth's shape is very regular, with the undulation of the geoid amounting to less than 100 m from the ellipsoidal model out of the 6.3 million m Earth radius. For irregular planetary bodies such as asteroids, however, sometimes models analogous to the geoid are used to project maps from. A fundamental projection classification is based on the type of projection surface onto which the globe is conceptually projected. The projections are described in terms of placing a gigantic surface in contact with the earth, followed by an implied scaling operation. These surfaces are cylindrical (e.g. Mercator), conic (e.g. Albers), and plane (e.g. stereographic). Many mathematical projections, however, do not neatly fit into any of these three conceptual projection methods. Hence other peer categories have been described in the literature, such as pseudoconic, pseudocylindrical, pseudoazimuthal, retroazimuthal, and polyconic. Another way to classify projections is according to properties of the model they preserve. Some of the more common categories are: - Preserving direction (azimuthal or zenithal), a trait possible only from one or two points to every other point - Preserving shape locally (conformal or orthomorphic) - Preserving area (equal-area or equiareal or equivalent or authalic) - Preserving distance (equidistant), a trait possible only between one or two points and every other point - Preserving shortest route, a trait preserved only by the gnomonic projection Because the sphere is not a developable surface, it is impossible to construct a map projection that is both equal-area and conformal. Projections by surfaceEdit The three developable surfaces (plane, cylinder, cone) provide useful models for understanding, describing, and developing map projections. However, these models are limited in two fundamental ways. For one thing, most world projections in use do not fall into any of those categories. For another thing, even most projections that do fall into those categories are not naturally attainable through physical projection. As L.P. Lee notes, No reference has been made in the above definitions to cylinders, cones or planes. The projections are termed cylindric or conic because they can be regarded as developed on a cylinder or a cone, as the case may be, but it is as well to dispense with picturing cylinders and cones, since they have given rise to much misunderstanding. Particularly is this so with regard to the conic projections with two standard parallels: they may be regarded as developed on cones, but they are cones which bear no simple relationship to the sphere. In reality, cylinders and cones provide us with convenient descriptive terms, but little else. Lee's objection refers to the way the terms cylindrical, conic, and planar (azimuthal) have been abstracted in the field of map projections. If maps were projected as in light shining through a globe onto a developable surface, then the spacing of parallels would follow a very limited set of possibilities. Such a cylindrical projection (for example) is one which: - Is rectangular; - Has straight vertical meridians, spaced evenly; - Has straight parallels symmetrically placed about the equator; - Has parallels constrained to where they fall when light shines through the globe onto the cylinder, with the light source someplace along the line formed by the intersection of the prime meridian with the equator, and the center of the sphere. (If you rotate the globe before projecting then the parallels and meridians will not necessarily still be straight lines. Rotations are normally ignored for the purpose of classification.) Where the light source emanates along the line described in this last constraint is what yields the differences between the various "natural" cylindrical projections. But the term cylindrical as used in the field of map projections relaxes the last constraint entirely. Instead the parallels can be placed according to any algorithm the designer has decided suits the needs of the map. The famous Mercator projection is one in which the placement of parallels does not arise by "projection"; instead parallels are placed how they need to be in order to satisfy the property that a course of constant bearing is always plotted as a straight line. The term "normal cylindrical projection" is used to refer to any projection in which meridians are mapped to equally spaced vertical lines and circles of latitude (parallels) are mapped to horizontal lines. The mapping of meridians to vertical lines can be visualized by imagining a cylinder whose axis coincides with the Earth's axis of rotation. This cylinder is wrapped around the Earth, projected onto, and then unrolled. By the geometry of their construction, cylindrical projections stretch distances east-west. The amount of stretch is the same at any chosen latitude on all cylindrical projections, and is given by the secant of the latitude as a multiple of the equator's scale. The various cylindrical projections are distinguished from each other solely by their north-south stretching (where latitude is given by φ): - North-south stretching equals east-west stretching (sec φ): The east-west scale matches the north-south scale: conformal cylindrical or Mercator; this distorts areas excessively in high latitudes (see also transverse Mercator). - North-south stretching grows with latitude faster than east-west stretching (sec2 φ): The cylindric perspective (or central cylindrical) projection; unsuitable because distortion is even worse than in the Mercator projection. - North-south stretching grows with latitude, but less quickly than the east-west stretching: such as the Miller cylindrical projection (sec 4/φ). - North-south distances neither stretched nor compressed (1): equirectangular projection or "plate carrée". - North-south compression equals the cosine of the latitude (the reciprocal of east-west stretching): equal-area cylindrical. This projection has many named specializations differing only in the scaling constant, such as the Gall–Peters or Gall orthographic (undistorted at the 45° parallels), Behrmann (undistorted at the 30° parallels), and Lambert cylindrical equal-area (undistorted at the equator). Since this projection scales north-south distances by the reciprocal of east-west stretching, it preserves area at the expense of shapes. In the first case (Mercator), the east-west scale always equals the north-south scale. In the second case (central cylindrical), the north-south scale exceeds the east-west scale everywhere away from the equator. Each remaining case has a pair of secant lines—a pair of identical latitudes of opposite sign (or else the equator) at which the east-west scale matches the north-south-scale. Normal cylindrical projections map the whole Earth as a finite rectangle, except in the first two cases, where the rectangle stretches infinitely tall while retaining constant width. Pseudocylindrical projections represent the central meridian as a straight line segment. Other meridians are longer than the central meridian and bow outward, away from the central meridian. Pseudocylindrical projections map parallels as straight lines. Along parallels, each point from the surface is mapped at a distance from the central meridian that is proportional to its difference in longitude from the central meridian. Therefore, meridians are equally spaced along a given parallel. On a pseudocylindrical map, any point further from the equator than some other point has a higher latitude than the other point, preserving north-south relationships. This trait is useful when illustrating phenomena that depend on latitude, such as climate. Examples of pseudocylindrical projections include: - Sinusoidal, which was the first pseudocylindrical projection developed. On the map, as in reality, the length of each parallel is proportional to the cosine of the latitude. The area of any region is true. - Collignon projection, which in its most common forms represents each meridian as two straight line segments, one from each pole to the equator. The term "conic projection" is used to refer to any projection in which meridians are mapped to equally spaced lines radiating out from the apex and circles of latitude (parallels) are mapped to circular arcs centered on the apex. When making a conic map, the map maker arbitrarily picks two standard parallels. Those standard parallels may be visualized as secant lines where the cone intersects the globe—or, if the map maker chooses the same parallel twice, as the tangent line where the cone is tangent to the globe. The resulting conic map has low distortion in scale, shape, and area near those standard parallels. Distances along the parallels to the north of both standard parallels or to the south of both standard parallels are stretched; distances along parallels between the standard parallels are compressed. When a single standard parallel is used, distances along all other parallels are stretched. Conic projections that are commonly used are: - Equidistant conic, which keeps parallels evenly spaced along the meridians to preserve a constant distance scale along each meridian, typically the same or similar scale as along the standard parallels. - Albers conic, which adjusts the north-south distance between non-standard parallels to compensate for the east-west stretching or compression, giving an equal-area map. - Lambert conformal conic, which adjusts the north-south distance between non-standard parallels to equal the east-west stretching, giving a conformal map. - Bonne, an equal-area projection on which most meridians and parallels appear as curved lines. It has a configurable standard parallel along which there is no distortion. - Werner cordiform, upon which distances are correct from one pole, as well as along all parallels. - American polyconic Azimuthal (projections onto a plane)Edit Azimuthal projections have the property that directions from a central point are preserved and therefore great circles through the central point are represented by straight lines on the map. These projections also have radial symmetry in the scales and hence in the distortions: map distances from the central point are computed by a function r(d) of the true distance d, independent of the angle; correspondingly, circles with the central point as center are mapped into circles which have as center the central point on the map. The radial scale is r′(d) and the transverse scale r(d)/(R sin d/) where R is the radius of the Earth. Some azimuthal projections are true perspective projections; that is, they can be constructed mechanically, projecting the surface of the Earth by extending lines from a point of perspective (along an infinite line through the tangent point and the tangent point's antipode) onto the plane: - The gnomonic projection displays great circles as straight lines. Can be constructed by using a point of perspective at the center of the Earth. r(d) = c tan d/; so that even just a hemisphere is already infinite in extent. - The General Perspective projection can be constructed by using a point of perspective outside the earth. Photographs of Earth (such as those from the International Space Station) give this perspective. - The orthographic projection maps each point on the earth to the closest point on the plane. Can be constructed from a point of perspective an infinite distance from the tangent point; r(d) = c sin d/. Can display up to a hemisphere on a finite circle. Photographs of Earth from far enough away, such as the Moon, approximate this perspective. - The stereographic projection, which is conformal, can be constructed by using the tangent point's antipode as the point of perspective. r(d) = c tan d/; the scale is c/(2R cos2 d/). Can display nearly the entire sphere's surface on a finite circle. The sphere's full surface requires an infinite map. Other azimuthal projections are not true perspective projections: - Azimuthal equidistant: r(d) = cd; it is used by amateur radio operators to know the direction to point their antennas toward a point and see the distance to it. Distance from the tangent point on the map is proportional to surface distance on the earth (; for the case where the tangent point is the North Pole, see the flag of the United Nations) - Lambert azimuthal equal-area. Distance from the tangent point on the map is proportional to straight-line distance through the earth: r(d) = c sin d/ - Logarithmic azimuthal is constructed so that each point's distance from the center of the map is the logarithm of its distance from the tangent point on the Earth. r(d) = c ln d/); locations closer than at a distance equal to the constant d0 are not shown. Projections by preservation of a metric propertyEdit Conformal, or orthomorphic, map projections preserve angles locally, implying that they map infinitesimal circles of constant size anywhere on the Earth to infinitesimal circles of varying sizes on the map. In contrast, mappings that are not conformal distort most such small circles into ellipses of distortion. An important consequence of conformality is that relative angles at each point of the map are correct, and the local scale (although varying throughout the map) in every direction around any one point is constant. These are some conformal projections: - Mercator: Rhumb lines are represented by straight segments - Transverse Mercator - Stereographic: Any circle of a sphere, great and small, maps to a circle or straight line. - Lambert conformal conic - Peirce quincuncial projection - Adams hemisphere-in-a-square projection - Guyou hemisphere-in-a-square projection Equal-area maps preserve area measure, generally distorting shapes in order to do that. Equal-area maps are also called equivalent or authalic. These are some projections that preserve area: - Albers conic - Cylindrical equal-area - Eckert II, IV and VI - Gall orthographic (also known as Gall–Peters, or Peters, projection) - Goode's homolosine - Lambert azimuthal equal-area - Lambert cylindrical equal-area - Snyder’s equal-area polyhedral projection, used for geodesic grids. - Tobler hyperelliptical These are some projections that preserve distance from some standard point or line: - Equirectangular—distances along meridians are conserved - Plate carrée—an Equirectangular projection centered at the equator - Azimuthal equidistant—distances along great circles radiating from centre are conserved - Equidistant conic - Sinusoidal—distances along parallels are conserved - Werner cordiform distances from the North Pole are correct as are the curved distance on parallels - Two-point equidistant: two "control points" are arbitrarily chosen by the map maker. Distance from any point on the map to each control point is proportional to surface distance on the earth. Great circles are displayed as straight lines: Direction to a fixed location B (the bearing at the starting location A of the shortest route) corresponds to the direction on the map from A to B: - Littrow—the only conformal retroazimuthal projection - Hammer retroazimuthal—also preserves distance from the central point - Craig retroazimuthal aka Mecca or Qibla—also has vertical meridians Compromise projections give up the idea of perfectly preserving metric properties, seeking instead to strike a balance between distortions, or to simply make things "look right". Most of these types of projections distort shape in the polar regions more than at the equator. These are some compromise projections: Which projection is best?Edit The mathematics of projection do not permit any particular map projection to be "best" for everything. Something will always be distorted. Thus, many projections exist to serve the many uses of maps and their vast range of scales. Modern national mapping systems typically employ a transverse Mercator or close variant for large-scale maps in order to preserve conformality and low variation in scale over small areas. For smaller-scale maps, such as those spanning continents or the entire world, many projections are in common use according to their fitness for the purpose, such as Winkel tripel, Robinson and Mollweide. Reference maps of the world often appear on compromise projections. Due to distortions inherent in any map of the world, the choice of projection becomes largely one of aesthetics. Thematic maps normally require an equal area projection so that phenomena per unit area are shown in correct proportion. However, representing area ratios correctly necessarily distorts shapes more than many maps that are not equal-area. The Mercator projection, developed for navigational purposes, has often been used in world maps where other projections would have been more appropriate. This problem has long been recognized even outside professional circles. For example, a 1943 New York Times editorial states: The time has come to discard [the Mercator] for something that represents the continents and directions less deceptively ... Although its usage ... has diminished ... it is still highly popular as a wall map apparently in part because, as a rectangular map, it fills a rectangular wall space with more map, and clearly because its familiarity breeds more popularity.:166 A controversy in the 1980s over the Peters map motivated the American Cartographic Association (now Cartography and Geographic Information Society) to produce a series of booklets (including Which Map Is Best) designed to educate the public about map projections and distortion in maps. In 1989 and 1990, after some internal debate, seven North American geographic organizations adopted a resolution recommending against using any rectangular projection (including Mercator and Gall–Peters) for reference maps of the world. - Snyder, J.P. (1989). Album of Map Projections, United States Geological Survey Professional Paper. United States Government Printing Office. 1453. - Snyder, John P. (1993). Flattening the earth: two thousand years of map projections. University of Chicago Press. ISBN 0-226-76746-9. - Snyder. Working Manual, p. 24. - "Projection parameters". - "Map projections". - Cheng, Y.; Lorre, J. J. (2000). "Equal Area Map Projection for Irregularly Shaped Objects". Cartography and Geographic Information Science. 27 (2): 91. doi:10.1559/152304000783547957. - Stooke, P. J. (1998). "Mapping Worlds with Irregular Shapes". The Canadian Geographer. 42: 61. doi:10.1111/j.1541-0064.1998.tb01553.x. - Shingareva, K.B.; Bugaevsky, L.M.; Nyrtsov, M. (2000). "Mathematical Basis for Non-spherical Celestial Bodies Maps" (PDF). Journal of Geospatial Engineering. 2 (2): 45–50. - Nyrtsov, M.V. (August 2003). "The Classification of Projections of Irregularly-shaped Celestial Bodies" (PDF). Proceedings of the 21st International Cartographic Conference (ICC): 1158–1164. - Clark, P. E.; Clark, C. S. (2013). "CSNB Mapping Applied to Irregular Bodies". Constant-Scale Natural Boundary Mapping to Reveal Global and Cosmic Processes. SpringerBriefs in Astronomy. p. 71. doi:10.1007/978-1-4614-7762-4_6. ISBN 978-1-4614-7761-7. - Snyder, John Parr (1987). Map Projections – a Working Manual. U.S. Government Printing Office. p. 192. - Lee, L.P. (1944). "The nomenclature and classification of map projections". Empire Survey Review. VII (51): 190–200. doi:10.1179/sre.1922.214.171.124. p. 193 - Weisstein, Eric W. "Sinusoidal Projection". MathWorld. - Carlos A. Furuti. "Conic Projections" - Weisstein, Eric W. "Gnomonic Projection". MathWorld. - "The Gnomonic Projection". Retrieved November 18, 2005. - Weisstein, Eric W. "Orthographic Projection". MathWorld. - Weisstein, Eric W. "Stereographic Projection". MathWorld. - Weisstein, Eric W. "Azimuthal Equidistant Projection". MathWorld. - Weisstein, Eric W. "Lambert Azimuthal Equal-Area Projection". MathWorld. - Snyder, John P. "Enlarging the Heart of a Map". Archived from the original on July 2, 2010. Retrieved April 14, 2016. - Snyder, John P. "Enlarging the Heart of a Map (accompanying figures)". Archived from the original on April 10, 2011. Retrieved November 18, 2005. (see figure 6-5) - Choosing a World Map. Falls Church, Virginia: American Congress on Surveying and Mapping. 1988. p. 1. ISBN 0-9613459-2-6. - Slocum, Terry A.; Robert B. McMaster; Fritz C. Kessler; Hugh H. Howard (2005). Thematic Cartography and Geographic Visualization (2nd ed.). Upper Saddle River, NJ: Pearson Prentice Hall. p. 166. ISBN 0-13-035123-7. - Bauer, H.A. (1942). "Globes, Maps, and Skyways (Air Education Series)". New York. p. 28 - Miller, Osborn Maitland (1942). "Notes on Cylindrical World Map Projections". Geographical Review. 32 (3): 424–430. doi:10.2307/210384. - Raisz, Erwin Josephus. (1938). General Cartography. New York: McGraw–Hill. 2d ed., 1948. p. 87. - Robinson, Arthur Howard. (1960). Elements of Cartography, second edition. New York: John Wiley and Sons. p. 82. - American Cartographic Association's Committee on Map Projections, 1986. Which Map is Best p. 12. Falls Church: American Congress on Surveying and Mapping. - Robinson, Arthur (1990). "Rectangular World Maps—No!". Professional Geographer. 42 (1): 101–104. doi:10.1111/j.0033-0124.1990.00101.x. - "Geographers and Cartographers Urge End to Popular Use of Rectangular Maps". American Cartographer. 16: 222–223. 1989. doi:10.1559/152304089783814089. - Fran Evanisko, American River College, lectures for Geography 20: "Cartographic Design for GIS", Fall 2002 - Map Projections—PDF versions of numerous projections, created and released into the Public Domain by Paul B. Anderson ... member of the International Cartographic Association's Commission on Map Projections - "An Album of Map Projections" (PDF). (12.6 MB), U.S. Geological Survey Professional Paper 1453, by John P. Snyder (USGS) and Philip M. Voxland (U. Minnesota), 1989. - Cartography at Curlie (based on DMOZ) - A Cornucopia of Map Projections, a visualization of distortion on a vast array of map projections in a single image. - G.Projector, free software can render many projections (NASA GISS). - Color images of map projections and distortion (Mapthematics.com). - Geometric aspects of mapping: map projection (KartoWeb.itc.nl). - Java world map projections, Henry Bottomley (SE16.info). - Map projections http://www.3dsoftware.com/Cartography/USGS/MapProjections/ at the Wayback Machine (archived January 4, 2007) (3DSoftware). - Map projections, John Savard. - Map Projections (MathWorld). - Map Projections An interactive JAVA applet to study deformations (area, distance and angle) of map projections (UFF.br). - Map Projections: How Projections Work (Progonos.com). - Map Projections Poster (U.S. Geographical Survey). - MapRef: The Internet Collection of MapProjections and Reference Systems in Europe - PROJ.4 – Cartographic Projections Library. - Projection Reference Table of examples and properties of all common projections (RadicalCartography.net). - "Understanding Map Projections" (PDF). (1.70 MB), Melita Kennedy (ESRI). - World Map Projections, Stephen Wolfram based on work by Yu-Sung Chang (Wolfram Demonstrations Project). - Compare Map Projections - Hazewinkel, Michiel, ed. (2001) , "Cartographic projection", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4
Interstellar space travel is manned or unmanned travel between stars. Interstellar travel is much more difficult than interplanetary travel: the distances between the planets in the Solar System are typically measured in standard astronomical units (AU)—whereas the distances between stars are typically hundreds of thousands of AU, and usually expressed in light-years. Because of this some combination of great speed (some percentage of the speed of light) and huge travel time (lasting from years to millennia) would be required. These speeds are far beyond what current methods of spacecraft propulsion can provide. The energy required to propel a spacecraft to these speeds, regardless of the propulsion system used, is enormous by today's standards of energy production. At these speeds, collisions by the spacecraft with interstellar dust and gas can produce very dangerous effects both to any passengers and the spacecraft itself. A number of widely differing strategies have been proposed to deal with these problems, ranging from giant arks that would carry entire societies and ecosystems very slowly, to microscopic space probes. Many different propulsion systems have been proposed to give spacecraft the required speeds: these range from different forms of nuclear propulsion, to beamed energy methods that would require megascale engineering projects, to methods based on speculative physics. For both unmanned and manned interstellar travel, considerable technological and economic challenges would need to be met. Even the most optimistic views about interstellar travel are that it might happen decades in the future; the more common view is that it is a century or more away. - 1 Challenges - 2 Prime targets for interstellar travel - 3 Proposed methods - 3.1 Slow, uncrewed probes - 3.2 Fast, uncrewed probes - 3.3 Slow, manned missions - 3.4 Island hopping through interstellar space - 3.5 Fast missions - 3.6 By transmission - 4 Propulsion - 4.1 Rocket concepts - 4.2 Non-rocket concepts - 4.3 Speculative methods - 5 Designs and studies - 6 Non-profit organisations - 7 Skepticism - 8 See also - 9 Notes - 10 Further reading - 11 External links The basic challenge facing interstellar travel is the immense distances between the stars. Astronomical distances are measured using different units of length, depending on the scale of the distances involved. Between the planets in the Solar System they are often measured in astronomical units (AU), defined as the average distance between the Sun and Earth, some 150 million kilometers (93 million miles). Mars, the closest other planet to Earth is (at closest approach) 0.38 AU away. Neptune, the furthest planet from the Sun, is 29.8 AU away. Voyager 1, the furthest man-made object from Earth, is 129.2 AU away. The closest known star Proxima Centauri, however, is some 268,332 AU away. Or 9000 times further away than even the furthest planet in the Solar System. \|The Moon\|\|0.0026\|\|1.3 seconds\| \|Mars (nearest planet)\|\|0.38\|\|3.16 minutes\| \|Neptune (furthest planet)\|\|29.8\|\|4.1 hours\| \|Voyager 1\|\|129.2\|\|17.9 hours\| \|Proxima Centauri (nearest star)\|\|268,332\|\|4.24 years\| Because of this, distances between stars are usually expressed in light-years, defined as the distance that a ray of light travels in a year. Light in a vacuum travels around 300,000 kilometers (186,000 miles) per second, so this is some 9.46 trillion kilometers (5.87 trillion miles) or 63,241 AU. Proxima Centauri is 4.243 light-years away. Another way of understanding the vastness of interstellar distances is by scaling: one of the closest stars to the sun, Alpha Centauri A (a Sun-like star), can be pictured by scaling down the Earth–Sun distance to one meter (~3.3 ft). On this scale, the distance to Alpha Centauri A would be 271 kilometers (169 miles). The fastest outward-bound spacecraft yet sent, Voyager 1, has covered 1/600th of a light-year in 30 years and is currently moving at 1/18,000th the speed of light. At this rate, a journey to Proxima Centauri would take 80,000 years. Some combination of great speed and long travel time are required. The time required by propulsion methods based on currently known physical principles would require years to millennia. A significant factor contributing to the difficulty is the energy that must be supplied to obtain a reasonable travel time. A lower bound for the required energy is the kinetic energy K = ½ mv2 where m is the final mass. If deceleration on arrival is desired and cannot be achieved by any means other than the engines of the ship, then the required energy is significantly increased. The velocity for a manned round trip of a few decades to even the nearest star is several thousand times greater than those of present space vehicles. This means that due to the v2 term in the kinetic energy formula, millions of times as much energy is required. Accelerating one ton to one-tenth of the speed of light requires at least 450 PJ or 4.5 ×1017 J or 125 billion kWh, without factoring in efficiency of the propulsion mechanism. This energy has to be generated on-board from stored fuel, harvested from the interstellar medium, or projected over immense distances. The mass of any craft capable of carrying humans would inevitably be substantially larger than that necessary for an unmanned interstellar probe. For instance, the first space probe, Sputnik 1, had a payload of 83.6 kg, whereas the first spacecraft carrying a living passenger (the dog Laika), Sputnik 2, had a payload six times that at 508.3 kg. This underestimates the difference in the case of interstellar missions, given the vastly greater travel times involved and the resulting necessity of a closed-cycle life support system. As technology continues to advance, combined with the aggregate risks and support requirements of manned interstellar travel, the first interstellar missions are unlikely to carry life forms. A major issue with traveling at extremely high speeds is that interstellar dust and gas may cause considerable damage to the craft, due to the high relative speeds and large kinetic energies involved. Various shielding methods to mitigate this problem have been proposed. Larger objects (such as macroscopic dust grains) are far less common, but would be much more destructive. The risks of impacting such objects, and methods of mitigating these risks, have been discussed in the literature, but many unknowns remain. Virtually all the material that would pose a problem is in the Solar System along the disk that contains the planets, asteroid belt, Oort cloud, comets, free asteroids, macro and micrometeroids, etc. so any device or projectile must be sent in a direction opposite of all of this material. The larger the object humans send, the greater the chances of it hitting something. One option is to project something very small where the chance of it striking something is virtually non-existent in the vacuum of interplanetary and interstellar space. An interstellar ship would face manifold hazards found in interplanetary travel, including vacuum, radiation, weightlessness, and micrometeoroids. Even the minimum multi-year travel times to the nearest stars are beyond current manned space mission design experience. More speculative approaches to interstellar travel offer the possibility of circumventing these difficulties. Special relativity offers the possibility of shortening the travel time through relativistic time dilation: if a starship with could reach velocities approaching the speed of light, the journey time as experienced by the traveler would be greatly reduced (see time dilation section). General relativity offers the theoretical possibility that faster-than-light travel could greatly shorten travel times, both for the traveler and those on Earth (see Faster-than-light travel section). It has been argued that an interstellar mission that cannot be completed within 50 years should not be started at all. Instead, assuming that a civilization is still on an increasing curve of propulsion system velocity, not yet having reached the limit, the resources should be invested in designing a better propulsion system. This is because a slow spacecraft would probably be passed by another mission sent later with more-advanced propulsion (the incessant obsolescence postulate). On the other hand, Andrew Kennedy has shown that if one calculates the journey time to a given destination as the rate of travel speed derived from growth (even exponential growth) increases, there is a clear minimum in the total time to that destination from now (see wait calculation). Voyages undertaken before the minimum will be overtaken by those who leave at the minimum, whereas those who leave after the minimum will never overtake those who left at the minimum. One argument against the stance of delaying a start until reaching fast propulsion system velocity is that the various other non-technical problems that are specific to long-distance travel at considerably higher speed (such as interstellar particle impact, possible dramatic shortening of average human life span during extended space residence, etc.) may remain obstacles that take much longer time to resolve than the propulsion issue alone, assuming that they can even be solved eventually at all. A case can therefore be made for starting a mission without delay, based on the concept of an achievable and dedicated but relatively slow interstellar mission using the current technological state-of-the-art and at relatively low cost, rather than banking on being able to solve all problems associated with a faster mission without having a reliable time frame for achievability of such. The round-trip delay time is the minimum time between an observation by the probe and the moment the probe can receive instructions from Earth reacting to the observation. Given that information can travel no faster than the speed of light, this is for the Voyager 1 about 36 hours, and near Proxima Centauri it would be 8 years. Faster reaction would have to be programmed to be carried out automatically. Of course, in the case of a manned flight the crew can respond immediately to their observations. However, the round-trip delay time makes them not only extremely distant from, but, in terms of communication, also extremely isolated from Earth (analogous to how past long distance explorers were similarly isolated before the invention of the electrical telegraph). Interstellar communication is still problematic – even if a probe could reach the nearest star, its ability to communicate back to Earth would be difficult given the extreme distance. See Interstellar communication. Prime targets for interstellar travel There are 59 known stellar systems within 20 light years from the Sun, containing 81 visible stars. The following could be considered prime targets for interstellar missions: \|Stellar system\|\|Distance (ly)\|\|Remarks\| \|Alpha Centauri\|\|4.3\|\|Closest system. Three stars (G2, K1, M5). Component A is similar to the Sun (a G2 star). Alpha Centauri B has one confirmed planet.\| \|Barnard's Star\|\|6\|\|Small, low-luminosity M5 red dwarf. Second closest to Solar System.\| \|Sirius\|\|8.7\|\|Large, very bright A1 star with a white dwarf companion.\| \|Epsilon Eridani\|\|10.8\|\|Single K2 star slightly smaller and colder than the Sun. Has two asteroid belts, might have a giant and one much smaller planet, and may possess a Solar-System-type planetary system.\| \|Tau Ceti\|\|11.8\|\|Single G8 star similar to the Sun. High probability of possessing a Solar-System-type planetary system: current evidence shows 5 planets with potentially two in the habitable zone.\| \|Gliese 581\|\|20.3\|\|Multiple planet system. The unconfirmed exoplanet Gliese 581 g and the confirmed exoplanet Gliese 581 d are in the star's habitable zone.\| \|Gliese 667C\|\|22\|\|A system with at least six planets. A record-breaking three of these planets are super-Earths lying in the zone around the star where liquid water could exist, making them possible candidates for the presence of life.\| \|Vega\|\|25\|\|At least one planet, and of a suitable age to have evolved primitive life \| Existing and near-term astronomical technology is capable of finding planetary systems around these objects, increasing their potential for exploration. Slow, uncrewed probes Slow interstellar missions based on current and near-future propulsion technologies are associated with trip times starting from about one hundred years to thousands of years. These missions consist of sending a robotic probe to a nearby star for exploration, similar to interplanetary probes such as used in the voyager program. By taking along no crew, the cost and complexity of the mission is significantly reduced although technology lifetime is still a significant issue next to obtaining a reasonable speed of travel. Proposed concepts include Project Daedalus, Project Icarus and Project Longshot. Fast, uncrewed probes Near-lightspeed nanospacecraft might be possible within the near future built on existing microchip technology with a newly developed nanoscale thruster. Researchers at the University of Michigan are developing thrusters that use nanoparticles as propellant. Their technology is called “nanoparticle field extraction thruster”, or nanoFET. These devices act like small particle accelerators shooting conductive nanoparticles out into space. Given the light weight of these probes, it would take much less energy to accelerate them. With on board solar cells they could continually accelerate using solar power. One can envision a day when a fleet of millions or even billions of these particles swarm to distant stars at nearly the speed of light and relay signals back to Earth through a vast interstellar communication network. Slow, manned missions In crewed missions, the duration of a slow interstellar journey presents a major obstacle and existing concepts deal with this problem in different ways. They can be distinguished by the "state" in which humans are transported on-board of the spacecraft. A generation ship (or world ship) is a type of interstellar ark in which the crew that arrives at the destination is descended from those who started the journey. Generation ships are not currently feasible because of the difficulty of constructing a ship of the enormous required scale and the great biological and sociological problems that life aboard such a ship raises. Scientists and writers have postulated various techniques for suspended animation. These include human hibernation and cryonic preservation. Although neither is currently practical, they offer the possibility of sleeper ships in which the passengers lie inert for the long duration of the voyage. Extended human lifespan A variant on this possibility is based on the development of substantial human life extension, such as the "Strategies for Engineered Negligible Senescence" proposed by Dr. Aubrey de Grey. If a ship crew had lifespans of some thousands of years, or had artificial bodies, they could traverse interstellar distances without the need to replace the crew in generations. The psychological effects of such an extended period of travel would potentially still pose a problem. A robotic space mission carrying some number of frozen early stage human embryos is another theoretical possibility. This method of space colonization requires, among other things, the development of a method to replicate conditions in a uterus, the prior detection of a habitable terrestrial planet, and advances in the field of fully autonomous mobile robots and educational robots that would replace human parents. A more speculative method of transporting humans to the stars is by using mind uploading or also called brain emulation. Frank J. Tipler speculates about the colonization of the universe by starships transporting uploaded humans. Hein presents a range of concepts how such missions could be conducted, using more or less speculative technologies, for example self-replicating machines, wormholes, and teleportation. One of the major challenges besides mind uploading itself are the means for downloading the uploads into physical entities, which can be biological or artficial or both. Island hopping through interstellar space Interstellar space is not completely empty; it contains trillions of icy bodies ranging from small asteroids (Oort cloud) to possible rogue planets. There may be ways to take advantage of these resources for a good part of an interstellar trip, slowly hopping from body to body or setting up waystations along the way. If a spaceship could average 10 percent of light speed (and decelerate at the destination, for manned missions), this would be enough to reach Proxima Centauri in forty years. Several propulsion concepts are proposed that might be eventually developed to accomplish this (see section below on propulsion methods), but none of them are ready for near-term (few decades) development at acceptable cost. Assuming one cannot travel faster than light, one might conclude that a human can never make a round-trip further from Earth than 40 light years if the traveler is active between the ages of 20 and 60. In this example a traveler would never be able to reach more than the very few star systems that exist within the limit of 10–20 light years from Earth. This, however, fails to take into account time dilation. Clocks aboard an interstellar ship would run slower than Earth clocks, so if a ship's engines were powerful enough the ship could reach mostly anywhere in the galaxy and return to Earth within 40 years ship-time. Upon return, there would be a difference between the time elapsed on the astronaut's ship and the time elapsed on Earth. If a spaceship travels to a star 32 light-years away and initially accelerates at a constant 1.03g (i.e. 10.1 m/s2) for 1.32 years (ship time) then stops its engines and coasts for the next 17.3 years (ship time) at a constant speed then decelerates again for 1.32 ship-years and comes to a stop at the destination. After a short visit the astronaut returns to Earth the same way. After the full round-trip, the clocks on board the ship show that 40 years have passed, but according to those on Earth, the ship comes back 76 years after launch. From the viewpoint of the astronaut, on-board clocks seem to be running normally. The star ahead seems to be approaching at a speed of 0.87 lightyears per ship-year. The universe would appear contracted along the direction of travel to half the size it had when the ship was at rest; the distance between that star and the Sun would seem to be 16 light years as measured by the astronaut. At higher speeds, the time onboard will run even slower, so the astronaut could travel to the center of the Milky Way (30 kly from Earth) and back in 40 years ship-time. But the speed according to Earth clocks will always be less than 1 lightyear per Earth year, so, when back home, the astronaut will find that 60 thousand years will have passed on Earth. Regardless of how it is achieved, if a propulsion system can produce 1 g of acceleration continuously from departure to destination, then this will be the fastest method of travel. If the propulsion system drives the ship faster and faster for the first half of the journey, then turns around and brakes the craft so that it arrives at the destination at a standstill, this is a constant acceleration journey. This would also have the advantage of producing constant gravity. From the planetary observer perspective the ship will appear to steadily accelerate but more slowly as it approaches the speed of light. The ship will be close to the speed of light after about a year of accelerating and remain at that speed until it brakes for the end of the journey. From the ship perspective there will be no top limit on speed – the ship keeps going faster and faster the whole first half. This happens because the ship's time sense slows down – relative to the planetary observer – the more it approaches the speed of light. The result is an impressively fast journey if you are in the ship. If physical entities could be transmitted as information and reconstructed at a destination, travel at nearly the speed of light would be possible, which for the "travelers" would be instantaneous. However, sending an atom-by-atom description of (say) a human body would be a daunting task. Extracting and sending only a computer brain simulation is a significant part of that problem. "Journey" time would be the light-travel time plus the time needed to encode, send and reconstruct the whole transmission. All rocket concepts are limited by the rocket equation, which sets the characteristic velocity available as a function of exhaust velocity and mass ratio, the ratio of initial (M0, including fuel) to final (M1, fuel depleted) mass. Very high specific power, the ratio of jet-power to total vehicle mass, is required to reach interstellar targets within sub-century time-frames. Some heat transfer is inevitable and a tremendous heating load must be adequately handled. Thus, for interstellar rocket concepts of all technologies, a key engineering problem (seldom explicitly discussed) is limiting the heat transfer from the exhaust stream back into the vehicle. Nuclear fission powered Nuclear-electric or plasma engines, operating for long periods at low thrust and powered by fission reactors, have the potential to reach speeds much greater than chemically powered vehicles or nuclear-thermal rockets. Such vehicles probably have the potential to power Solar System exploration with reasonable trip times within the current century. Because of their low-thrust propulsion, they would be limited to off-planet, deep-space operation. Electrically powered spacecraft propulsion powered by a portable power-source, say a nuclear reactor, producing only small accelerations, would take centuries to reach for example 15% of the velocity of light, thus unsuitable for interstellar flight during a single human lifetime. Fission-fragment rockets use nuclear fission to create high-speed jets of fission fragments, which are ejected at speeds of up to 12,000 km/s. With fission, the energy output is approximately 0.1% of the total mass-energy of the reactor fuel and limits the effective exhaust velocity to about 5% of the velocity of light. For maximum velocity, the reaction mass should optimally consist of fission products, the "ash" of the primary energy source, in order that no extra reaction mass need be book-kept in the mass ratio. This is known as a fission-fragment rocket. thermal-propulsion engines such as NERVA produce sufficient thrust, but can only achieve relatively low-velocity exhaust jets, so to accelerate to the desired speed would require an enormous amount of fuel. Based on work in the late 1950s to the early 1960s, it has been technically possible to build spaceships with nuclear pulse propulsion engines, i.e. driven by a series of nuclear explosions. This propulsion system contains the prospect of very high specific impulse (space travel's equivalent of fuel economy) and high specific power. Project Orion team member, Freeman Dyson, proposed in 1968 an interstellar spacecraft using nuclear pulse propulsion that used pure deuterium fusion detonations with a very high fuel-burnup fraction. He computed an exhaust velocity of 15,000 km/s and a 100,000-tonne space vehicle able to achieve a 20,000 km/s delta-v allowing a flight-time to Alpha Centauri of 130 years. Later studies indicate that the top cruise velocity that can theoretically be achieved by a Teller-Ulam thermonuclear unit powered Orion starship, assuming no fuel is saved for slowing back down, is about 8% to 10% of the speed of light (0.08-0.1c). An atomic (fission) Orion can achieve perhaps 3%-5% of the speed of light. A nuclear pulse drive starship powered by Fusion-antimatter catalyzed nuclear pulse propulsion units would be similarly in the 10% range and pure Matter-antimatter annihilation rockets would be theoretically capable of obtaining a velocity between 50% to 80% of the speed of light. In each case saving fuel for slowing down halves the max. speed. The concept of using a magnetic sail to decelerate the spacecraft as it approaches its destination has been discussed as an alternative to using propellant, this would allow the ship to travel near the maximum theoretical velocity. Alternative designs utilizing similar principles include Project Longshot, Project Daedalus, and Mini-Mag Orion. The principle of external nuclear pulse propulsion to maximize survivable power has remained common among serious concepts for interstellar flight without external power beaming and for very high-performance interplanetary flight. In the 1970s the Nuclear Pulse Propulsion concept further was refined by Project Daedalus by use of externally triggered inertial confinement fusion, in this case producing fusion explosions via compressing fusion fuel pellets with high-powered electron beams. Since then, lasers, ion beams, neutral particle beams and hyper-kinetic projectiles have been suggested to produce nuclear pulses for propulsion purposes. A current impediment to the development of any nuclear-explosion-powered spacecraft is the 1963 Partial Test Ban Treaty, which includes a prohibition on the detonation of any nuclear devices (even non-weapon based) in outer space. This treaty would therefore need to be renegotiated, although a project on the scale of an interstellar mission using currently foreseeable technology would probably require international cooperation on at least the scale of the International Space Station. Nuclear fusion rockets Fusion rocket starships, powered by nuclear fusion reactions, should conceivably be able to reach speeds of the order of 10% of that of light, based on energy considerations alone. In theory, a large number of stages could push a vehicle arbitrarily close to the speed of light. These would "burn" such light element fuels as deuterium, tritium, 3He, 11B, and 7Li. Because fusion yields about 0.3–0.9% of the mass of the nuclear fuel as released energy, it is energetically more favorable than fission, which releases <0.1% of the fuel's mass-energy. The maximum exhaust velocities potentially energetically available are correspondingly higher than for fission, typically 4–10% of c. However, the most easily achievable fusion reactions release a large fraction of their energy as high-energy neutrons, which are a significant source of energy loss. Thus, although these concepts seem to offer the best (nearest-term) prospects for travel to the nearest stars within a (long) human lifetime, they still involve massive technological and engineering difficulties, which may turn out to be intractable for decades or centuries. Early studies include Project Daedalus, performed by the British Interplanetary Society in 1973–1978, and Project Longshot, a student project sponsored by NASA and the US Naval Academy, completed in 1988. Another fairly detailed vehicle system, "Discovery II", designed and optimized for crewed Solar System exploration, based on the D3He reaction but using hydrogen as reaction mass, has been described by a team from NASA's Glenn Research Center. It achieves characteristic velocities of >300 km/s with an acceleration of ~1.7•10−3 g, with a ship initial mass of ~1700 metric tons, and payload fraction above 10%. Although these are still far short of the requirements for interstellar travel on human timescales, the study seems to represent a reasonable benchmark towards what may be approachable within several decades, which is not impossibly beyond the current state-of-the-art. Based on the concept's 2.2% burnup fraction it could achieve a pure fusion product exhaust velocity of ~3,000 km/s. An antimatter rocket would have a far higher energy density and specific impulse than any other proposed class of rocket. If energy resources and efficient production methods are found to make antimatter in the quantities required and store it safely, it would be theoretically possible to reach speeds approaching that of light. Then relativistic time dilation would become more noticeable, thus making time pass at a slower rate for the travelers as perceived by an outside observer, reducing the trip time experienced by human travelers. Supposing the production and storage of antimatter should become practical, two further problems would present and need to be solved. First, in the annihilation of antimatter, much of the energy is lost in very penetrating high-energy gamma radiation, and especially also in neutrinos, so that substantially less than mc2 would actually be available if the antimatter were simply allowed to annihilate into radiations thermally. Even so, the energy available for propulsion would probably be substantially higher than the ~1% of mc2 yield of nuclear fusion, the next-best rival candidate. Second, once again heat transfer from exhaust to vehicle seems likely to deposit enormous wasted energy into the ship, considering the large fraction of the energy that goes into penetrating gamma rays. Even assuming biological shielding were provided to protect the passengers, some of the energy would inevitably heat the vehicle, and may thereby prove limiting. This requires consideration for serious proposals if useful accelerations are to be achieved, because the energies involved (e.g. for 0.1g ship acceleration, approaching 0.3 trillion watts per ton of ship mass) are very large. Rockets with an external energy source Rockets deriving their power from external sources, such as a laser, could bypass the ordinary rocket equation, potentially reducing the mass of the ship greatly and allowing much higher travel speeds. Geoffrey A. Landis has proposed for an interstellar probe, with energy supplied by an external laser from a base station powering an Ion thruster. A problem with all traditional rocket propulsion methods is that the spacecraft would need to carry its fuel with it, thus making it very massive, in accordance with the rocket equation. Some concepts attempt to escape from this problem (): In 1960, Robert W. Bussard proposed the Bussard ramjet, a fusion rocket in which a huge scoop would collect the diffuse hydrogen in interstellar space, "burn" it on the fly using a proton–proton fusion reaction, and expel it out of the back. Later calculations with more accurate estimates suggest that the thrust generated would be less than the drag caused by any conceivable scoop design. Yet the idea is attractive because the fuel would be collected en route (commensurate with the concept of energy harvesting), so the craft could theoretically accelerate to near the speed of light. A light sail or magnetic sail powered by a massive laser or particle accelerator in the home star system could potentially reach even greater speeds than rocket- or pulse propulsion methods, because it would not need to carry its own reaction mass and therefore would only need to accelerate the craft's payload. Robert L. Forward proposed a means for decelerating an interstellar light sail in the destination star system without requiring a laser array to be present in that system. In this scheme, a smaller secondary sail is deployed to the rear of the spacecraft, whereas the large primary sail is detached from the craft to keep moving forward on its own. Light is reflected from the large primary sail to the secondary sail, which is used to decelerate the secondary sail and the spacecraft payload. A magnetic sail could also decelerate at its destination without depending on carried fuel or a driving beam in the destination system, by interacting with the plasma found in the solar wind of the destination star and the interstellar medium. \|Mission\|\|Laser Power\|\|Vehicle Mass\|\|Acceleration\|\|Sail Diameter\|\|Maximum Velocity (% of the speed of light)\| \|1. Flyby - Alpha Centauri, 40 years\| \|outbound stage\|\|65 GW\|\|1 t\|\|0.036 g\|\|3.6 km\|\|11% @ 0.17 ly\| \|2. Rendezvous - Alpha Centauri, 41 years\| \|outbound stage\|\|7,200 GW\|\|785 t\|\|0.005 g\|\|100 km\|\|21% @ 4.29 ly\| \|deceleration stage\|\|26,000 GW\|\|71 t\|\|0.2 g\|\|30 km\|\|21% @ 4.29 ly\| \|3. Manned - Epsilon Eridani, 51 years (including 5 years exploring star system)\| \|outbound stage\|\|75,000,000 GW\|\|78,500 t\|\|0.3 g\|\|1000 km\|\|50% @ 0.4 ly\| \|deceleration stage\|\|21,500,000 GW\|\|7,850 t\|\|0.3 g\|\|320 km\|\|50% @ 10.4 ly\| \|return stage\|\|710,000 GW\|\|785 t\|\|0.3 g\|\|100 km\|\|50% @ 10.4 ly\| \|deceleration stage\|\|60,000 GW\|\|785 t\|\|0.3 g\|\|100 km\|\|50% @ 0.4 ly\| Achieving start-stop interstellar trip times of less than a human lifetime require mass-ratios of between 1,000 and 1,000,000, even for the nearer stars. This could be achieved by multi-staged vehicles on a vast scale. Alternatively large linear accelerators could propel fuel to fission propelled space-vehicles, avoiding the limitations of the Rocket equation. Scientist T. Marshall Eubanks believes that nuggets of condensed quark matter may exist at the centers of some asteroids, created during the Big Bang and each nugget with a mass of 1010 to 1011 kg. If so these could be an enormous source of energy, as the nuggets could be used to generate huge quantities of antimatter—about a million tonnes of antimatter per nugget. This would be enough to propel a spacecraft close to the speed of light. Hawking radiation rockets In a black hole starship, a parabolic reflector would reflect Hawking radiation from an artificial black hole. In 2009, Louis Crane and Shawn Westmoreland of Kansas State University published a paper investigating the feasibility of this idea. Their conclusion was that it was on the edge of possibility, but that quantum gravity effects that are presently unknown may make it easier or make it impossible. Magnetic monopole rockets If some of the Grand unification models are correct, e.g. 't Hooft–Polyakov, it would be possible to construct a photonic engine that uses no antimatter thanks to the magnetic monopole that hypothetically can catalyze the decay of a proton to a positron and π0-meson: π0 decays rapidly to two photons, and the positron annihilates with an electron to give two more photons. As a result, a hydrogen atom turns into four photons and only the problem of a mirror remains unresolved. A magnetic monopole engine could also work on a once-through scheme such as the Bussard ramjet (see below). Scientists and authors have postulated a number of ways by which it might be possible to surpass the speed of light. Even the most serious-minded of these are speculative. It is also debated whether this is possible, in part, because of causality concerns, because in essence travel faster than light is equivalent to going back in time. Proposed mechanisms for faster-than-light travel within the theory of general relativity require the existence of exotic matter. General relativity may permit the travel of an object faster than light in curved spacetime. One could imagine exploiting the curvature to take a "shortcut" from one point to another. This is one form of the warp drive concept. In physics, the Alcubierre drive is based on an argument that the curvature could take the form of a wave in which a spaceship might be carried in a "bubble". Space would be collapsing at one end of the bubble and expanding at the other end. The motion of the wave would carry a spaceship from one space point to another in less time than light would take through unwarped space. Nevertheless, the spaceship would not be moving faster than light within the bubble. This concept would require the spaceship to incorporate a region of exotic matter, or "negative mass". Artificial gravity control Scientist Lance Williams believes that gravity can be controlled artificially through electromagnetic control. Wormholes are conjectural distortions in spacetime that theorists postulate could connect two arbitrary points in the universe, across an Einstein–Rosen Bridge. It is not known whether wormholes are possible in practice. Although there are solutions to the Einstein equation of general relativity that allow for wormholes, all of the currently known solutions involve some assumption, for example the existence of negative mass, which may be unphysical. However, Cramer et al. argue that such wormholes might have been created in the early universe, stabilized by cosmic string. The general theory of wormholes is discussed by Visser in the book Lorentzian Wormholes. Designs and studies The Enzmann starship, as detailed by G. Harry Stine in the October 1973 issue of Analog, was a design for a future starship, based on the ideas of Dr. Robert Duncan-Enzmann. The spacecraft itself as proposed used a 12,000,000 ton ball of frozen deuterium to power 12–24 thermonuclear pulse propulsion units. Twice as long as the Empire State Building and assembled in-orbit, the spacecraft was part of a larger project preceded by interstellar probes and telescopic observation of target star systems. NASA has been researching interstellar travel since its formation, translating important foreign language papers and conducting early studies on applying fusion propulsion, in the 1960s, and laser propulsion, in the 1970s, to interstellar travel. The NASA Breakthrough Propulsion Physics Program (terminated in FY 2003 after a 6-year, $1.2-million study, because "No breakthroughs appear imminent.") identified some breakthroughs that are needed for interstellar travel to be possible. Geoffrey A. Landis of NASA's Glenn Research Center states that a laser-powered interstellar sail ship could possibly be launched within 50 years, using new methods of space travel. "I think that ultimately we're going to do it, it's just a question of when and who," Landis said in an interview. Rockets are too slow to send humans on interstellar missions. Instead, he envisions interstellar craft with extensive sails, propelled by laser light to about one-tenth the speed of light. It would take such a ship about 43 years to reach Alpha Centauri, if it passed through the system. Slowing down to stop at Alpha Centauri could increase the trip to 100 years, whereas a journey without slowing down raises the issue of making sufficiently accurate and useful observations and measurements during a fly-by. 100 Year Starship study The 100 Year Starship (100YSS) is the name of the overall effort that will, over the next century, work toward achieving interstellar travel. The effort will also go by the moniker 100YSS. The 100 Year Starship study is the name of a one year project to assess the attributes of and lay the groundwork for an organization that can carry forward the 100 Year Starship vision. Dr. Harold ("Sonny") White from NASA's Johnson Space Center is a member of Icarus Interstellar, the nonprofit foundation whose mission is to realize interstellar flight before the year 2100. At the 2012 meeting of 100YSS, he reported using a laser to try to warp spacetime by 1 part in 10 million with the aim of helping to make interstellar travel possible. - Project Orion, manned interstellar ship (1958–1968). - Project Daedalus, unmanned interstellar probe (1973–1978). - Starwisp, unmanned interstellar probe (1985). - Project Longshot, unmanned interstellar probe (1987–1988). - Starseed/launcher, fleet of unmanned interstellar probes (1996) - Project Valkyrie, manned interstellar ship (2009) - Project Icarus, unmanned interstellar probe (2009–2014). - Sun-diver, unmanned interstellar probe A few organisations dedicated to interstellar propulsion research and advocacy for the case exist worldwide. These are still in their infancy, but are already backed up by a membership of a wide variety of scientists, students and professionals. - Icarus Interstellar - Tau Zero Foundation (USA) - Institute for Interstellar Studies (UK) - Fourth Millennium Foundation (Belgium) - Space Development Cooperative (Canada) The energy requirements make interstellar travel very difficult. It has been reported that at the 2008 Joint Propulsion Conference, multiple experts opined that it was improbable that humans would ever explore beyond the Solar System. Brice N. 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Callan, Jr. (1982). "Dyon-fermion dynamics". Phys. Rev. D 26 (8): 2058–2068. Bibcode:1982PhRvD..26.2058C. doi:10.1103/PhysRevD.26.2058. - B. V. Sreekantan (1984). "Searches for Proton Decay and Superheavy Magnetic Monopoles". Journal of Astrophysics and Astronomy 5: 251–271. Bibcode:1984JApA....5..251S. doi:10.1007/BF02714542. - Remote Sensing Tutorial Page A-10 - Williams, Lance (6 April 2012). "Electromagnetic Control of Spacetime and Gravity: The Hard Problem of Interstellar Travel". Astronomical Review 7 (2). Bibcode:2012AstRv...7b...5W. - "Ideas Based On What We’d Like To Achieve: Worm Hole transportation". NASA Glenn Research Center. - John G. Cramer, Robert L. Forward, Michael S. Morris, Matt Visser, Gregory Benford, and Geoffrey A. Landis, "Natural Wormholes as Gravitational Lenses," Phys. Rev. D51 (1995) 3117–3120 - M. Visser (1995) Lorentzian Wormholes: from Einstein to Hawking, AIP Press, Woodbury NY, ISBN 1-56396-394-9 - Enzmann Starship - Gilster, Paul (April 1, 2007). "A Note on the Enzmann Starship". Centauri Dreams. - "Icarus Interstellar - Project Hyperion". Retrieved 13 April 2013. - http://www.grc.nasa.gov/WWW/bpp "Breakthrough Propulsion Physics" project at NASA Glenn Research Center, Nov 19, 2008 - http://www.nasa.gov/centers/glenn/technology/warp/warp.html Warp Drive, When? Breakthrough Technologies January 26, 2009 - Malik, Tariq, "Sex and Society Aboard the First Starships." Science Tuesday, Space.com March 19, 2002. - Moskowitz, Clara (17 September 2012). "Warp Drive May Be More Feasible Than Thought, Scientists Say". space.com. - Forward, R. L. (May–June 1985). "Starwisp - An ultra-light interstellar probe". Journal of Spacecraft and Rockets 22 (3): 345–350. Bibcode:1985JSpRo..22..345F. doi:10.2514/3.25754. - Benford, James; Benford, Gregory. "Near-Term Beamed Sail Propulsion Missions: Cosmos-1 and Sun-Diver". Department of Physics, University of California, Irvine. - O’Neill, Ian (Aug 19, 2008). "Interstellar travel may remain in science fiction". Universe Today. - Hein, A. M.; et al. (2012). "World Ships - Architectures & Feasibility Revisited". Journal of the British Interplanetary Society 65: 119–133. - Hein, A.M. (September 2012). "Evaluation of Technological-Social and Political Projections for the Next 100-300 Years and the Implications for an Interstellar Mission". Journal of the British Interplanetary Society 33 (09/10): 330–340. - Long, Kelvin (2012). Deep Space Propulsion: A Roadmap to Interstellar Flight. Springer. ISBN 978-1461406068. - Mallove, Eugene (1989). The Starflight Handbook. John Wiley & Sons, Inc. ISBN 0-471-61912-4. - Woodward, James (2013). Making Starships and Stargates: The Science of Interstellar Transport and Absurdly Benign Wormholes. Springer. ISBN 978-1461456223. - Zubrin, Robert (1999). Entering Space: Creating a Spacefaring Civilization. Tarcher / Putnam. ISBN 1-58542-036-0. - Leonard David – Reaching for interstellar flight (2003) – MSNBC (MSNBC Webpage) - NASA Breakthrough Propulsion Physics Program (NASA Webpage) - Bibliography of Interstellar Flight (source list) - DARPA seeks help for interstellar starship
This is a Clilstore unit. You can . Hi there, welcome to Math Antics! So far, in our series on geometry, we've learned about points, lines, planes and angles. In this lesson, we're going to learn about another important element of geometry. We're going to learn about polygons. You probably already know a lot about polygons because you see them all the time. Here's some common examples that you might recognize. These shapes are all polygons. That's because a polygon just means a multi-sided shape, and these shapes all have multiple sides. Okay, so that's a basic definition of a polygon, but to really understand what is a polygon and what is NOT a polygon, we need to learn about the specific propertes that all polygons have in common. First we need to know the three parts that make up all polygons. And these parts are: sides, vertices, and angles. The sides are just the straight line segments that make up a polygon. And the vertices are points where the sides intersect. And the angles are formed by the intersecting lines. In fact, in Greek, the word polygon literally means "many-angles". So all polygons have sides, vertices and angles.This polygon here has 5 sides, 5 vertices and it forms 5 angles. The next thing we need to know about polygons is that they're "closed" shapes. Now what does it mean for a shape to be closed you ask? Well, it means that the sides are connected so that there are no gaps. The area inside the shape is separated from the area outside the shape, and there's no way to get from the inside to the outside without crossing a line. It might help to think of a closed shape like a cage. If you put an ant inside the cage, there's no way for it to get out without crossing a line. But if the shape is open, then there is a way out. So these are all examples of closed shapes, and these are all examples of open shapes. And the important thing to remember is that a polygon must be closed. And the last thing we need to know about polygons is that they're 2 dimensional, or flat shapes. And that means that all the vertices must lie on the same plane. If any one of the vertices were to move forwards or backwards, so that is wasn't in the same plane as all the other vertices, then it wouldn't be a flat shape anymore. Flat shapes are also called planar shapes because all of their points are on the same plane. And even though polygons themselves can't be 3D shapes, you can use polygons to make 3D shapes. Like a box, for example. The box is not a polygon. But each of its flat sides is a polygon. Alright then. We now have a specific definition of a polygon. A polygon is a multi-sided shape that has sides, vertices and angles. A polygon is a closed shape, and a polygon is a 2 dimensional, or flat shape. And now that you know that, it's time to play "Polygon or NOT a Polygon!". Now here's your host: me! Thank you, thank you! Alright. Now the rules of the game are simple. I'm gonna show you a shape, and you tell me if it's a shape, and you tell me if it's a polygon or not a polygon. Are you ready to play? Our first shape is a square! Is a square a polygon? Yes! A square has 4 sides and 4 vertices and it's a closed, 2D shape. So it is a polygon. And next we have, hmmm. I'm not exactly sure what to call this, but, is it a polygon? Nope! It's close but because it's an open shape, it can't be a polygon. Alright, what about this one? Polygon or not a polygon? Yep! It is a polygon. Even though the sides are not all the same length, it is a closed, 2D, multi-sided shape. In fact, if you count, you'll see it has 7 sides. Ah, what about this one? is a circle a polygon? Well, it is a closed, 2D shape, but how many sides does it have? Now that's the problem. A circle doesn't have any straight sides, vertices or angles. It's a curved shape, so it's not a polygon. Next we have a star shape, just like me! Is this a polygon? Yup! It has straight sides and vertices, and it's a closed, 2D shape. That means it's a polygon! And what about this one? Right you are, this is not a polygon! It's a dog! Ahh, here's an interesting one. It's a closed, 2D shape that does have straight sides and vertices, but, it also has this curved part here. Can still be a polygon with that curve there? No! The curved part disqualifies it as a polygon. A polygon has to have only straight sides, so this is not a polygon. And what about this guy here? Is this a polygon? Well, it is just a straight lines, but two of those lines cross, and if any line cross it can't be a polygon. Plus, he has this big open end here. So this guy is definitely not a polygon. And last of all, what about this one? Right you are, this is not a polygon because it's a 3D shape. It's made from polygons, but the whole shape is not a polygon itself. Well, that's all the time we have for this week. Join us next week as we decide: "Is it Bigger than One?" Okay, so after playing that game, you should have a really good idea of what a polygon is, and what it is not. The last thing I want to mention is that some polygons have special names depending on how many sides they have. Here's a list of the most important ones to know: - 3-sided polygons are called triangles. Triangles are so important in geometry, that they'll get a whole video of their own. - 4-sided polygons are called quadrilaterals. Wow! Now that's a fancy math word! But it helps if you just remember that the first part, "quad" means "4". Quadrilaterals are shapes like squares, rectangles and parallelograms. They'll also get a video of their own. - 5-sided polygons are called pentagons. - 6-sided polygons are called hexagons. - and 8-sided polygons are called octagons. By the way, polygons that have 5,6,8 or however many sides like this, are called regular polygons if all their angles are equal, and irregular polygons if their angles are not equal. Of course, there are a lot more polygons than that, but you probably won't need to know their names. As long as you know what polygons are, and how to identify them, then you're ready to move on. The exercises for this section are pretty easy, so no excuses! Good luck! Thanks for watching Math Antics, and I'll see you next time. Learn more at mathantics.com Short url: http://multidict.net/cs/2820
Resources to mark the 100th day of school with math activities. Challenge students to generate 100 different ways to represent the number 100. Students will easily generate 99 + 1 and 50 + 50, but encourage them to think out of the box. Challenge them to include examples from all of the NCTM Standards strands: number sense, numerical operations, geometry, measurement, algebra, patterns, data analysis, probability, discrete math, Create a class list to record the best entries. Some teachers write 100 in big bubble numeral style and then record the entries inside the numerals. Using math templates during instruction keeps each student actively involved and allows the teacher to informally assess each student's proficiency with the skills and concepts addressed in the day's lesson. Many teachers regularly use whiteboards to have students record answers, write terms, draw pictures, etc. The use of templates in sheet protectors extends this practice and eliminates the time spent drawing diagrams, etc., allowing students more time to demonstrate mathematical proficiency. Teachers who regularly use math templates include planned task items that assess student proficiency. Careful observation of student responses allows teachers to form flexible small groups for additional instruction or enrichment and also better plan for instruction. Students place markers on the numbers 2-12. Students toss two 6-sided dice, find the sum and remove a marker from that number, if there is still one. The first player to remove all markers wins the game. This game can be used as addition practice or as an introduction to the probability of the different outcomes of rolling two dice. This game was developed by a Monmouth University student for the Probability Fair. These games help students acquire proficiency in addition and subtraction facts. Introduce elementary students to the concept of functions by investigating growing patterns. Visual patterns formed with manipulatives are especially effective for elementary students and allow them to concretely build understanding as they first reproduce, then extend the pattern to the next couple of stages. Students today develop proficiency with many different algorithms for multiplication. This approach insures that each student will find a method that works effectively for him/her. Teachers model the different algorithms and encourage students to use and practice each method before selecting a favorite. September is a great time for data collection activities as students are naturally curious about their new classmates. Ask questions that require students to analyze data and support their conclusions. Every math teacher struggles to find ways to encourage students to master their basic facts. Whether for addition and subtraction facts or for multiplication and division facts, teachers collect many ideas from which they can draw activities to meet the varied needs of learners in their classes. Games and Who Has? activities are especially motivational and continual play can help students develop fact fluency in an effort to master the games and capture the most points. Using two different coins and recording the results of both coins helps students dispel this initial misconception as they analyze the graph results. Class discussion should focus on analyzing the data to determine if the game is fair or not. Directions and gameboard are included in the download. These activities support students as they conceptually develop a sense of how probability affects the outcome of games. Students will find that applying their knowledge of probability will help them win some of the games These activities help students use organized lists and systematic counting to solve combination problems. Map coloring and networks are also discrete math problems that students can relate to real-world applications. Students must think about the factors of each number as they play this game. Students quickly learn the value of selecting prime numbers as a strategy. The beauty of the game design is that students will review the factors of many numbers and mentally add the sum of these factors together in search of the "best move." Gingerbread men and gingerbread houses enjoy special popularity around the holidays, but many of these gingerbread activities are timeless and complement literature titles that teachers use at the beginning of school or after the holidays. It's very easy to incorporate mathematics into a study of gingerbread men, and students will enjoy the data collection activities and games while learning math skills and deepening their understanding of important mathematical concepts. Look through these math activities and add some to your repertoire. Consider broadening the gingerbread math to include measurement, games and problem solving this year. Students learn the patterns in the hundred board by assembling puzzles. Teachers are able to assess student use of patterns in rows and columns by observing the student at work. This task is easily differentiated to accommodate the varied levels in a first grade class by changing the number of pieces and the shape of the pieces. Puzzle bags should be sequentially lettered so that students progress through harder versions of the task. Finally, students are asked to create their own puzzles for classmates to solve. These strategies support active student participation in math lessons and allow teachers to assess the developing proficiency levels of all students in the class by walking around to monitor student responses. These strategies are especially effective during the Mental Math part of an Everyday Mathematics lesson. Dominoes have become a staple in most primary classrooms. They build upon dice patterns and are often used to model decomposition of numbers, building student knowledge of addition facts. They are an excellent manipulative for primary students to use and these are some examples of how students might use dominoes in the math center. Try these domino games with students to improve math skills and number recognition. Encourage students to play these games at home with their families, using real dominoes or paper copies. These activities were designed to introduce or reinforce important math concepts and skills using seasonal themes. The games capitalize on students' fascination with spiders at Halloween time.
Functions of General Angles Acute angles in standard position are all in the first quadrant, and all of their trigonometric functions exist and are positive in value. This is not necessarily true of angles in general. Some of the six trigonometric functions of quadrantal angles are undefined, and some of the six trigonometric functions have negative values, depending on the size of the angle. Angles in standard position have their terminal side in or between one of the four quadrants. Figure shows a point A (x, y) located on the terminal side of angle θ with r as the distance AO. Note that r is always positive. Based on the figures, Positive angles in various quadrants. If angle θ is a quadrantal angle, then either x or y will be 0, yielding the undefined values if the denominator is zero. The sign, positive or negative, of the trigonometric functions depends on which quadrant this point A (x, y) is located in. Table 1 summarizes this information. One way to remember which functions are positive and which are negative in the various quadrants is to remember a simple four-letter acronym, ASTC. This acronym can remind you that All are positive in quadrant I, the Sine is positive in quadrant II, the Tangent is positive in quadrant III, and the Cosine is positive in quadrant IV. This acronym could stand for Arizona State Teacher's College, AllStudents Take Classes, or some other four-word expression that will help you remember the relationships. Table 2 summarizes the values of the trigonometric functions of quadrantal angles. Note that undefined values result from division by 0. The six trigonometric functions of angles that are not acute can be converted back to functions of acute angles. These acute angles are called the reference angles. The value of the function depends on the quadrant of the angle. If angle θ is in the second, third, or fourth quadrant, then the six trigonometric functions of θ can be converted to equivalent functions of an acute angle. Geometrically, if the angle is in quadrant II, reflect about the y-axis. If the angle is in quadrant IV, reflect about thex-axis. If the angle is in quadrant III, rotate 180°. Keep in mind the sign of the functions during these conversions to the reference angle Example 1: Find the six trigonometric functions of an angle α that is in standard position and whose terminal side passes through the point (−5, 12). From the Pythagorean theorem, the hypotenuse can be found. Then, the six trigonometric functions follow from the definitions (Figure 2 ). Example 2: If sin θ = 1/3, what is the value of the other five trigonometric functions if cos θ is negative? Because sin θ is positive and cos θ is negative, θ must be in the second quadrant. From the Pythagorean theorem, and then it follows that Example 3: What is the exact sine, cosine, and tangent of 330°? Because 330° is in the fourth quadrant, sin 330° and tan 330° are negative and cos 330° is positive. The reference angle is 30°. Using the 30° − 60° − 90° triangle relationship, the ratios of the three sides are 1, 2,
\|Table of contents\| \|1 Crore+ students have signed up on EduRev. Have you?\| In this unit we are going to be looking at logarithms. However, before we can deal with logarithms. we need to revise indices. This is because logarithms and indices are closely related, and in order to understand logarithms a good knowledge of indices is required. We know that 16 = 24 Here, the number 4 is the power. Sometimes we call it an exponent. Sometimes we call it an index. In the expression 24, the number 2 is called the base. We know that 64 = 82. In this example 2 is the power, or exponent, or index. The number 8 is the base. Why do we study logarithms ? In order to motivate our study of logarithms, consider the following: we know that 16 = 24. We also know that 8 = 23 Suppose that we wanted to multiply 16 by 8. One way is to carry out the multiplication directly using long-multiplication and obtain 128. But this could be long and tedious if the numbers were larger than 8 and 16. Can we do this calculation another way using the powers ? Note that 16 × 8 can be written 24 × 23 This equals = 27 using the rules of indices which tell us to add the powers 4 and 3 to give the new power, 7. What was a multiplication sum has been reduced to an addition sum. Similarly if we wanted to divide 16 by 8: 16 ÷ 8 can be written 24 ÷ 23 This equals = 21 or simply 2 using the rules of indices which tell us to subtract the powers 4 and 3 to give the new power, 1. If we had a look-up table containing powers of 2, it would be straightforward to look up 27 and obtain 27 = 128 as the result of finding 16 × 8. Notice that by using the powers, we have changed a multiplication problem into one involving addition (the addition of the powers, 4 and 3). Historically, this observation led John Napier (1550-1617) and Henry Briggs (1561-1630) to develop logarithms as a way of replacing multiplication with addition, and also division with subtraction. Consider the expression 16 = 24. Remember that 2 is the base, and 4 is the power. An alternative, yet equivalent, way of writing this expression is log2 16 = 4. This is stated as ‘log to base 2 of 16 equals 4’. We see that the logarithm is the same as the power or index in the original expression. It is the base in the original expression which becomes the base of the logarithm. The two statements are equivalent statements. If we write either of them, we are automatically implying the other. So the two sets of statements, one involving powers and one involving logarithms are equivalent. In the general case we have: if x = an then equivalently loga x = n loga a = 1 Let us develop this a little more. Because 10 = 101 we can write the equivalent logarithmic form log10 10 = 1. Similarly, the logarithmic form of the statement 21 = 2 is log2 2 = 1. In general, for any base a, a = a1 and so loga a = 1 We can see from the Examples above that indices and logarithms are very closely related. In the same way that we have rules or laws of indices, we have laws of logarithms. These are developed in the following sections. x = an and y = am then the equivalent logarithmic forms are loga x = n and loga y = m .....(1) Using the first rule of indices xy = an× am = an+m Now the logarithmic form of the statement xy = an+m is loga xy = n + m. But n = loga x and m = loga y from (1) and so putting these results together we have loga xy = loga x + loga y So, if we want to multiply two numbers together and find the logarithm of the result, we can do this by adding together the logarithms of the two numbers. This is the first law. loga xy = loga x + loga y Suppose x = an, or equivalently loga x = n. Suppose we raise both sides of x = an to the power m: xm = (an)m Using the rules of indices we can write this as xm = anm Thinking of the quantity xm as a single term, the logarithmic form is loga xm = nm = mloga x This is the second law. It states that when finding the logarithm of a power of a number, this can be evaluated by multiplying the logarithm of the number by that power. loga xm = mloga x As before, suppose x = an and y = am with equivalent logarithmic forms loga x = n and loga y = m ....(2) Consider x ÷ y. using the rules of indices. In logarithmic form which from (2) can be written This is the third law. Recall that any number raised to the power zero is 1: a0 = 1. The logarithmic form of this is loga 1 = 0 loga 1 = 0 The logarithm of 1 in any base is 0. Example 1: Suppose we wish to find log2 512. This is the same as being asked ‘what is 512 expressed as a power of 2 ?’ Now 512 is in fact 29 and so log2 512 = 9. Example2: Suppose we wish to find log8 1/64 This is the same as being asked ‘what is 1/64 expressed as a power of 8 ?’ Now 1/64 can be written 64−1. Noting also that 82 = 64 it follows that using the rules of indices. So log8 = 1/64 = -2 Example3: Suppose we wish to find log5 25. This is the same as being asked ‘what is 25 expressed as a power of 5 ?’ Now 52 = 25 and so log5 25 = 2. Example4: Suppose we wish to find log25 5. This is the same as being asked ‘what is 5 expressed as a power of 25 ?’ We know that 5 is a square root of 25, that is 5 = √25. So 25 1/2 = 5 and so log25 5 = 1/2. Notice from the last two examples that by interchanging the base and the number This is true more generally: Example5: Consider log2 8. We are asking ‘what is 8 expressed as a power of 2 ?’ We know that 8 = 23 and so log2 8 = 3. What about log8 2 ? Now we are asking ‘what is 2 expressed as a power of 8 ?’ Now 23 = 8 and so 2 = ∛8 or 81/3. So log8 2 =1/3. We see again There are two bases which are used much more commonly than any others and deserve special mention. These are base 10 and base e Logarithms to base 10, log10, are often written simply as log without explicitly writing a base down. So if you see an expression like log x you can assume the base is 10. Your calculator will be pre-programmed to evaluate logarithms to base 10. Look for the button marked log. The second common base is e. The symbol e is called the exponential constant and has a value approximately equal to 2.718. This is a number like π in the sense that it has an infinite decimal expansion. Base e is used because this constant occurs frequently in the mathematical modelling of many physical, biological and economic applications. Logarithms to base e, loge, are often written simply as ln. If you see an expression like ln x you can assume the base is e. Such logarithms are also called Naperian or natural logarithms. Your calculator will be pre-programmed to evaluate logarithms to base e. Look for the button marked ln. where e is the exponential constant. log 10 = 1, ln e = 1 We can use logarithms to solve equations where the unknown is in the power. Suppose we wish to solve the equation 3x = 5. We can solve this by taking logarithms of both sides. Whilst logarithms to any base can be used, it is common practice to use base 10, as these are readily available on your calculator. So, log 3x = log 5 Now using the laws of logarithms, the left hand side can be re-written to give x log 3 = log 5 This is more straight forward. The unknown is no longer in the power. Straightaway If we wanted, this value can be found from a calculator.
In contemporary political thought, the term ‘civil rights’ is indissolubly linked to the struggle for equality of American blacks during the 1950s and 60s. The aim of that struggle was to secure the status of equal citizenship in a liberal democratic state. Civil rights are the basic legal rights a person must possess in order to have such a status. They are the rights that constitute free and equal citizenship and include personal, political, and economic rights. No contemporary thinker of significance holds that such rights can be legitimately denied to a person on the basis of race, color, sex, religion, national origin, or disability. Antidiscrimination principles are thus a common ground in contemporary political discussion. However, there is much disagreement in the scholarly literature over the basis and scope of these principles and the ways in which they ought to be implemented in law and policy. In addition, debate exists over the legitimacy of including sexual orientation among the other categories traditionally protected by civil rights law, and there is an emerging literature examining issues of how best to understand discrimination based on disability. - 1. Rights - 2. Free and Equal Citizenship - 3. Discrimination - 4. Sexual Orientation - 5. Disability - 6. Legal Cases and Statutes - Academic Tools - Other Internet Resources - Related Entries Until the middle of the 20th century, civil rights were usually distinguished from ‘political rights’. The former included the rights to own property, make and enforce contracts, receive due process of law, and worship one's religion. Civil rights also covered freedom of speech and the press (Amar 1998: 216–17). But they did not include the right to hold public office, vote, or to testify in court. The latter were political rights, reserved to adult males. Accordingly, the woman's emancipation movement of the 19th century, which aimed at full sex equality under the law, pressed for equal “civil and political equality” (Taylor 1851/1984: 397 emphasis added) The civil-political distinction was conceptually and morally unstable insofar as it was used to sort citizens into different categories. It was part of an ideology that classified women as citizens entitled to certain rights but not to the full panoply to which men were entitled. As that ideology broke down, the civil-political distinction began to unravel. The idea that a certain segment of the adult citizenry could legitimately possess one bundle of rights, while another segment would have to make do with an inferior bundle, became increasingly implausible. In the end, the civil-political distinction could not survive the cogency of the principle that all citizens of a liberal democracy were entitled, in Rawls's words, to “a fully adequate scheme of equal basic liberties” (2001: 42). It may be possible to retain the distinction strictly as one for sorting rights, rather than sorting citizens (Marshall, 1965; Waldron 1993). But it is difficult to give a convincing account of the principles by which this sorting is done. It seems neater and cleaner simply to think of civil rights as the general category of basic rights needed for free and equal citizenship. Yet, it remains a matter of contention which claims are properly conceived as belonging to the category of civil rights (Wellman, 1999). Analysts have distinguished among “three generations” of civil rights claims and have argued over which claims ought to be treated as true matters of civil rights. The claims for which the American civil rights movement initially fought belong to the first generation of civil rights claims. Those claims included the pre-20th century set of civil rights — such as the rights to receive due process and to make and enforce contracts — but covered political rights as well. However, many thinkers and activists argued that these first-generation claims were too narrow to define the scope of free and equal citizenship. They contended that such citizenship could be realized only by honoring an additional set of claims, including rights to food, shelter, medical care, and employment. This second generation of economic “welfare rights,” the argument went, helped to ensure that the political, economic, and legal rights belonging to the first generation could be made effective in protecting the vital interests of citizens and were not simply paper guarantees. Yet, some scholars have argued that these second-generation rights should not be subsumed under the category of civil rights. Thus, Cranston writes, “The traditional ‘political and civil rights’ can…be readily secured by legislation. Since the rights are for the most part rights against government interference…the legislation needed had to do no more than restrain the executive's own arm. This is no longer the case when we turn to the ‘right to work’, the ‘right to social security’ and so forth” (1967: 50–51). However, Cranston fails to recognize that such first-generation rights as due process and the right to vote also require substantial government action and the investment of considerable public resources. Holmes and Sunstein (1999) have made the case that all of the first-generation civil rights require government to do more than simply “restrain the executive's own arm.” It seems problematic to think that a significant distinction can be drawn between first and second-generation rights on the ground that the former, but not the latter, simply require that government refrain from interfering with the actions of persons. Moreover, even if some viable distinction could be drawn along those lines, it would not follow that second-generation rights should be excluded from the category of civil rights. The reason is that the relevant standard for inclusion as a civil right is whether a claim is part of the package of rights constitutive of free and equal citizenship. There is no reason to think that only those claims that can be “readily secured by legislation” belong to that package. And the increasingly dominant view is that welfare rights are essential to adequately satisfying the conditions of free and equal citizenship (Marshall 1965; Waldron 1993; Sunstein 2001). In the United States, however, the law does not treat issues of economic well-being per se as civil rights matters. Only insofar as economic inequality or deprivation is linked to race, gender or some other traditional category of antidiscrimination law is it considered to be a question of civil rights. In legal terms, poverty is not a “suspect classification.” On the other hand, welfare rights are protected as a matter of constitutional principle in other democracies. For example, section 75 of the Danish Constitution provides that “any person unable to support himself or his dependents shall, where no other person is responsible for his or their maintenance, be entitled to receive public assistance.” And the International Covenant on Economic, Social, and Cultural Rights (see Other Internet Resources) provides that the state parties to the agreement “recognize the right of everyone to an adequate standard of living for himself and his family, including adequate food, clothing and housing, and to the continuous improvement of living conditions.” A third generation of claims has received considerable attention in recent years, what may be broadly termed “rights of cultural membership.” These include language rights for members of cultural minorities and the rights of indigenous peoples to preserve their cultural institutions and practices and to exercise some measure of political autonomy. There is some overlap with the first-generation rights, such as that of religious liberty, but rights of cultural membership are broader and more controversial. Article 27 of the International Covenant on Civil and Political Rights (see Other Internet Resources) declares that third-generation rights ought to be protected: In those States in which ethnic, religious or linguistic minorities exist, persons belonging to such minorities shall not be denied the right, in community with the other members of their group, to enjoy their own culture, to profess and practice their own religion, or to use their own language. Similarly, the Canadian Charter of Rights and Freedoms protects the language rights of minorities and section 27 provides that “This Charter shall be interpreted in a manner consistent with the preservation and enhancement of the multicultural heritage of Canadians.” In the United States, there is no analogous protection of language rights or multiculturalism, although constitutional doctrine does recognize native Indian tribes as “domestic dependent nations” with some attributes of political self-rule, such as sovereign immunity (Oklahoma Tax Commission v. Citizen Band Potawatomi Indian Tribe). There is substantial philosophical controversy over the legitimacy and scope of rights of cultural membership. Kymlicka has argued that the liberal commitment to protect the equal rights of individuals requires society to protect such rights, suitably defined (1989; 1994; 1995). He distinguishes among three sorts of rights that have been claimed as part of this third generation by various groups whose culture differs from the dominant culture of a country: (1) rights of self-government, involving a claim to a degree of political autonomy to be exercised through the minority culture's own of institutions, (2) polyethnic rights, involving special claims by members of the minority culture to assist in their integration into the larger society, and (3) representational rights, involving a special claim of the minority culture to have its members serve in legislatures and other political bodies (1995: 27–33). Kymlicka argues that these three sorts of group rights can, in principle, be justified for those populations that he designates as “national minorities,” such as native Americans in the United States and the Québécois and Aboriginals in Canada. A national minority is “an intergenerational community, more or less institutionally complete, occupying a given territory or homeland, [and] sharing a distinct language and history”(18). Kymlicka contends that “granting special representational rights, land claims, or language rights to a [national] minority … can be seen as putting … [it] on a more equal footing [with the majority], by reducing the extent to which the smaller group is vulnerable to the larger” (36–37). Such special rights do not involve granting to the national minority the authority to take away the civil rights of its members. Rather, the rights are “external protections,” providing the group with powers and immunities with which it can protect its culture against the potentially harmful decisions of the broader society (35). In contrast to national minorities, immigrants who have left their original cultures are entitled only to a much more limited set of group rights, according to Kymlicka. These “polyethnic rights” are claims to have certain adjustments or accommodations made in the prevailing laws and regulations so as give individuals access to mainstream institutions and practices. Thus Kymlicka thinks that Orthodox Jews in the U.S. Armed Forces should have the legal right to wear a yarmulke while on duty and Canadian Sikhs have a legitimate claim to be exempt from motorcycle helmet laws (31). Waldron (1995) criticizes Kymlicka for exaggerating the importance for the individual of membership in her particular culture and for underestimating the mutability and interpenetration of cultures. Individual freedom requires some cultural context of choice, but it does not require the preservation of the particular context in which the individual finds herself. Liberal individuals must be free to evaluate their culture and to distance themselves from it. Kukathas criticizes Kymlicka for implying that the liberal commitment to the protection of individual rights is insufficient to treat the interests of minorities with equal consideration. Kukathas contends that “we need to reassert the importance of individual liberty or individual rights and question the idea that cultural minorities have collective rights” (1995: 230). But the system of uniform legal rules that he endorses would keep the state from intervening even when a minority culture inflicts significant harm on its more vulnerable members, e.g., when cultural norms strongly discourage females from seeking the same educational and career opportunities as males. Barry (2001) asserts that “there are certain rights against oppression, exploitation, and injury, to which every single human being is entitled to lay claim, and…appeals to cultural diversity and pluralism under no circumstances trump the value of basic liberal rights” (132–33). The legal system should protect those rights by impartially imposing the same rules on all persons, regardless of their cultural or religious membership. Barry allows for a few exceptions, such as the accommodation of a Sikh boy whose turban violated school dress regulations, but thinks that the conditions under which such exceptions will be justified “are rarely satisfied” (2001: 62). Barry's position reflects and elaborates Gitlin's earlier condemnation of views advocating distinctive rights for cultural and ethnic minorities. Gitlin condemned such views on the ground that they represent a “swerve from civil rights, emphasizing a universal condition and universalizable rights, to cultural separatism, emphasizing difference and distinct needs” (1995: 153). At the other end of the spectrum, Taylor (1994) argues for a form of communitarianism that attaches intrinsic importance to the survival of cultures. In his view, differential treatment under the law for certain practices is sometimes justifiable on the ground that such treatment is important for keeping a culture alive. Taylor goes as far as to claim that cultural survival can sometimes trump basic individual rights, such as freedom of speech. Accordingly, he defends legal restrictions on the use of English in Quebec, invoking the survival of Quebec's French culture. However, it is unclear why intrinsic value should attach to cultural survival as such. Following John Dewey (1939), Kymlicka (1995) rightly emphasizes that liberty would have little or no value to the individual apart from the life-options and meaningful choices provided by culture. But both thinkers also reasonably contend that human interests are ultimately the interests of individual human beings. In light of that contention, it would seem that a culture that could not gain the uncoerced and undeceived adherence of enough individuals to survive would have no moral claim to its continuation. Legal restrictions on basic liberties that are designed to perpetuate a given culture have the cart before the horse: persons should have their basic liberties protected first, as those protections serve the most important human interests. Only when those interests are protected can we then say that a culture should survive, not because the culture is intrinsically valuable, but rather because it has the uncoerced adherence of a sufficient number of persons. The treatment of blacks under slavery and Jim Crow presents a history of injustice and cultural annihilation that is similar in some respects to the treatment of Native Americans. However, civil rights principles played a very different role in the struggle of Native Americans against the injustices perpetrated against them by whites. Civil rights principles demand inclusion of the individuals from a disadvantaged group in the major institutions of society on an equal basis with the individuals who are already treated as full citizens. The principles do not require that the disadvantaged group be given a right to govern its own affairs. A right of political self-determination, in contrast, demands that a group have the freedom to order its affairs at it sees fit, and, to that extent, political self-determination has a separatist aspect, even if something less than complete sovereignty is involved. The pursuit of civil rights by American blacks overshadowed the pursuit of political self-determination. The fact that American blacks lacked any territory of their own on which they could rule themselves favored the civil rights strategy, although arguments were made that there was sufficient geographical concentration of blacks in certain parts of the South (the so-called “Black Belt”) for the African-Americans there to form their own self-governing nation. Thus, shortly after World War II, Harry Haywood advocated black political self-determination on the ground that the only way to solve “the issue of Negro equality” was through their “full development as a nation” (1948: 143). But there was stronger support among American blacks for a strategy that demanded their inclusion as free and equal citizens in the body politic of the United States. The civil war amendments, and the civil rights laws that accompanied them, promised such inclusion, and, in their struggle to defeat Jim Crow, blacks repeatedly called upon white Americans live up to the promise. Equal civil and political rights for blacks as individuals, and integration into the mainstream institutions of society, rather than separate nationhood, was the goal of most American blacks, as shown by the widespread support among blacks for their civil rights movement. For America's blacks during the 1950's and 60's, the alternative to the civil rights movement was not the intolerable perpetuation of Jim Crow, but rather a form of black nationalism, the main goal of which was obtaining increased resources from the broader society for black institutions and communities. Black self-government along the lines suggested by Haywood did not seem politically possible to most blacks during the civil rights era, but resources for strengthening black businesses and schools and improving black housing was a quite reasonable demand to make on whites. And so many black nationalists argued that, unless and until black communities and their institutions were strengthened, the promise of racial justice through integration and equal civil rights for individuals would prove hollow (Ture and Hamilton). Valls has recently developed a “liberal black nationalism” (2010: 479) by adapting Kymlicka's account of group rights and arguing that, because American blacks are kind of national minority victimized by historical injustice at the hands of the white population, “justice demands the support of black institutions and communities by the broader society” (474). After this support is forthcoming, Valls contends, individual blacks will be in position to make a free and fair choice as whether, and to what degree, to participate in black institutions and to live in black communities or to become integrated into racially-mixed areas of society. But Elizabeth Anderson has argued, against black nationalism, that segregation is a “fundamental cause of social inequality and undemocratic practices,” (2010: 2) and “[c]omprehensive racial integration is a necessary condition for a racially just future” (189). Anderson's argument entails that Vall's form of black nationalism is self-defeating: segregation itself works to prevent the white support for black communities and institutions for which such nationalism calls. However, her argument is consistent with Tommie Shelby's “pragmatic nationalism,” which holds that “black solidarity is merely a contingent strategy for creating greater freedom and social equality for blacks, a pragmatic but principled approach to achieving racial justice” (2005: 10). Shelby's form of black nationalism endorses the liberal principles of free and equal citizenship for all individuals, as does Valls's version, but, unlike the latter, Shelby's account does not reject the integrationist strategy advocated by Anderson. At the same time, it is difficult to see how black equality can be achieved without a much greater investment of social resources in black neighborhoods and institutions, and, perhaps, Anderson and Shelby can agree with Valls on the need for such investment In contrast to the civil rights movement of American blacks, Native Americans sought to mitigate the injustices perpetrated against them mainly by pursuing political self-determination, in the form of tribal self-rule. Even after the brutal tribal removals of the early 19th century and the efforts at the end of that century to destroy tribal control of lands through individual allotments, tribes still retained some territorial basis on which a measure of self-rule was possible. And during the black civil rights movement of the 1950's and 60's, there was tension between Native Americans and blacks due to their different attitudes toward self-determination and civil rights. Some Native Americans looked askance at the desire of blacks for inclusion and integration into white society, and they thought that the desire was hopelessly naïve (Deloria, 1988: 169–70). Such Native Americans were more in tune with radical black nationalists who favored Haywood's call for blacks to govern themselves politically in those jurisdictions where they were concentrated. In 1968, Congress enacted an Indian Civil Rights Act (ICRA). The act extended the reach of certain individual constitutional rights against government to intratribal affairs. Tribal governments would for the first time be bound by constitutional principles concerning free speech, due process, cruel and unusual punishment, and equal protection, among others. Freedom of religion was omitted from the law as a result of the protests of the Pueblo, whose political arrangements were theocratic, but the law was a major incursion on tribal self-determination, nonetheless (Norgren and Shattuck, 1993: 169). A married pueblo woman brought suit in federal court, claiming that the tribe's marriage ordinances constituted sex discrimination against her and other women of the tribe, thus violating the ICRA. (Santa Clara Pueblo v. Martinez) The ordinances excluded from tribal membership the children of a Pueblo woman who married outside of the tribe, while the children of men who married outsiders were counted as members. Martinez had initially sought relief in tribal forums, to no avail, before turning to the federal courts. The Supreme Court held that federal courts did not have jurisdiction to hear the case: the substantive provisions of the ICRA did apply to the Pueblo, but the inherent sovereign powers of the tribe meant that the tribal government had exclusive jurisdiction in the case. The ruling has been both questioned and defended by feminist legal scholars (MacKinnon, 1987; Valencia-Weber 2004). In contrast to the United States, the Canadian Indian Act provides that men and women are to be treated equally when it comes to the band membership of their children (Johnston, 1995: 190). This law and the Santa Clara case raise the general issue of whether and when it is justifiable for a liberal state to impose liberal principles on illiberal (or not fully liberal) political communities that had been involuntary incorporated into the larger state. Addressing this issue, Kymlicka (1995) argues that “there is relatively little scope for legitimate coercive interference” because efforts to impose liberal principles tend to be counterproductive, provoking the charge that they amount to “paternalistic colonialism.” Moreover, “liberal institutions can only really work if liberal beliefs have been internalized.” Kymlicka concludes, then, that liberals on the outside of an illiberal culture should support the efforts of those insiders who seek reform but should generally stop short of coercively imposing liberal principles (1995: 167). At the same time, Kymlicka acknowledges that there are cases in which a liberal state is clearly permitted to impose its laws, citing with approval the decision in a case that involved the application of Canadian law to a tribe that had kidnapped a member and forced him to undergo an initiation ceremony (44). Applying Kymlicka's general line of thinking might prove contentious in many cases. Consider Santa Clara. His arguments could be used to support the decision in that case: the exercise of jurisdiction might be deemed “paternalistic colonialism.” But one might argue, instead, that jurisdiction is needed to vindicate the basic liberal right of gender equality. However, it does seem that, if a wrong akin to kidnapping or worse is required before federal courts can legitimately step in, then the Santa Clara case falls short of meeting such a requirement. The argument might then shift to whether the requirement imposes an excessively high hurdle for the exercise of federal jurisdiction. Accordingly, Kymlicka's approach might not settle the disagreement over Santa Clara, but it does provide a very reasonable normative framework in terms of which liberal thought can address the difficult issues presented by the case and, more generally, by the problem of extending liberal principles to Native American tribes. The term ‘Jewish emancipation’ refers to those political processes, occurring from the last decades of the 18th century to the second half of the 19th century, through which the Jews of Western and Central Europe (roughly: Britain, France, Belgium, Holland, Germany, Italy, Switzerland, and Austria-Hungary) attained equal rights under the law. Its first major event was the declaration of equal citizenship for Jews by the French National Assembly (1791). However, Jewish emancipation was not a single process but a collection of them, proceeding in different ways and at different rates in the different parts of the continent. It also involved considerable backsliding at various points. From the 16th until end of the 18th century, Jews across Europe had been segregated by law into specified rural areas, towns, and city ghettos. They were prohibited from owning land or farming and from joining guilds, which monopolized craft production at the time. Severe restrictions were placed on their travel and special taxes imposed on them. More generally, Jews were regarded by the broader Christian society as an alien people, who had no right to be in Europe at all and could be legitimately expelled by any country that did not desire to tolerate their presence. And Jews were expelled at various times from many European jursidictions, including, England, Spain, Portugal, France, Holland and more than a few German and Italian states and cities. At the end of the 18th century, the German philosopher, Fichte, expressed a common view when he suggested that Jews were a “state within a state” and, addressing the Christians of Europe, asked rhetorically, “If you give [Jews] civic rights in your states, will not your other citizens be completely trod under foot?” (Fichte 1793/1995: 309) In the areas they inhabited, Jews were permitted to organize themselves into self-governing communities, called kehillot, which had governing councils with the authority to impose and collect taxes and to punish Jews who had violated community norms and religious rules. The councils also had the power of excommunication, which involved prohibiting all members of the community from any interaction with the excommunicated individual (Katz 1961: chaps. IX-XI). And, although their communal autonomy had already begun to weaken in the 17th and 18th centuries (Ettinger 1976: 750), Jewish communities in Europe at the outset of emancipation fit the main features of groups that Kymlicka characterizes as “national minorities” with the right of self-government (1995: 18; see section 1.2 above). During the period of emancipation, some Jews wanted to have strengthened “external protections” (see section 1.2 above) for their communal autonomy, but the main force of emancipation pushed in a different direction. Jewish emancipation was tied closely to the Enlightenment and the French Revolution, with their commitment to the equality and freedom of human individuals, and the dominant ethical concern of emancipation was not protection for communal autonomy but rather the attainment of equal rights. Still, Arendt argues that Jewish emancipation arose, not only from the political ideal of equality, but also from the European state's need for financial credit, which only Jews were prepared to meet at the time (1951/1976: 11–12). Accordingly, she claims that Jewish emancipation had an “ever-present equivocal meaning” (12): on the one hand, it could be construed as movement for equal rights, but, on the other, it could be seen as the bestowal of privileges on Jews by the ruling powers for services rendered. This double meaning is reflected in the different understandings that Bruno Bauer and Karl Marx had of Jewish emancipation. Bauer, a German theologian and one of the left-wing “Young Hegelians,” complained that “[t]he emancipation problem has until now been treated in a basically wrong manner by considering it one-sidedly as a Jewish problem … Not only Jews but, we [Christians], also want to be emancipated.” (1843/1958: 63) Bauer regarded emancipation as an effort by Jews to gain special privileges that would allow them to continue living apart from Christian society, following their own comprehensive religious law. In Bauer's eyes, the Jews' idea that they were God's chosen people made a mockery of the suggestion that they could ever regard themselves as equal citizens, to be treated just the same as Christians. On the other hand, from Bauer's perspective, although Christianity was “the perfection of Judaism” (83) insofar as it did not treat any particular nation as the chosen people and offered salvation to all nations, Christians, too, were exclusionary in their own way, by regarding themselves as meriting a privileged political and legal status in contrast with non-Christians. For Bauer, then, the only route to genuinely free and equal citizenship under the law was for Jews to give up Judaism and not become Christians, and for Christian to simply give up Christianity. In contrast, Marx, notwithstanding his hostility toward Jews and their alleged worship of money, criticized Bauer for thinking that free and equal citizenship depended upon citizens relinquishing their faiths. Marx, who was a fellow young Hegelian at the time, understood Jewish emancipation as part of a more general process in which “the state emancipates itself from religion” by no longer requiring its members to declare which faith they embrace and, instead, establishing a strict separation of church and state, such as was found in the United States (1843/1994: 5–8). Making religion legally and politically irrelevant, not making it disappear, was the aim and accomplishment of a democratic republic. The result, in Marx's eyes, was not that such a republic achieved the highest form of human freedom for its citizens,–for that achievement, religion would have to disappear, but a democratic republic could provide for its citizens the highest form of freedom possible within the context of a society dominated by money and the pursuit of profit. Jewish emancipation was a success in certain respects, but, ultimately, a catastrophic failure. During the second half of the 19th century, Jews achieved equal rights under the law throughout Western and Central Europe and became integrated into the mainstream institutions of society. Their economic situation had improved dramatically over the course of the century, and they filled professional occupations, such as law and university teaching, which had previously been closed to them (Richarz 1975; Ettinger 1976). However, antisemitism remained a strong and growing social force, and political parties with explicitly antisemitic platforms first began to form and gain support in the latter part of the century (Arendt 1950/1976: 35–50). In response to the continued antisemitism, Theodore Herzl proposed Zionism as the solution, a movement to form an independent Jewish state in Palestine to which European Jewry could and should emigrate. The movement attracted some Jews and was strongly opposed by others. (Medez-Flohr and Reinharz 1995: chap. 10) But the ultimate failure of Jewish emancipation would occur prior to establishment of a Jewish state and would arrive with the rise of the Nazi Party to power. In little more than a decade, Jews went from being equal citizens of the European countries they inhabited to being a stateless people deprived of all legal rights and targeted for physical and cultural annihilation. No other civil rights movement has ever suffered such a devastating reversal, and only the military defeat of Nazi Germany prevented the total destruction of European Jewry. Civil rights are those rights that constitute free and equal citizenship in a liberal democracy. Such citizenship has two main dimensions, both tied to the idea of autonomy. Accordingly, civil rights are essentially connected to securing the autonomy of the citizen. To be a free and equal citizen is, in part, to have those legal guarantees that are essential to fully adequate participation in public discussion and decisionmaking. A citizen has a right to an equal voice and an equal vote. In addition, she has the rights needed to protect her “moral independence,” that is, her ability to decide for herself what gives meaning and value to her life and to take responsibility for living in conformity with her values (Dworkin, 1995: 25). Accordingly, equal citizenship has two main dimensions: “public autonomy,” i.e., the individual's freedom to participate in the formation of public opinion and society's collective decisions; and “private autonomy,” i.e., the individual's freedom to decide what way of life is most worth pursuing (Habermas: 1996). The importance of these two dimensions of citizenship stem from what Rawls calls the “two moral powers” of personhood: the capacity for a sense of justice and the capacity for a conception of the good (1995: 164; 2001: 18). A person stands as an equal citizen when society and its political system give equal and due weight to the interest each citizen has in the development and exercise of those capacities. The idea of equal citizenship can be traced back to Aristotle's political philosophy and his claim that true citizens take turns ruling and being ruled (Politics: 1252a16). In modern society, the idea has been transformed, in part by the development of representative government and its system of elections (Manin: 1997). For modern liberal thought, by contrast, citizenship is no longer a matter of having a direct and equal share in governance, but rather consists in a legal status that confers a certain package of rights that guarantee to an individual a voice, a vote, and a zone of private autonomy. The other crucial differences between modern liberalism and earlier political theories concern the range of human beings who are regarded as having the capacity for citizenship and the scope of private autonomy to which each citizen is entitled as a matter of basic right. Modern liberal theory is more expansive on both counts than its ancient and medieval forerunners. It is true that racist and sexist assumptions plagued liberal theory well into the twentieth-century. However, two crucial liberal ideas have made possible an internal critique of racism, sexism, and other illegitimate forms of hierarchy. The first is that society is constructed by humans, a product of human will, and not some preordained natural or God-given order. The second is that social arrangements need to be justified before the court of reason to each individual who lives under them and who is capable of reasoning. The conjunction of these ideas made possible an egalitarianism that was not available to ancient and medieval political thought, although this liberal egalitarianism emerged slowly out of the racist and sexist presuppositions that infused much liberal thinking until recent decades. Many contemporary theorists have argued that taking liberal egalitarianism to its logical conclusion requires the liberal state to pursue a program of deliberately reconstructing informal social norms and cultural meanings. They contend that social stigma and denigration still operate powerfully to deny equal citizenship to groups such as blacks, women, and gays. Accordingly, Kernohan has argued that “the egalitarian liberal state should play an activist role in cultural reform” (1998: xi), and Koppelman has taken a similar position: “the antidiscrimination project seeks to reconstruct social reality to eliminate or marginalize the shared meanings, practices and institutions that unjustifiably single out certain groups of citizens for stigma and disadvantage” (1996: 8). This position is deeply at odds with at least some of the ideas that lie behind the advocacy of third-generation civil rights. Those rights ground claims of cultural survival, whether or not a culture's meanings, practices and institutions stigmatize and disadvantage the members of some ascriptively-defined group. The egalitarian proponents of cultural reconstruction can be understood as advocating a different kind of “third-generation” for the civil rights movement: one in which the state, having attacked legal, political and economic barriers to equal citizenship, now takes on cultural obstacles. A cultural-reconstruction phase of the civil rights movement would run contrary to Kukathas's argument that it is too dangerous to license the state to intervene against cultures that engage in social tyranny (2001). It also raises questions about whether state-supported cultural reconstruction would violate basic liberties, such as freedom of private association. The efforts of New Jersey to apply antidiscrimination law to the Boy Scouts, a group which discriminates against gays, illustrates the potential problems. The Supreme Court invalidated those efforts on grounds of free association (Boys Scouts v. Dale). Nonetheless, it may be necessary to reconceive the scope and limits of some basic liberties if the principle of free and equal citizenship is followed through to its logical conclusions. In liberal democracies, civil rights claims are typically conceptualized in terms of the idea of discrimination (Brest, 1976). Persons who make such claims assert that they are the victims of discrimination. In order to gain an understanding of current discussion and debate regarding civil rights, it is important to disentangle the various descriptive and normative senses of ‘discrimination’. In one of its central descriptive senses, ‘discrimination’ means the differential treatment of persons, however justifiable or unjustifiable the treatment may be. In a distinct but still primarily descriptive sense, it means the disadvantageous (or, less commonly, the advantageous) treatment of some persons relative to others. This sense is not purely descriptive in that an evaluative judgment is involved in determining what counts as a disadvantage. But the sense is descriptive insofar as no evaluative judgment is made regarding the justifiability of the disadvantageous treatment. In addition to its descriptive senses, there are two normative senses of ‘discrimination’. In the first, it means any differential treatment of the individual that is morally objectionable. In the second sense, ‘discrimination’ means the wrongful denial or abridgement of the civil rights of some persons in a context where others enjoy their full set of rights. The two normative senses are distinct because there can be morally objectionable forms of differential treatment that do not involve the wrongful denial or abridgement of civil rights. If I treat one waiter rudely and another nicely, because one is a New York Yankees fan and the other is a Boston Red Sox fan, then I have acted in a morally objectionable way but have not violated anyone's civil rights. Discrimination that does deny civil rights is a double wrong against its victims. The denial of civil rights is by itself a wrong, whether or not others have such rights. When others do have such rights, the denial of civil rights to persons who are entitled to them involves the additional wrong of unjustified differential treatment. On the other hand, if everyone is denied his civil rights, then the idea of discrimination would be misapplied to the situation. A despot who oppresses everyone equally is not guilty of discrimination in any of its senses. In contrast, discrimination is a kind of wrong that is found in systems that are liberal democratic but imperfectly so: it is the characteristic injustice of liberal democracy. The first civil rights law, enacted in 1866, embodied the idea of discrimination as wrongful denial of civil rights to some while others enjoyed their full set of rights. It declared that “all persons” in the United States were to have “the same right…to make and enforce contracts…and to the full and equal benefit of all laws…as is enjoyed by white citizens” 42 U.S.C.A. 1981. The premise was that whites enjoyed a fully adequate scheme of civil rights and that everyone else who was entitled to citizenship was to be legally guaranteed that same set of rights. It is a notable feature of civil rights law that its prohibitions do not protect only citizens. Any person within a given jurisdiction, citizen or not, can claim the protection of the law, at least within certain limits. Thus, noncitizens are protected by fair housing and equal employment statutes, among other antidiscrimination laws. Noncitizens can also claim the legal protections of due process if charged with a crime. Even illegal aliens have limited due process rights if they are within the legal jurisdiction of the country. On the other hand, noncitizens cannot claim under U.S. law that the denial of political rights amounts to wrongful discrimination. Noncitizens can vote in local and regional elections in certain countries (Benhabib, 2006: 46), but the denial of equal political rights would seem to be central to the very status of noncitizen. The application of much of civil rights law to noncitizens indicates that many of the rights in question are deeper than simply the rights that constitute citizenship. They are genuine human rights to which every person is entitled, whether she is in a location where she has a right to citizenship or not. And civil rights issues are, for that reason, regarded as broader in scope than issues regarding the treatment of citizens. Antidiscrimination laws typically pick out certain categories such as race and sex for legal protection, define certain spheres such as employment and public accommodations in which discrimination based on the protected categories is prohibited, and establish special government agencies, such as the Equal Employment Opportunity Commission, to assist in the laws' enforcement. There are many questions that can be raised concerning the justifiability of such laws. Some of the central philosophical questions derive from the fact that the laws restrict freedom of association, including the liberty of employers to decide whom they will hire. Some have argued that the liberal commitment to free association requires the rejection of antidiscrimination laws, including those that ban employment discrimination such as the Civil Rights Act of 1964 (Epstein, 1992). Most liberals thinkers reject this view, but any liberal defense of antidiscrimination laws must cite considerations sufficiently strong to override the infringements on freedom of association that the laws involve. There are two different approaches within liberal thought to the justification of antidiscrimination laws. Both approaches hold that, in certain important areas of life, such as employment opportunities and access to public accommodations, individuals have a moral right to be be legally protected against any disadvantage being imposed upon them on account of their race, sex, or membership in some other socially salient group. However, on one approach, the only genuine form of discrimination involves the action of an agent who aims at disadvantaging an individual on account of the individual's race, sex, etc. Such an action is often called “direct discrimination” (or, in American law, “disparate-treatment” discrimination). In contrast, the second approach holds that there is another form of discrimination from which individuals have a right to be protected against and which does not necessarily involve an agent who aims at disadvantaging them because of their race or sex or other social-group membership. Often called “indirect discrimination” (or, in American law, “disparate-impact” discrimination), this form is said to consist in actions, policies, or systems of rules that have the effect of disproportionately disadvantaging the members of a particular socially-salient group. Thinkers who take this second approach contend that antidiscrimination law should prohibit, not only direct discrimination, but the indirect form as well, while those who take the first approach deny that “indirect” discrimination really counts as discrimination at all. In its interpretation of the U.S. Constitution, the Supreme Court appears to have adopted the first approach (Balkin 2001), but many legal scholars endorse some version of the second in understanding the constitutional guarantee of equality (Karst 1989). (For a more complete examination of the distinction between direct and indirect discrimination and of the question of what makes discrimination a wrong against individuals, see the entry on discrimination.) Many debates over civil rights issues turn on assumptions about the scope and effects of existing discrimination (i.e., objectionable disadvantageous treatment) against particular groups. For example, some thinkers hold that systemic discrimination based on race and gender is largely a thing of the past in contemporary liberal democracies (at least in economically advanced ones) and that the current situation allows persons to participate in society as free and equal citizens, regardless of race or gender (Thernstom and Thernstrom, 1997; Sommers, 1994). Many others reject that view, arguing that white skin privilege and patriarchy persist and operate to substantially and unjustifiably diminish the life-prospects of nonwhites and women (Bobo, 1997; Smith 1993). These differences drive debates over affirmative action, race-conscious electoral districting, and pornography, among other issues. Questions about the scope and effects of discrimination are largely but not entirely empirical in character. Such questions concern the degree to which participation in society as a free and equal citizen is hampered by one's race or sex. And addressing that concern presupposes some normative criteria for determining what is needed to possess the status of such a citizen. Moreover, there are subtle aspects of discrimination that are not captured by thinking strictly in terms of categories such as race, sex, religion, sexual orientation, and so on. Piper analyzes “higher-order” forms of discrimination in which certain traits, such as speaking style, come to be arbitrarily disvalued on account of their association with a disvalued race or sex (2001). Determining the presence and effects of such forms of discrimination in society at large would be a very complicated conceptual and empirical task. Additional complications stem from the fact that different categories of discrimination might intersect in ways that produce distinctive forms of unjust disadvantage. Thus, some thinkers have asserted that the intersection of race and sex creates a form of discrimination against black women which has not been adequately recognized or addressed by judges or liberal legal theorists. (Crenshaw, 1998) And other thinkers have begun to argue that our understanding of discrimination must be expanded beyond the white-black paradigm to include the distinctive ways in which Asian-Americans and other minority groups are subjected to discriminatory attitudes and treatment (Wu, 2002). Among the most careful empirical studies of discrimination have been those conducted by Ayers (2001). He found evidence of “pervasive discrimination” in several types of markets, including retail car sales, bail-bonding, and kidney-transplantation. Yet, his assessment is that “we still do not know the current ambit of race and gender discrimination in America” (425). Some civil rights laws in the United States protect persons from discrimination based on sexual orientation, but many people contest the legitimacy of the laws. The state of Colorado went so far as to ratify an amendment to its constitution that would prohibit any jurisdiction within the state from enacting a civil rights law that would protect homosexuals. The amendment was eventually invalidated by the U.S. Supreme Court on the ground that it was the product of simple prejudice and served no legitimate state purpose, thus violating the Equal Protection Clause (Romer v. Evans). Much of the discussion of “gay rights” involves the question of whether sexual orientation is genetically determined, socially determined, or the product of individual choice. However, it is not clear why the question is relevant. The discussion appears to assume that genetic determination would vindicate the civil rights claims of gays, because sexual orientation would then be like race or sex insofar as it would be biologically fixed and immutable. But it is a mistake to think that racial or sex discrimination is morally objectionable because of the biological fixity or unchosen nature of race and sex. It is objectionable because it expresses ill-will or indifference, and it is unjust because it treats an individual in a morally arbitrary manner and, under current conditions, reinforces social patterns of disadvantage that seriously diminish the life prospects of many persons. The view that sexual orientation is like race or sex in a morally relevant way should focus on the analogous features of discrimination based on sexual orientation. Wintermute (1995) and Koppelman (1994 and 1997) assert that discrimination based on sexual orientation is not just analogous to sex discrimination but that it is a form of sex discrimination. If it is legally permissible for Jane to have sex with John, then banning Joe's having sex with John would seem to amount to discrimination (disadvantageous treatment) against Joe on grounds of his sex. If Joe were a woman, his having sex with John would be permitted, so he is being treated differently because of his sex. However, Koppelman contends that this formal argument should be supplemented by more substantive ones referring to the systemic patterns of social disadvantage from which gays and lesbians suffer. In fact, one can argue that the treatment of gays and lesbians is an injustice to them as individuals and amounts to a systemic pattern of unjust disadvantage. The individual injustice arises from the arbitrary nature of denying persons valuable life-opportunities, such as employment and marriage, on the basis of their sexual orientation. The systemic injustice arises from the repeated and widespread acts of individual injustice. The most controversial civil rights issues regarding sexual orientation concern the principle of equal treatment for same-sex and heterosexual couples. Most scholars endorse such a principle (Wardle 1996) and argue that equal treatment requires that same-sex marriages be legalized (Eskridge 1996). Moreover, it is often argued in the literature that a person's choice of sex partner is central to her life and protected under a right of privacy. In Bowers v. Hardwick, the United States Supreme Court rejected this argument, upholding the criminalization of homosexual sodomy. The decision was condemned by legal and political thinkers and was overturned by the Court in Lawrence v. Texas. The Court invoked the right of privacy in declaring the state's criminal ban on sodomy between same-sex partners. Nonetheless, some scholars who argue for the equal legal treatment of same-sex relations contend that privacy-based arguments are inadequate. They point out that one can hold the view that adults have a right to engage in same-sex intimacies even as one contends that such intimacies are morally abominable and ought not to receive any encouragement from government (Sandel 1996: 107; Koppelman 1997: 1646). Such a view would reject equal legal treatment for those in intimate same-sex relationships. Finnis takes such a view, arguing that same-sex relations are “manifestly unworthy of the human being and immoral” and should not be encouraged by the state, but finding that criminalizing same-sex relations violates rights of individual privacy (1996: 14). Lee and George also find such relations to be morally defective and unworthy of equal treatment by the state (1997), though George (1993) does not think that any sound a priori principle prohibits criminalization. Finnis, Lee and George argue for their condemnation of same-sex relations on the ground of natural law theory. However, unlike traditional versions of natural law theory, their version does not rest on any explicit theological or metaphysical claims. Rather, it invokes independent principles of practical reasoning that articulate the basic reasons for action. Such reasons are the fundamental goods that action is capable of realizing and, for Finnis, Lee and George, include “marriage, the conjuntio of man and woman” (Finnis 1996: 4). Homosexual conduct, masturbation, and all extra-marital sex aim strictly at “individual gratification” and can be no part of any “common good.” Such actions “harm the character” of those voluntarily choosing them (Lee and George, 1997: 135). In taking the actions, a person becomes a slave to his passions, allowing his reason to be overridden by his raw desire for sensuous pleasure. On Finnis's account, when consensual sexual conduct is private, government may not outlaw it, but government “can rightly judge that it has a compelling interest in denying that ‘gay lifestyles’ are a valid and humanly acceptable choice and form of life” (1996: 17). And for Finnis, Lee and George, equal treatment of same-sex and heterosexual relations is out of the question due to the morally defective character of same-sex relations. Macedo responds to Finnis by arguing that “all of the goods that can be shared by sterile heterosexual couples can also be shared by committed homosexual couples” (1996: 39). Macedo points out that Finnis does not condemn sexual intercourse by sterile heterosexual couples. But Finnis replies that there is a relevant difference between homosexual couples and sterile heterosexual ones: the latter but not the former are united “biologically” when they have intercourse. Lee and George make essentially the same point: only heterosexual couples can “truly become one body, one organism” (1997: 150). But Macedo points out that, biologically, it is not the man and woman who unite but the sperm and the egg (1996: 37). It can be added that the “biological unity” argument seems to run contrary to Finnis's claim that his position “does not seek to infer normative conclusions from non-normative (natural-fact) premises” (1997: 16). More importantly, Macedo and Koppelman make the key point that the human good possible through intimate relations is a function of “mutual commitment and stable engagement” (Macedo, 1996: 40) and that same-sex couples can achieve “the precise kind of human good” that is available to heterosexual ones (Koppelman, 1997: 1649; also see Corvino,2005). Accordingly, equal treatment under the law for same-sex couples, including the recognition of same-sex marriage, would remove unjustifiable obstacles faced by same-sex couples to the achievement of that human good. The issue of same-sex marriage remains hotly contested in the courts and political arena. In response to political efforts in some states to legalize same-sex marriage, the U.S. Congress enacted the Defense of Marriage Act (DOMA), a statute restricting the term ‘marriage’ as it appears in national legislation and administrative policy to the union of a man and a woman. And the voters of California approved Proposition 8, an initiative amending the state's constitution to declare that “[o]nly marriage between a man and a woman is valid or recognized in California.” But, as of the time of this writing, a federal Circuit Court of Appeals has struck down the Proposition, writing, “Proposition 8 serves no purpose, and has no effect, other than to lessen the status and human dignity of gays and lesbians in California, and to officially reclassify their relationships and families as inferior to those of opposite-sex couples. The Constitution simply does not allow for ‘laws of this sort.’” (Perry v Brown, quoting Romer v. Evans). Additionally, two federal district courts have invalidated DOMA on constitutional grounds, and five states and the District of Columbia currently issue marriage licenses to same-sex couples. Internationally, same-sex couples also have the right to marry in Canada, Spain, Portugal, Iceland, Sweden, Norway, South Africa, Mexico and Argentina. During the 1970's and 80's, persons with disabilities increasingly argued that they were second-class citizens. They organized into a civil rights movement that pressed for legislation that would help secure for them the status of equal citizens. Protection against discrimination based on disability was written into the Canadian Charter of Rights and Freedoms and The Charter of Fundamental Rights of the European Union. The disability rights movement in the U.S. culminated with the passage of the Americans With Disabilities Act of 1990 (ADA). The ADA has served as a model for legislation in countries such as Australia, India and Israel The traditional model for understanding disability is called the “medical model.” It is reflected in many pre-ADA laws and in some philosophical discussions of disability which treat it as an issue of the just distribution of health care (Daniels, 1987). According to the medical model, a disabled person is one who falls below some baseline level that defines normal human functioning. That level is a natural one, on this view, in that it is determined by biological facts about the human species. Thus, the medical model supposes that the question of who counts as disabled can be answered in a way that is value-free and that abstracts from existing social practices and the physical environment those practices have constructed. It also gives the medical profession a privileged position in determining who is disabled, as the study and treatment of normal and subnormal human functioning is the specialty of that profession. The consensus among current disability theorists is that the medical model should be rejected. Any determination that a certain level of function is normal for the species will presuppose judgments that do not simply describe biological reality but impose on them some system of evaluation. Moreover, the level of functioning a person can achieve does not depend solely on her own individual abilities: it depends as well on the social practices and the physical environment those practices have shaped. Disability theorists thus posit an important analogy between the categories of ‘race’ and ‘disability’. As they understand it, neither category refers to any real distinctions in nature. Just as there is variation in skin color, there is variation in acuity of vision, physical strength, ability to walk and run and so on (Amundson, 2000). And just as there is no natural line dividing one “race” from another, there is no natural line dividing those who are functionally “abnormal” from those who are not so. The rejection of the medical model has led to a “social model,” according to which certain physical or biological properties are turned into dysfunctions by social practices and the socially-constructed physical environment (Francis and Silvers, 2000). For example, lack of mobility for those who are unable to walk is not simply a function of their physical characteristics: it is also a function of building practices that employ stairs instead of ramps and by automotive design practices that require the use of one's legs to drive a car. There is nothing necessary about such practices. Accordingly, the social model conceives of disability as socially-imposed dysfunction. The social model brings attention to how engineering and design practices can work to the disadvantage of persons with certain physical characteristics. And the idea of dysfunction is certainly a value-laden one. But it seems no more accurate to think that dysfunction is entirely imposed by society than it is to think that it is entirely the product of an individual's physical or mental characteristics. Individual characteristics in the context of the socially-constructed environment determine the level of functioning that a person can achieve (Amundson, 1992). And some individual characteristics would impair a person's functioning under all or almost all practicable alternatives to current social practices. Moreover, despite the fact that “normal human functioning” is a value-laden concept, it does not follow that it is entirely subjective or that reasonable efforts to specify the elements of some morally acceptable level of human functioning are misguided (Nussbaum and Sen, 1993). Indeed, some defensible understanding of what counts as better or worse human functioning would seem to be necessary to determine when some social practice has turned a physical (or mental) characteristic into a significant disadvantage for a person. In addition, the social model's conception of what it is to be a disabled person seems overbroad. The social practice of requiring students to pass courses in order to receive a degree creates a barrier that some persons cannot surmount. It does not seem that such people are, ipso facto, disabled. Such examples of “exclusionary” social practices could be multiplied indefinitely. Some thinkers may not be troubled by the implication that everyone is disabled in every respect in which she is excluded or otherwise disadvantaged by some social practice. But it is difficult to see how the idea of disability would then be of much use. The disability rights movement began with the idea that discrimination on the basis of disability was not different in any morally important way from discrimination based on race. The aim of the movement was to enshrine in law the same kind of antidiscrimination principle that protected persons based on their race. But some theorists have questioned how well the analogy holds. They point out that applying the antidiscrimination norm to disability requires taking account of physical or mental differences among people. This seems to be treatment based on a person's physical (or mental) features, apparently the exact opposite of the ideal of “colorblindness” behind the traditional antidiscrimination principle. Even race-based affirmative action does not really seem to be parallel to antidiscrimination policies that take account of disability. Advocates of affirmative action assert that the social ideal is for persons not to be treated on the basis of their race or color at all. Race-conscious policies are seen as instruments that will move society toward that ideal (Wasserstrom, 2001). In contrast, policies designed to counter discrimination based on disability are not sensibly understood as temporary measures or steps toward a goal in which people are not treated based on their disabilities. The policies permanently enshrine the idea that in designing buildings or buses or constructing some other aspect of our physical-social environment, we must be responsive to the disabilities people have in order for the disabled to have “fair equality of opportunity” (Rawls, 2001: 43–44). The need for a permanent “accommodation” of persons with disabilities seems to mark an important difference in how the antidiscrimination norm should be understood in the context of disability, as opposed to the context of race. However, it is important to recognize that, at the level of fundamental principle, the reasons why disability-based discrimination is morally objectionable and even unjust are essentially the same as the reasons why racial discrimination is so. At the individual level, disadvantageous treatment of the disabled is often rooted in ill-will, disregard, and moral arbitrariness. At the systemic level, such treatment creates a social pattern of disadvantage that reduces the disabled to second-class status. In those two respects, the grounds of civil rights law are no different when it comes to the disabled. Another way in which disability is thought to be fundamentally different from race concerns the special needs that the disabled often have that make life more costly for them. These extra costs would exist even if the socially-constructed physical environment were built to provide the disabled with fair equality of opportunity and their basic civil and political liberties were secured. In order to function effectively, disabled persons may need to buy medications or therapies or other forms of assistance that the able-bodied do not need for their functioning. And there does not seem to be any parallel in matters of race to the special needs of some of those who are disabled. The driving idea of the civil rights movement was that blacks did not have any special needs: all they needed was to have the burdens of racism lifted from them and, once that was accomplished, they would flourish or fail like everyone else in society. However, Silvers (1998) argues that the parallel between race and disability still holds: all the disabled may claim from society as a matter of justice is that they have fair equality of opportunity and the same basic civil rights as everyone else. Any special needs that the disabled may have do not provide the grounds of any legitimate claims of justice. On the other hand, Kittay (2000) argues that the special needs of the disabled are a matter of basic justice. She focuses on the severely mentally disabled, for whom fair opportunity in the labor markets and political rights in the public sphere will have no significance, and on the families which have the responsibility of caring for the severely disabled. Pogge (2000) also questions Silvers' view, suggesting that it is implausible to deny that justice requires that society provide resources for meeting the needs of the severely disabled. Still, it may be the case that some version of Silvers' approach may be justifiable when it comes to disabled persons who have the capacity “to participate fully in the political and civic institutions of the society and, more broadly, in its public life” (Pogge, 2000: 45). In the case of such persons, the basic civil right to equal citizenship would require that they have the equal opportunity to participate in such institutions, regardless of their disability. Although there may be some aspects of the racial model that cannot be applied to persons with severe forms of mental disability, the principles behind the American civil rights struggles of the 1950's and 60's remain crucial normative resources for understanding and combating forms of unjust discrimination that have only more recently been addressed by philosophers and by society more broadly. The emergence of the issue of disability rights has posed an important challenge for versions of liberalism inspired by the social contract tradition. One of the putative advantages of such forms of liberalism is that they better reflect strong and widely held intuitions about justice and individual rights than does utilitarianism. As Rawls famously wrote, “Each person possesses an inviolability founded on justice that even the welfare of society as a whole cannot override” (1999: 3). However, several thinkers have argued that Rawls's own theory does not make adequate room for the rights of the disabled. Social contract theory is commonly divided between two competing versions: contractarianism and contractualism. The former represents principles of justice as principles that would be agreed to by rational and self-interested individuals for the regulation of a society in which they are to cooperate with one another (Gauthier 1986). The principles chosen will, like a typical contract, result from bargaining among the parties in which each party offers to bring something of value to the others (i.e., his potential cooperative efforts and the fruits thereof) on the condition that the others bring something of sufficient value to him. Thus, contractarian justice is justice understood in terms of mutual advantage. In contrast, contractualism represents principles of justice as principles that would be agreed to individuals who are not only advantage-seeking but also “reasonable,” in the sense that they are seeking terms of cooperation that can be justified to all of the parties as “free and equal citizens” (Rawls 1993: 48–54). Contractualist justice is justice understood in terms of mutual respect and reciprocity. Contractarianism runs into the problem that (some of) the disabled might simply be excluded from the bargaining altogether, because they do not bring anything of sufficient value to the table to make it worthwhile for the parties to bargain with them. Thus, Nussbaum (2006) construes Rawls's theory as (in part) contractarian and criticizes it as exclusionary when it comes to the disabled. But Becker defends the contractarian view of justice in terms of mutual advantage, arguing that it can incorporate a conception of reciprocity sufficiently rich to underwrite principles that truly do justice to the disabled. Stark (2007) and Brighouse (2001) argue that Rawls's theory can be extended or modified to take account of disabled, without repudiating its contractarian core. 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Enhanced bibliography for this entry at PhilPapers, with links to its database. - Civil Rights Division, U.S. Department of Justice. - The Civil Rights Project, UCLA. - U.S. Commission on Civil Rights - Cornell University Legal Information Institute: Civil Rights - U.S. Equal Employment Opportunity Commission - European Convention on Human Rights - Human Rights Quarterly - International Covenant on Civil and Political Rights - International Covenant on Economic, Social and Cultural Rights - International Human Rights Instruments - National Constitutions The editors would like to thank Jesse Gero for spotting several typographical errors and formatting errors of other kinds, and for taking the time to bring these to our attention.
Radio waves are a type of electromagnetic radiation with wavelengths in the electromagnetic spectrum longer than infrared light. Radio waves have frequencies as high as 300 gigahertz (GHz) to as low as 30 hertz (Hz). At 300 GHz, the corresponding wavelength is 1 mm, and at 30 Hz is 10,000 km. Like all other electromagnetic waves, radio waves travel at the speed of light. They are generated by electric charges undergoing acceleration, such as time varying electric currents. Naturally occurring radio waves are emitted by lightning and astronomical objects. Radio waves are generated artificially by transmitters and received by radio receivers, using antennas. Radio waves are very widely used in modern technology for fixed and mobile radio communication, broadcasting, radar and other navigation systems, communications satellites, wireless computer networks and many other applications. Different frequencies of radio waves have different propagation characteristics in the Earth's atmosphere; long waves can diffract around obstacles like mountains and follow the contour of the earth (ground waves), shorter waves can reflect off the ionosphere and return to earth beyond the horizon (skywaves), while much shorter wavelengths bend or diffract very little and travel on a line of sight, so their propagation distances are limited to the visual horizon. To prevent interference between different users, the artificial generation and use of radio waves is strictly regulated by law, coordinated by an international body called the International Telecommunications Union (ITU), which defines radio waves as "electromagnetic waves of frequencies arbitrarily lower than 3 000 GHz, propagated in space without artificial guide". The radio spectrum is divided into a number of radio bands on the basis of frequency, allocated to different uses. Discovery and exploitationEdit Radio waves were first predicted by mathematical work done in 1867 by Scottish mathematical physicist James Clerk Maxwell. Maxwell noticed wavelike properties of light and similarities in electrical and magnetic observations. His mathematical theory, now called Maxwell's equations, described light waves and radio waves as waves of electromagnetism that travel in space, radiated by a charged particle as it undergoes acceleration. In 1887, Heinrich Hertz demonstrated the reality of Maxwell's electromagnetic waves by experimentally generating radio waves in his laboratory, showing that they exhibited the same wave properties as light: standing waves, refraction, diffraction, and polarization. Radio waves, originally called "Hertzian waves", were first used for communication in the mid 1890s by Guglielmo Marconi, who developed the first practical radio transmitters and receivers. The modern term "radio wave" replaced the original name "Hertzian wave" around 1912. Speed, wavelength, and frequencyEdit Radio waves in vacuum travel at the speed of light. When passing through a material medium, they are slowed according to that object's permeability and permittivity. Air is thin enough that in the Earth's atmosphere radio waves travel very close to the speed of light. The wavelength is the distance from one peak of the wave's electric field (wave's peak/crest) to the next, and is inversely proportional to the frequency of the wave. The distance a radio wave travels in one second, in a vacuum, is 299,792,458 meters (983,571,056 ft) which is the wavelength of a 1 hertz radio signal. A 1 megahertz radio signal has a wavelength of 299.8 meters (984 ft). The study of radio propagation, how radio waves move in free space and over the surface of the Earth, is vitally important in the design of practical radio systems. Radio waves passing through different environments experience reflection, refraction, polarization, diffraction, and absorption. Different frequencies experience different combinations of these phenomena in the Earth's atmosphere, making certain radio bands more useful for specific purposes than others. Practical radio systems mainly use three different techniques of radio propagation to communicate: - Line of sight: This refers to radio waves that travel in a straight line from the transmitting antenna to the receiving antenna. It does not necessarily require a cleared sight path; at lower frequencies radio waves can pass through buildings, foliage and other obstructions. This is the only method of propagation possible at frequencies above 30 MHz. On the surface of the Earth, line of sight propagation is limited by the visual horizon to about 64 km (40 mi). This is the method used by cell phones, FM and television broadcasting and radar. By using dish antennas to transmit beams of microwaves, point-to-point microwave relay links transmit telephone and television signals over long distances up to the visual horizon. Ground stations can communicate with satellites and spacecraft billions of miles from Earth. - Indirect propagation: Radio waves can reach points beyond the line-of-sight by diffraction and reflection. Diffraction allows a radio wave to bend around obstructions such as a building edge, a vehicle, or a turn in a hall. Radio waves also reflect from surfaces such as walls, floors, ceilings, vehicles and the ground. These propagation methods occur in short range radio communication systems such as cell phones, cordless phones, walkie-talkies, and wireless networks. A drawback of this mode is multipath propagation, in which radio waves travel from the transmitting to the receiving antenna via multiple paths. The waves interfere, often causing fading and other reception problems. - Ground waves: At lower frequencies below 2 MHz, in the medium wave and longwave bands, due to diffraction vertically polarized radio waves can bend over hills and mountains, and propagate beyond the horizon, traveling as surface waves which follow the contour of the Earth. This allows mediumwave and longwave broadcasting stations to have coverage areas beyond the horizon, out to hundreds of miles. As the frequency drops, the losses decrease and the achievable range increases. Military very low frequency (VLF) and extremely low frequency (ELF) communication systems can communicate over most of the Earth, and with submarines hundreds of feet underwater. - Skywaves: At medium wave and shortwave wavelengths, radio waves reflect off conductive layers of charged particles (ions) in a part of the atmosphere called the ionosphere. So radio waves directed at an angle into the sky can return to Earth beyond the horizon; this is called "skip" or "skywave" propagation. By using multiple skips communication at intercontinental distances can be achieved. Skywave propagation is variable and dependent on atmospheric conditions; it is most reliable at night and in the winter. Widely used during the first half of the 20th century, due to its unreliability skywave communication has mostly been abandoned. Remaining uses are by military over-the-horizon (OTH) radar systems, by some automated systems, by radio amateurs, and by shortwave broadcasting stations to broadcast to other countries. In radio communication systems, information is carried across space using radio waves. At the sending end, the information to be sent, in the form of a time-varying electrical signal, is applied to a radio transmitter. The information signal can be an audio signal representing sound from a microphone, a video signal representing moving images from a video camera, or a digital signal representing data from a computer. In the transmitter, an electronic oscillator generates an alternating current oscillating at a radio frequency, called the carrier because it serves to "carry" the information through the air. The information signal is used to modulate the carrier, altering some aspect of it, "piggybacking" the information on the carrier. The modulated carrier is amplified and applied to an antenna. The oscillating current pushes the electrons in the antenna back and forth, creating oscillating electric and magnetic fields, which radiate the energy away from the antenna as radio waves. The radio waves carry the information to the receiver location. At the receiver, the oscillating electric and magnetic fields of the incoming radio wave push the electrons in the receiving antenna back and forth, creating a tiny oscillating voltage which is a weaker replica of the current in the transmitting antenna. This voltage is applied to the radio receiver, which extracts the information signal. The receiver first uses a bandpass filter to separate the desired radio station's radio signal from all the other radio signals picked up by the antenna, then amplifies the signal so it is stronger, then finally extracts the information-bearing modulation signal in a demodulator. The recovered signal is sent to a loudspeaker or earphone to produce sound, or a television display screen to produce a visible image, or other devices. A digital data signal is applied to a computer or microprocessor, which interacts with a human user. The radio waves from many transmitters pass through the air simultaneously without interfering with each other. They can be separated in the receiver because each transmitter's radio waves oscillate at a different rate, in other words each transmitter has a different frequency, measured in kilohertz (kHz), megahertz (MHz) or gigahertz (GHz). The bandpass filter in the receiver consists of a tuned circuit which acts like a resonator, similarly to a tuning fork. It has a natural resonant frequency at which it oscillates. The resonant frequency is set equal to the frequency of the desired radio station. The oscillating radio signal from the desired station causes the tuned circuit to oscillate in sympathy, and it passes the signal on to the rest of the receiver. Radio signals at other frequencies are blocked by the tuned circuit and not passed on. Biological and environmental effectsEdit Radio waves are nonionizing radiation, which means they do not have enough energy to separate electrons from atoms or molecules, ionizing them, or break chemical bonds, causing chemical reactions or DNA damage. The main effect of absorption of radio waves by materials is to heat them, similarly to the infrared waves radiated by sources of heat such as a space heater or wood fire. The oscillating electric field of the wave causes polar molecules to vibrate back and forth, increasing the temperature; this is how a microwave oven cooks food. However, unlike infrared waves, which are mainly absorbed at the surface of objects and cause surface heating, radio waves are able to penetrate the surface and deposit their energy inside materials and biological tissues. The depth to which radio waves penetrate decreases with their frequency, and also depends on the material's resistivity and permittivity; it is given by a parameter called the skin depth of the material, which is the depth within which 63% of the energy is deposited. For example, the 2.45 GHz radio waves (microwaves) in a microwave oven penetrate most foods approximately 2.5 to 3.8 cm (1 to 1.5 inches). Radio waves have been applied to the body for 100 years in the medical therapy of diathermy for deep heating of body tissue, to promote increased blood flow and healing. More recently they have been used to create higher temperatures in hyperthermia treatment, to kill cancer cells. Looking into a source of radio waves at close range, such as the waveguide of a working radio transmitter, can cause damage to the lens of the eye by heating. A strong enough beam of radio waves can penetrate the eye and heat the lens enough to cause cataracts. Since the heating effect is in principle no different from other sources of heat, most research into possible health hazards of exposure to radio waves has focused on "nonthermal" effects; whether radio waves have any effect on tissues besides that caused by heating. Electromagnetic radiation has been classified by the International Agency for Research on Cancer (IARC) as "Possibly carcinogenic to humans". The conceivable evidence of cancer risk via Personal exposure to RF-EMF with mobile telephone use was identified. Radio waves can be shielded against by a conductive metal sheet or screen, an enclosure of sheet or screen is called a Faraday cage. A metal screen shields against radio waves as well as a solid sheet as long as the holes in the screen are smaller than about 1/20 of wavelength of the waves. Since radio frequency radiation has both an electric and a magnetic component, it is often convenient to express intensity of radiation field in terms of units specific to each component. The unit volts per meter (V/m) is used for the electric component, and the unit amperes per meter (A/m) is used for the magnetic component. One can speak of an electromagnetic field, and these units are used to provide information about the levels of electric and magnetic field strength at a measurement location. Another commonly used unit for characterizing an RF electromagnetic field is power density. Power density is most accurately used when the point of measurement is far enough away from the RF emitter to be located in what is referred to as the far field zone of the radiation pattern. In closer proximity to the transmitter, i.e., in the "near field" zone, the physical relationships between the electric and magnetic components of the field can be complex, and it is best to use the field strength units discussed above. Power density is measured in terms of power per unit area, for example, milliwatts per square centimeter (mW/cm²). When speaking of frequencies in the microwave range and higher, power density is usually used to express intensity since exposures that might occur would likely be in the far field zone. - C. A. Altgelt, The World's Largest "Radio" Station - Ellingson, Steven W. (2016). Radio Systems Engineering. Cambridge University Press. pp. 16–17. ISBN 1316785165. - ITU Radio Regulations, Chapter I, Section I, General terms – Article 1.5, definition: radio waves or hertzian waves - Harman, Peter Michael (1998). The natural philosophy of James Clerk Maxwell. Cambridge, England: Cambridge University Press. p. 6. ISBN 0-521-00585-X. - "Heinrich Hertz: The Discovery of Radio Waves". Juliantrubin.com. Retrieved 2011-11-08. - "22. Word Origins". earlyradiohistory.us. - "FREQUENCY & WAVELENGTH CALCULATOR". www.1728.org. Retrieved 15 January 2018. - "National Radio Astronomy Observatory - National Radio Astronomy Observatory". National Radio Astronomy Observatory. Retrieved 15 January 2018. - Seybold, John S. (2005). Introduction to RF Propagation. John Wiley and Sons. pp. 3–10. ISBN 0471743682. - Brain, Marshall (2000-12-07). "How Radio Works". HowStuffWorks.com. Retrieved 2009-09-11. - Kitchen, Ronald (2001). RF and Microwave Radiation Safety Handbook. Newnes. pp. 64–65. ISBN 0750643552. - VanderVorst, André; Rosen, Arye; Kotsuka, Youji (2006). RF / Microwave Interaction with Biological Tissues. John Wiley and Sons. pp. 121–122. ISBN 0471752045. - Graf, Rudolf F.; Sheets, William (2001). Build Your Own Low-power Transmitters: Projects for the Electronics Experimenter. Newnes. p. 234. ISBN 0750672447. - Elder, Joe Allen; Cahill, Daniel F. (1984). Biological Effects of Radiofrequency Radiation. US Environmental Protection Agency. pp. 5.116–5.119. - Hitchcock, R. Timothy; Patterson, Robert M. (1995). Radio-Frequency and ELF Electromagnetic Energies: A Handbook for Health Professionals. John Wiley and Sons. pp. 177–179. ISBN 0471284548. - http://www.iarc.fr/en/media-centre/pr/2011/pdfs/pr208_E.pdf and http://monographs.iarc.fr/ENG/Classification/index.php - Gerke, Daryl (2018). Electromagnetic Compatibility in Medical Equipment: A Guide for Designers and Installers. Routledge. p. 6.67. ISBN 1351453378. - Broadcasters, National Association of (1996). Antenna & Tower Regulation Handbook. NAB, Science and Technology Department. ISBN 9780893242367. Archived from the original on 2018-05-01. - James Clerk Maxwell, "A Dynamical Theory of the Electromagnetic Field", Philosophical Transactions of the Royal Society of London 155, 459–512 (1865). - Heinrich Hertz: "Electric waves; being researches on the propagation of electric action with finite velocity through space" (1893). Cornell University Library Historical Monographs Collection. Reprinted by Cornell University Library Digital Collections. - Karl Rawer: "Wave Propagation in the Ionosphere". Kluwer, Dordrecht 1993. ISBN 0-7923-0775-5
G-CO.A.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G-CO.A.2: Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). G-CO.A.3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. G-CO.A.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. G-CO.A.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. G-CO.B.6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. G-CO.C.9: Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent, and conversely prove lines are parallel; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. G-CO.C.10: Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent, and conversely prove a triangle is isosceles; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; and the medians of a triangle meet at a point. G-CO.C.11: Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. G-CO.C.11.a: Prove theorems about polygons. Theorems include the measures of interior and exterior angles. Apply properties of polygons to the solutions of mathematical and contextual problems. G-CO.D.12: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Constructions include: copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. G-CO.D.13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. G-SRT.A.1: Verify experimentally the properties of dilations given by a center and a scale factor: G-SRT.A.1.a: A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. G-SRT.A.1.b: The dilation of a line segment is longer or shorter in the ratio given by the scale factor. G-SRT.A.2: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. G-SRT.A.3: Use the properties of similarity transformations to establish the Angle-Angle (AA) criterion for two triangles to be similar. G-SRT.B.4: Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. G-SRT.B.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. G-SRT.C.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. G-SRT.C.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. G-C.A.2: Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. G-C.A.3: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral and other polygons inscribed in a circle. G-GPE.A.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. G-GPE.A.2: Derive the equation of a parabola given a focus and directrix. G-GPE.A.3: Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. G-GPE.A.3.a: Use equations and graphs of conic sections to model real-world problems. G-GMD.A.1: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. G-GMD.A.2: Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures. G-GMD.A.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. G-MG.A.4: Use dimensional analysis for unit conversions to confirm that expressions and equations make sense. Correlation last revised: 9/24/2019
Math is a vast and diverse field with a lot of different facts. Here are a few examples: -There are over 200 billion math facts in the world. -In the United States, there are over 115 million math students. -In China, there are over 1.3 billion math students. Here are a few more examples: -There are over 300 different types of math problems. -There are over 100 different ways to solve math problems. -There are over 5,000 different math concepts. -There are over 100 million math problems that can be solved. There may be more math facts than you can shake a stick at, but that doesn’t mean they’re all worth knowing. In fact, some math facts can be downright confusing and even seem counterintuitive. So, how do you properly store and use math facts? Here are a few tips: 1. Sort facts by importance. There are essential math facts that play a very important role in the flow of amath conversation or equation. For example, the square root of a number is a very important math fact that’s often used in chemistry or physics. However, other important math facts like factoring a number are less important and should be relegated to the back burner. 2. Make sure you use the right terms. Many of the terms used in math are specific to the mathematical discipline in which they’re used. For example, the square root of a number is called a square root of a number. However, in physics, it’s called a fermi surface. So, you need to be careful when translating terms to ensure you’re using the right one. 3. Don’t be afraid to ask for help. If you feel like you’re struggling with a math fact, don’t be afraid to ask a friend or tutor for help. They may be more than happy to help you out. How Many Math Facts Should A Fourth Grader Know In A Minute There are math facts that most fourth graders should know in a minute. Here are a few: -In order to find the square of a number, divide it by 2. -To find the hypotenuse of a right triangle, find the length of the hypotenuse and add the length of the other side. -To find the value of a number if it is between two numbers, take the greater of the two numbers and add it to the number. -To find the value of a number if it is between two numbers and one of the numbers is negative, take the number that is negative and divide it by the number that is greater. How Many Seconds Is A Math Fact There are a lot of math facts that people keep forgetting. Here are a few examples: -In base 5, 42 is equal to 6.9 -In base 10, 1, 2, 3, 5, 10 are equal to 26 -In base 12, 2, 4, 7, 11 are equal to 37 -In base 13, 3, 6, 11, 13 are equal to 47 What Are Math Flashcards A Math Flashcard is a collection of facts and formulas that can be used to help you in math class. They can also be used in other areas of math such as science and economics. What Does It Mean To Be Fluent In Mathematics There is no one answer to this question. A person’s fluency in mathematics can vary greatly depending on their level of mathematical experience and background. However, generally speaking, a person who is fluent in mathematics is able to do basic math calculations and understand complex mathematical concepts. Additionally, a person who is fluent in mathematics is also likely to be able to solve complex mathematical problems. What Are 4th Grade Math Facts 4th Grade Math Facts is a series of posts that will help students learn about algebra, geometry, trigonometry, and calculus. These posts will focus on fundamental concepts and will help students understand how these skills can be used in real-world situations. Algebra is the study of equations and algebraic equations are equations that have a specific form. For example, the equation x^4 + y^3 = 16 is an algebraic equation. Geometry is the study of the shapes of objects and their relationship to one another. For example, an object that is in the shape of a triangle is said to be a eligible triangle. Trigonometry is the study of the relationships between angles and distances. For example, the angles between angle A and angle B are 120 degrees. Calculus is the study of the relationship between velocity and displacement. For example, the displacement of a particle is the distance it has moved from its initial position. What Are Math Facts 2nd Grade What are math facts 2nd grade? Math facts are important for understanding mathematical concepts and for practicing math skills. What Math Facts Should 5th Graders Know Math facts should fifth graders know about: -The relationships between numbers -The order of operations -The operations that can be done with parentheses -The order of operations in percentages -The order of operations in square roots -The order of operations in order to create linear equations -The order of operations to solve equations -The order of operations to solve systems of linear equations -The order of operations to solve systems of linear equations in order to find the value of a variable -The order of operations to solve systems of linear equations to find a solution What Math Facts Should 2nd Graders Know Math facts are important for students in all grades, but especially for students in grades 2 through 4. In grades 2 through 4, students learn how to do math. This includes understanding how to solve problems, graphing data, and dealing with fractions and decimals. Some of the most important math facts for students in grades 2 through 4 are: -To convert a number to a system of numbers, like 1, 2, 3, 4, 5, 6, 7, 8, etc., you need to know the order of operations. This is called the order of operations. -To multiply two numbers, you need to know the order of operations. This is called the order of multiplication. -To divide two numbers, you need to know the order of operations. This is called the order of division. -To add two numbers, you need to know the order of operations. This is called the order of addition. -To subtract two numbers, you need to know the order of operations. This is called the order of subtraction. What Is A Math Fact A math fact is something that is true and indisputable. It’s something that can be proved by mathematics. What Is Mathmath In A Flash Mathmath is a term that is often used in mathematics to refer to the various branches of mathematics. It is usually used to refer to calculus, statistics, and geometry, but can also be used to refer to other branches of mathematics that are not typically considered as part of the mathematical field. What Is Amazingmaths Facts In A Flash There are a lot of amazingmaths facts in a flash! Here are a few examples: -In 1853, a group of British mathematicians created a system of tables of prime numbers -In 1892, British mathematician John Wallis discovered a way to automatically terminate a sequence of equations -In 1861, American mathematician George Washington White discovered a way to solve systems of linear equations -In 1881, French mathematician Auguste Comte discovered the concept of order in mathematics -In 1912, American mathematician John Wallis published a paper that won him the Nobel Prize in mathematics What Is The Maximum Number You Can Put On A Flash Card There is no definitive answer to this question- it depends on the specific flash card and the user’s hardware and software capabilities. However, a general rule of thumb is that a flash card can hold up to 128 characters. What Are The Decimals Flash Cards Flashcards are a convenient way to learn math. They are cards with tiny pictures that you can flash back to remember the answer to a math question.
The existence of supermassive black holes at the hearts of the universe's first galaxies fit hand in glove with www.finaltheories.com that says that Big Bang took place in an existing universe filled with "old" black holes and barren burnt out celestial bodies. Illustration courtesy A. Hobart, CXC/NASA Published June 15, 2011 Theorists had suspected that such enormous black holes existed just a billion years after the big bang, since most if not all of mature large galaxies have the matter-gobbling monsters at their centers. Matter falling in to black holes collides at blinding speeds and bleeds energy, ultimately generating bright x-rays, so scientists turned to the space-based Chandra X-ray Observatory to provide proof for very distant—and therefore very early—black holes. But at first even a 45-day stare into deep space—the longest and deepest yet in the x-ray spectrum—didn't provide compelling evidence. Now, by pooling those Chandra images and looking for correlations in the data, astronomers have found the missing x-rays. The rays took at least 13 billion years to reach Earth's telescopes, so they were emitted by perhaps the first supermassive black holes ever formed in the universe. Many of the black holes are a hundred thousand to a million times heftier than our sun. (Related: "Huge Black Hole Found in Dwarf Galaxy.") "These are probably the progenitors of the supermassive black holes we see now. We got them right at the very beginning," said study leader Ezequiel Treister, an astrophysicist at the University of Hawaii. More "Baby" Black Holes Yet to Be Found? To find the missing black holes, Treister and colleagues started looking at distant galaxies in the Hubble Space Telescope's famous Ultradeep Field, a long-term observation that captured light from galaxies about 13 billion years old. Because of limits on the speed of light, the farther away a celestial object is, the younger it must be. Since our universe is estimated to be 13.75 billion years old, the Hubble galaxies are from the dawn of the universe. For its record x-ray observation, Chandra stared in the same spot as Hubble, so astronomers could map Chandra's x-ray imagery on top of Hubble's visible light images. While the x-ray observations alone didn't indicate black holes in the galaxies, the new analysis revealed noticeable signals in 197 of the galaxies, or about 30 percent. Treister suspects all of the early galaxies may have supermassive black holes that we aren't yet able to detect. The team mostly found energetic x-rays instead of the "soft," lower-energy x-rays black holes typically emit. Thick material blanketing the supermassive black holes might have allowed only the most powerful x-rays to escape, the team surmises. "Large amounts of gas and dust may explain why we haven't seen anything before. They're all hidden," Treister said. In the future, Treister would like to see an even longer x-ray stare that peers deeper into space and further back in time. Doing so may allow astronomers to find other early supermassive black holes—and solve a greater mystery about the universe. "Galaxy formation and supermassive black holes have a strong connection, but we're not sure to what extent which causes the other. It's a chicken-and-egg problem," he said. "Looking back further in time may give us some clues." The early black hole study will be published June 16 in the journal Nature. Feed the World How do we feed nine billion people by 2050, and how do we do so sustainably? We've made our magazine's best stories about the future of food available in a free iPad app. Latest From Nat Geo These cooing Casanovas use showstopping plumage to court females and fend off rivals. Meet a trapper who keeps Florida's streets, sewers, and Kennedy Space Center alligator free.
Is the absolute value of [math]x^2-y^2[/math] less than or x <= y represents the Boolean statement “x is less than or equal to y”. It is equivalent to the function call _leequal(x,y) . x >= y represents the Boolean statement “ x is greater than or equal to y ”.... Section 4.3 Graphing Inequalities with Two Variables. Because an inequality does not represent . one. exact answer (a > –3), but a definite . set . of many answers, when we try to plot an inequality with two variables, the solution is a region containing many points. Example. Graph the inequality : y > x + 4. First we plot the boundary line by recognizing that the slope of the line is 1 Inequalities? Yahoo Answers 3.Graph the vertical lines x=-3, x=4, and x=5/7 on the same set of axes. 4.Graph the linear inequality y is less than 9x-5 on a suitable viewing window. Is the orgin in the solution set of this inequality?... For example, if you say x is 3, then insert it into the equation like this: y=1/3(3)+2. 1/3 times 3 is 1, plus 2 is 3. So then if x is 3, then y is 3, making a point with the coordinates (3,3). Draw this point on a graph by going 3 right (since 3 is positive) of 0 on the x axis and 3 up (since 3 is positive) from 0 on the y axis. Now you have drawn a point that is on the line y=1/3x+6. To draw Write and solve an inequality for the following: three-fourths of a number is greater than or equal to -48. how to start and run a commercial art gallery Solve the following system of linear inequalities by graphing. 3x + 4y is less than or equal to 12 x + 3y is less than or equal to 6 x is greater than or equal to 0 y is greater than or equal to 0 … Solving Inequalities 3 Falmouth Exeter Plus 10 graph the following solution set x+y less than or equal to sign 4 x greater than sign 0 y greater than sign 0 12 solve the inequality 1/4y - 1/3 < y + 2 give the result in set notation and graph it 13 graph the inequality y greater than or equal to sign -3 14 solve the inequality 3 less than or equal to sign 4 + 3x/2 less than equal sign 2 how to solve library conflicts in maven scala 17/03/2009 · This video will show you how to solve inequalities (less than or equal) WWW.I-HATE-MATH.COM. How long can it take? What is the graph x plus 3y is less than or equal to 6? - 2x-y(less than equal to)2 Algebra Homework Help Algebra - SOLUTION The second of three numbers is 7 less than 3 - y/3=3/2 solution - How to solve this inequality (Less than or equal to) YouTube How To Solve Y 2-y 3 3 Less Than 7 3/02/2017 · Find the area of the surface obtained by rotating the curve about the -axis. x = (1/3)(y^2 + 2)^(3/2), 1 less than y less than 2. - I think it could be -2, -1, and 1 Any other positive number greater than 1 makes it false.-2 + 6 = 4-1 + 6 = 5 1 + 6 = 7 All of these make the statement true because 4, 5, and 7 are all greater than -3 and less than 7, and 7 is equal to 7. - \|2x+7\| less than or equal to 27 is equal to -10 less than or equal to x less than or equal to 10. try writing it in a math form and you will get your answer. - in between the "points of interest", the function is either greater than zero (>0) or less than zero (<0) then pick a test value to find out which it is (>0 or <0) Here is an example: - An equation says that two expressions are equal, while an inequality says that one expression is greater than, greater than or equal to, less than, or less than or equal to, another. As with equations, a value of the variable for which the inequality is true is a solution of the inequality, and the set of all such solutions is the solution set of the inequality. Two inequalities with the same
Help With Geometry Help With Geometry Geometry is an interesting area of Math that requires a proper understanding of the basics. The fundamentals of different types of angles like Acute angles, Triangles, rectangles and rectilinear figures should be properly taught in order to understand higher concepts. Get Geometry help online with TutorVista's team of highly qualified and experienced online tutors. Understand the concept and achieve proper learning on the subject. Transition from basic to advanced concepts and also get help with your homework with TutorVista. Join our geometry tutoring and grab your free help now. Geometry Topics Get help from expert online geometry tutors from Tutorvista and go ahead with the subject. Given below are some of the main topics covered in Geometry Help: Lines: There are different types of lines as given below: --Straight lines --Parrallel lines --Perpendicular lines Know More About Free Chemistry Help Page No. :- 1/6 Quadrilaterals: Quadrialteral is any shape which has four sides. Given below are some of the quadrilaterals that are covered in Geometry Help. --Rectangles --Parrallelograms --Rhombus --Square --Trapezium Circles: Circle is a shape which has a center and is made by joining points which are equidistant from the center. Triangles: Triangles are those which has three sides and three angles. Based on sides and angles, triangles are divided into six sides. Angles: Besides the geometric shapes, another thing that is very important in Geometry is angles. Understand all these concepts from our online tutors and improve your knowledge. This tutorial deals with all the formulas and Proofs related to Geometry. Grab this learning now! Geometry CurriculumBack to Top Geometry comes under the study of lower grade math to higher grade math and therefore we provide geometry online tutoring for all grades. By Grades Grade 12 Grade 7 Grade 11 Grade 6 Grade 10 Grade 5 Grade 9 Grade 4 Grade 8 Grade 3 Learn More Geometry Tutor Tutorvista.com Page No. :- 2/6 Solving Algebra Problems Solving Algebra Problems Get answers to all Algebra word problems online with TutorVista. Our online Algebra tutoring program is designed to help you get all the answers to your Algebra word problems giving you the desired edge in excelling in the subject. To gain a proper understanding for algebra, you need to have clear concept over algebra 1 problems and algebra 2 problems as well. We provide help with algebra from basics to advance and thus include college algebra help as well. Get help with algebra 1 and algebra 2 from our tutors and achieve a complete learning over the whole algebra subject. The online Algebra tutors serve as the Algebra solvers with whose help students can solve problems under Algebra. Online Algebra Questions Our Algebra tutoring covers all grades and levels. So whether you are a middle or high school student or a college level student our Algebra tutors can help you. Get college level Algebra Help, regular algebra homework help, and exam prep help with TutorVista's expert tutors. Page No. :- 3/6 From Framing of Formules to Expansions, Indices, Linear Equations to Factorization and Quadratic Equations, solving Algebra problems gets easy with our expert tutors. Our highly qualified and experienced tutors will work with you to make you explain concepts better and help you score well in the subject. They are like the personal Algebra solvers who would aid with Algbera problems anytime. Example A three digit number consists of 7, 8 and one more number. When these digits are reversed and subtracted from the original number the answer yielded will be consisting of the same digits arranged yet in a different order. Solve the word problem and find the another digit? Solution :- Let the unknown digit = n. The given number is then, 700 + 80 + n = 780 + n. When reversed the new number is, 100n + 80 + 7 = 87 + 100n. Subtracting these two numbers we get, After solving, we get 693 = 99n. The digit can be arranged in 3 ways or 6 ways. We have already investigated 2 of these ways. Read More About Solve My Equation Tutorvista.com Page No. :- 4/6 We can now try one of the remaining 4 ways. One of these are n = 95 100n + 70 + 8 = 693 - 99n 199n = 615 After solving, we get N=3 Answer: The unknown digit is 3. College Algebra Word Problem Solver College Algebra solvers help students to solve the word problems step by step. They teach students how to understand the data given in the statement and solve for the value to be found out. The online Algebra tutors serve as free Algebra Solver who would help students in interpreting the word problems. Let us go over a few important Math equivalents of English for numbers and algebra word problems so as to make the interpretation of word problems easier. --Add---- sum, total of, added to, together, increased by --Subtract-difference between, minus, less than, fewer than --Multiplication-of times, by a factor --Division-per, out of, ratio of, percent The above words are suggestive of the operations associated with them. Students can learn more in depth about them on understanding algebra word problems and tke the help of online Algebra Solvers. Page No. :- 5/6 Get Geometry help online with TutorVista's team of highly qualified and experienced online tutors. Understand the concept and achieve proper...
Base-pairing properties of DNA were used to construct tiny structures that accumulated a silica outer skeleton similar to shell-building organisms known as diatoms. Credit: Yan Lab. [downloaded from https://phys.org/news/2018-07-single-celled-architects-nanotechnology.html] The gif below isn’t quite so pretty as the image above but it’s both an example of the kind of imagery (lots of grey), that scientists routinely work with and it shows the work in more detail, 3D cube made using DNA Origami Silicification (DOS), which deposits a fine layer of silica onto the DNA origami framework. Credit: Yan Lab [downloaded from https://phys.org/news/2018-07-single-celled-architects-nanotechnology.html] Diatoms are tiny, unicellular creatures, inhabiting oceans, lakes, rivers, and soils. Through their respiration, they produce close to a quarter of the oxygen on earth, nearly as much as the world’s tropical forests. In addition to their ecological success across the planet, they have a number of remarkable properties. Diatoms live in glasslike homes of their own design, visible under magnification in an astonishing and aesthetically beautiful range of forms. Researchers have found inspiration in these microscopic, jewel-like products of nature since their discovery in the late 18th century. In a new study, Arizona State University (ASU) scientists led by Professor Hao Yan, in collaboration with researchers from the Shanghai Institute of Applied Physics of the Chinese Academy of Sciences and Shanghai Jiaotong University led by Prof. Chunhai Fan, have designed a range of diatom-like nanostructures. To achieve this, they borrow techniques used by naturally-occurring diatoms to deposit layers of silica—the primary constituent in glass—in order to grow their intricate shells. Using a technique known as DNA origami, the group designed nanoscale platforms of various shapes to which particles of silica, drawn by electrical charge, could stick. The new research demonstrates that silica deposition can be effectively applied to synthetic, DNA-based architectures, improving their elasticity and durability. The work could ultimately have far-reaching applications in new optical systems, semiconductor nanolithography, nano-electronics, nano-robotics and medical applications, including drug delivery. Researchers like Yan and Fan create sophisticated nanoarchitectures in 2- and 3-dimensions, using DNA as a building material. The method, known as DNA origami, relies on the base-pairing properties of DNA’s four nucleotides, whose names are abbreviated A,T,C and G. The ladder-like structure of the DNA double-helix is formed when complementary strands of nucleotides bond with each other—the C nucleotides always pairing with Gs and the As always pairing with Ts. This predictable behavior can be exploited in order to produce a virtually limitless variety of engineered shapes, which can be designed in advance. The nanostructures then self-assemble in a test tube. In the new study, researchers wanted to see if architectures designed with DNA, each measuring just billionths of a meter in diameter, could be used as structural frameworks on which diatom-like exoskeletons composed of silica could grow in a precise and controllable manner. Their successful results show the power of this hybrid marriage of nature and nanoengineering, which the authors call DNA Origami Silicification (DOS). “Here, we demonstrated that the right chemistry can be developed to produce DNA-silica hybrid materials that faithfully replicate the complex geometric information of a wide range of different DNA origami scaffolds. Our findings established a general method for creating biomimetic silica nanostructures,” said Yan. Among the geometric DNA frameworks designed and constructed in the experiments were 2D crosses, squares, triangles and DOS-diatom honeycomb shapes as well as 3D cubes, tetrahedrons, hemispheres, toroid and ellipsoid forms, occurring as single units or lattices. Once the DNA frameworks were complete, clusters of silica particles carrying a positive charge were drawn electrostatically to the surfaces of the electrically negative DNA shapes, accreting over a period of several days, like fine paint applied to an eggshell. A series of transmission- and scanning electron micrographs were made of the resulting DOS forms, revealing accurate and efficient diatom-like silicification. The method proved effective for silicification of framelike, curved and porous nanostructures ranging in size from 10-1000 nanometers, (the largest structures are roughly the size of bacteria). Precise control over silica shell thickness is achieved simply by regulating the duration of growth. The hybrid DOS-diatom nanostructures were initially characterized using a pair of powerful tools capable of unveiling their tiny forms, Transmission Electron Microscopy (TEM) and Atomic Force Microscopy (AFM). The resulting images reveal much clearer outlines for the nanostructures after the deposition of silica. The method of nanofabrication is so precise, researchers were able to produce triangles, squares and hexagons with uniform pores measuring less than 10 nm in diameter—by far the smallest achieved to date, using DNA origami lithography. Further, the technique outlined in the new study equips researchers with more accurate control over the construction of 3D nanostructures in arbitrary forms that are often challenging to produce through existing methods. One property of natural diatoms of great interests to nanoengineers like Yan and Fan is the specific strength of their silica shells. Specific strength refers to a material’s resistance to breakage relative to its density. Scientists have found that the silica architectures of diatoms are not only inspiringly elegant but exceptionally tough. Indeed, the silica exoskeletons enveloping diatoms have the highest specific strength of any biologically produced material, including bone, antlers, and teeth. In the current study, researchers used AFM to measure the resistance to breakage of their silica-augmented DNA nanostructures. Like their natural counterparts, these forms showed far greater strength and resilience, displaying a 10-fold increase in the forces they could withstand, compared with the unsilicated designs, while nevertheless retaining considerable flexibility. The study also shows that the enhanced rigidity of DOS nanostructures increases with their growth time. As the authors note, these results are in agreement with the characteristic mechanical properties of biominerals produced by nature, coupling impressive durability with flexibility. A final experiment involved the design of a new 3D tetrahedral nanostructure using gold nanorods as supportive struts for a DOS fabricated device. This novel structure was able to faithfully retain its shape compared with a similar structure lacking silication that deformed and collapsed. The research opens a pathway for nature-inspired innovations in nanotechnology in which DNA architectures act as templates that may be coated with silica or perhaps other inorganic materials, including calcium phosphate, calcium carbonate, ferric oxide or other metal oxides, yielding unique properties. “We are interested in developing methods to create higher order hybrid nanostructures. For example, multi-layered/multi-component hybrid materials may be achieved by a stepwise deposition of different materials to further expand the biomimetic diversity,” said Fan. Such capabilities will open up new opportunities to engineer highly programmable solid-state nanopores with hierarchical features, new porous materials with designed structural periodicity, cavity and functionality, plasmonic and meta-materials. The bio-inspired and biomimetic approach demonstrated in this paper represents a general framework for use with inorganic device nanofabrication that has arbitrary 3D shapes and functions and offers diverse potential applications in fields such as nano-electronics, nano-photonics, and nano-robotics. Libraries, archives, records management, oral history, etc. there are many institutions and names for how we manage collective and personal memory. You might call it a peculiarly human obsession stretching back into antiquity. For example, there’s the Library of Alexandria (Wikipedia entry) founded in the third, or possibly 2nd, century BCE (before the common era) and reputed to store all the knowledge in the world. It was destroyed although accounts differ as to when and how but its loss remains a potent reminder of memory’s fragility. These days, the technology community is terribly concerned with storing ever more bits of data on materials that are reaching their limits for storage.I have news of a possible solution, an interview of sorts with the researchers working on this new technology, and some very recent research into policies for cryptocurrency mining and development. That bit about cryptocurrency makes more sense when you read what the response to one of the interview questions. It seems University of Alberta researchers may have found a way to increase memory exponentially, from a July 23, 2018 news item on ScienceDaily, The most dense solid-state memory ever created could soon exceed the capabilities of current computer storage devices by 1,000 times, thanks to a new technique scientists at the University of Alberta have perfected. “Essentially, you can take all 45 million songs on iTunes and store them on the surface of one quarter,” said Roshan Achal, PhD student in Department of Physics and lead author on the new research. “Five years ago, this wasn’t even something we thought possible.” Previous discoveries were stable only at cryogenic conditions, meaning this new finding puts society light years closer to meeting the need for more storage for the current and continued deluge of data. One of the most exciting features of this memory is that it’s road-ready for real-world temperatures, as it can withstand normal use and transportation beyond the lab. “What is often overlooked in the nanofabrication business is actual transportation to an end user, that simply was not possible until now given temperature restrictions,” continued Achal. “Our memory is stable well above room temperature and precise down to the atom.” Achal explained that immediate applications will be data archival. Next steps will be increasing readout and writing speeds, meaning even more flexible applications. “With this last piece of the puzzle now in-hand, atom-scale fabrication will become a commercial reality in the very near future,” said Wolkow. Wolkow’s Spin-off [sic] company, Quantum Silicon Inc., is hard at work on commercializing atom-scale fabrication for use in all areas of the technology sector. To demonstrate the new discovery, Achal, Wolkow, and their fellow scientists not only fabricated the world’s smallest maple leaf, they also encoded the entire alphabet at a density of 138 terabytes, roughly equivalent to writing 350,000 letters across a grain of rice. For a playful twist, Achal also encoded music as an atom-sized song, the first 24 notes of which will make any video-game player of the 80s and 90s nostalgic for yesteryear but excited for the future of technology and society. As noted in the news release, there is an atom-sized song, which is available in this video, For interested parties, you can find Quantum Silicon (QSI) here. My Edmonton geography is all but nonexistent, still, it seems to me the company address on Saskatchewan Drive is a University of Alberta address. It’s also the address for the National Research Council of Canada. Perhaps this is a university/government spin-off company? I sent some questions to the researchers at the University of Alberta who very kindly provided me with the following answers. Roshan Achal passed on one of the questions to his colleague Taleana Huff for her response. Both Achal and Huff are associated with QSI. Unfortunately I could not find any pictures of all three researchers (Achal, Huff, and Wolkow) together. Roshan Achal (left) used nanotechnology perfected by his PhD supervisor, Robert Wolkow (right) to create atomic-scale computer memory that could exceed the capacity of today’s solid-state storage drives by 1,000 times. (Photo: Faculty of Science) (1) SHRINKING THE MANUFACTURING PROCESS TO THE ATOMIC SCALE HAS ATTRACTED A LOT OF ATTENTION OVER THE YEARS STARTING WITH SCIENCE FICTION OR RICHARD FEYNMAN OR K. ERIC DREXLER, ETC. IN ANY EVENT, THE ORIGINS ARE CONTESTED SO I WON’T PUT YOU ON THE SPOT BY ASKING WHO STARTED IT ALL INSTEAD ASKING HOW DID YOU GET STARTED? I got started in this field about 6 years ago, when I undertook a MSc with Dr. Wolkow here at the University of Alberta. Before that point, I had only ever heard of a scanning tunneling microscope from what was taught in my classes. I was aware of the famous IBM logo made up from just a handful of atoms using this machine, but I didn’t know what else could be done. Here, Dr. Wolkow introduced me to his line of research, and I saw the immense potential for growth in this area and decided to pursue it further. I had the chance to interact with and learn from nanofabrication experts and gain the skills necessary to begin playing around with my own techniques and ideas during my PhD. (2) AS I UNDERSTAND IT, THESE ARE THE PIECES YOU’VE BEEN WORKING ON: (1) THE TUNGSTEN MICROSCOPE TIP, WHICH MAKE[s] (2) THE SMALLEST QUANTUM DOTS (SINGLE ATOMS OF SILICON), (3) THE AUTOMATION OF THE QUANTUM DOT PRODUCTION PROCESS, AND (4) THE “MOST DENSE SOLID-STATE MEMORY EVER CREATED.” WHAT’S MISSING FROM THE LIST AND IS THAT WHAT YOU’RE WORKING ON NOW? One of the things missing from the list, that we are currently working on, is the ability to easily communicate (electrically) from the macroscale (our world) to the nanoscale, without the use of a scanning tunneling microscope. With this, we would be able to then construct devices using the other pieces we’ve developed up to this point, and then integrate them with more conventional electronics. This would bring us yet another step closer to the realization of atomic-scale (3) PERHAPS YOU COULD CLARIFY SOMETHING FOR ME. USUALLY WHEN SOLID STATE MEMORY IS MENTIONED, THERE’S GREAT CONCERN ABOUT MOORE’S LAW. IS THIS WORK GOING TO CREATE A NEW LAW? AND, WHAT IF ANYTHING DOES ;YOUR MEMORY DEVICE HAVE TO DO WITH QUANTUM COMPUTING? That is an interesting question. With the density we’ve achieved, there are not too many surfaces where atomic sites are more closely spaced to allow for another factor of two improvement. In that sense, it would be difficult to improve memory densities further using these techniques alone. In order to continue Moore’s law, new techniques, or storage methods would have to be developed to move beyond atomic-scale The memory design itself does not have anything to do with quantum computing, however, the lithographic techniques developed through our work, may enable the development of certain quantum-dot-based quantum (4) THIS MAY BE A LITTLE OUT OF LEFT FIELD (OR FURTHER OUT THAN THE OTHERS), COULD;YOUR MEMORY DEVICE HAVE AN IMPACT ON THE DEVELOPMENT OF CRYPTOCURRENCY AND BLOCKCHAIN? IF SO, WHAT MIGHT THAT I am not very familiar with these topics, however, co-author Taleana Huff has provided some thoughts: Taleana Huff (downloaded from https://ca.linkedin.com/in/taleana-huff] “The memory, as we’ve designed it, might not have too much of an impact in and of itself. Cryptocurrencies fall into two categories. Proof of Work and Proof of Stake. Proof of Work relies on raw computational power to solve a difficult math problem. If you solve it, you get rewarded with a small amount of that coin. The problem is that it can take a lot of power and energy for your computer to crunch through that problem. Faster access to memory alone could perhaps streamline small parts of this slightly, but it would be very slight. Proof of Stake is already quite power efficient and wouldn’t really have a drastic advantage from better faster computers. Now, atomic-scale circuitry built using these new lithographic techniques that we’ve developed, which could perform computations at significantly lower energy costs, would be huge for Proof of Work coins. One of the things holding bitcoin back, for example, is that mining it is now consuming power on the order of the annual energy consumption required by small countries. A more efficient way to mine while still taking the same amount of time to solve the problem would make bitcoin much more attractive as a currency.” Thank you to Roshan Achal and Taleana Huff for helping me to further explore the implications of their work with Dr. Wolkow. As usual, after receiving the replies I have more questions but these people have other things to do so I’ll content myself with noting that there is something extraordinary in the fact that we can imagine a near future where atomic scale manufacturing is possible and where as Achal says, ” … storage methods would have to be developed to move beyond atomic-scale [emphasis mine] storage”. In decades past it was the stuff of science fiction or of theorists who didn’t have the tools to turn the idea into a reality. With Wolkow’s, Achal’s, Hauff’s, and their colleagues’ work, atomic scale manufacturing is attainable in the foreseeable future. Hopefully we’ll be wiser than we have been in the past in how we deploy these new manufacturing techniques. Of course, before we need the wisdom, scientists, as Achal notes, need to find a new way to communicate between the macroscale and the nanoscale. A study [behind a paywall] published in Energy Research & Social Science warns that failure to lower the energy use by Bitcoin and similar Blockchain designs may prevent nations from reaching their climate change mitigation obligations under the Paris Agreement. The study, authored by Jon Truby, PhD, Assistant Professor, Director of the Centre for Law & Development, College of Law, Qatar University, Doha, Qatar, evaluates the financial and legal options available to lawmakers to moderate blockchain-related energy consumption and foster a sustainable and innovative technology sector. Based on this rigorous review and analysis of the technologies, ownership models, and jurisdictional case law and practices, the article recommends an approach that imposes new taxes, charges, or restrictions to reduce demand by users, miners, and miner manufacturers who employ polluting technologies, and offers incentives that encourage developers to create less energy-intensive/carbon-neutral Blockchain. “Digital currency mining is the first major industry developed from Blockchain, because its transactions alone consume more electricity than entire nations,” said Dr. Truby. “It needs to be directed towards sustainability if it is to realize its potential advantages. “Many developers have taken no account of the environmental impact of their designs, so we must encourage them to adopt consensus protocols that do not result in high emissions. Taking no action means we are subsidizing high energy-consuming technology and causing future Blockchain developers to follow the same harmful path. We need to de-socialize the environmental costs involved while continuing to encourage progress of this important technology to unlock its potential economic, environmental, and social benefits,” explained Dr. Truby. As a digital ledger that is accessible to, and trusted by all participants, Blockchain technology decentralizes and transforms the exchange of assets through peer-to-peer verification and payments. Blockchain technology has been advocated as being capable of delivering environmental and social benefits under the UN’s Sustainable Development Goals. However, Bitcoin’s system has been built in a way that is reminiscent of physical mining of natural resources – costs and efforts rise as the system reaches the ultimate resource limit and the mining of new resources requires increasing hardware resources, which consume huge amounts of electricity. Putting this into perspective, Dr. Truby said, “the processes involved in a single Bitcoin transaction could provide electricity to a British home for a month – with the environmental costs socialized for private benefit. “Bitcoin is here to stay, and so, future models must be designed without reliance on energy consumption so disproportionate on their economic or social benefits.” The study evaluates various Blockchain technologies by their carbon footprints and recommends how to tax or restrict Blockchain types at different phases of production and use to discourage polluting versions and encourage cleaner alternatives. It also analyzes the legal measures that can be introduced to encourage technology innovators to develop low-emissions Blockchain designs. The specific recommendations include imposing levies to prevent path-dependent inertia from constraining innovation: Registration fees collected by brokers from digital coin buyers. “Bitcoin Sin Tax” surcharge on digital currency ownership. Green taxes and restrictions on machinery purchases/imports (e.g. Bitcoin mining machines). Smart contract transaction charges. According to Dr. Truby, these findings may lead to new taxes, charges or restrictions, but could also lead to financial rewards for innovators developing carbon-neutral Blockchain. The press release doesn’t fully reflect Dr. Truby’s thoughtfulness or the incentives he has suggested. it’s not all surcharges, taxes, and fees constitute encouragement. Here’s a sample from the conclusion, The possibilities of Blockchain are endless and incentivisation can help solve various climate change issues, such as through the development of digital currencies to fund climate finance programmes. This type of public-private finance initiative is envisioned in the Paris Agreement, and fiscal tools can incentivize innovators to design financially rewarding Blockchain technology that also achieves environmental goals. Bitcoin, for example, has various utilitarian intentions in its White Paper, which may or may not turn out to be as envisioned, but it would not have been such a success without investors seeking remarkable returns. Embracing such technology, and promoting a shift in behaviour with such fiscal tools, can turn the industry itself towards achieving innovative solutions for environmental goals. I realize Wolkow, et. al, are not focused on cryptocurrency and blockchain technology per se but as Huff notes in her reply, “… new lithographic techniques that we’ve developed, which could perform computations at significantly lower energy costs, would be huge for Proof of Work coins.” Whether or not there are implications for cryptocurrencies, energy needs, climate change, etc., it’s the kind of innovative work being done by scientists at the University of Alberta which may have implications in fields far beyond the researchers’ original intentions such as more efficient computation and data storage. ETA Aug. 6, 2018: Dexter Johnson weighed in with an August 3, 2018 posting on his Nanoclast blog (on the IEEE [Institute of Electrical and Electronics Engineers] website), Researchers at the University of Alberta in Canada have developed a new approach to rewritable data storage technology by using a scanning tunneling microscope (STM) to remove and replace hydrogen atoms from the surface of a silicon wafer. If this approach realizes its potential, it could lead to a data storage technology capable of storing 1,000 times more data than today’s hard drives, up to 138 terabytes per square inch. As a bit of background, Gerd Binnig and Heinrich Rohrer developed the first STM in 1986 for which they later received the Nobel Prize in physics. In the over 30 years since an STM first imaged an atom by exploiting a phenomenon known as tunneling—which causes electrons to jump from the surface atoms of a material to the tip of an ultrasharp electrode suspended a few angstroms above—the technology has become the backbone of so-called nanotechnology. In addition to imaging the world on the atomic scale for the last thirty years, STMs have been experimented with as a potential data storage device. Last year, we reported on how IBM (where Binnig and Rohrer first developed the STM) used an STM in combination with an iron atom to serve as an electron-spin resonance sensor to read the magnetic pole of holmium atoms. The north and south poles of the holmium atoms served as the 0 and 1 of digital logic. The Canadian researchers have taken a somewhat different approach to making an STM into a data storage device by automating a known technique that uses the ultrasharp tip of the STM to apply a voltage pulse above an atom to remove individual hydrogen atoms from the surface of a silicon wafer. Once the atom has been removed, there is a vacancy on the surface. These vacancies can be patterned on the surface to create devices and memories. If you have the time, I recommend reading Dexter’s posting as he provides clear explanations, additional insight into the work, and more historical detail. … the path to greater benefits – whether economic, social, or environmental – from nanomanufactured goods and services is not yet clear. A recent review article in ACS Nano (“Nanomanufacturing: A Perspective”) by J. Alexander Liddle and Gregg M. Gallatin, takes silicon integrated circuit manufacturing as a baseline in order to consider the factors involved in matching processes with products, examining the characteristics and potential of top-down and bottom-up processes, and their combination. The authors also discuss how a careful assessment of the way in which function can be made to follow form can enable high-volume manufacturing of nanoscale structures with the desired useful, and exciting, properties. Although often used interchangeably, it makes sense to distinguish between nanofabrication and nanomanufacturing using the criterion of economic viability, suggested by the connotations of industrial scale and profitability associated with the word ‘manufacturing’. Here’s a link to and a citation for the paper Berger is reviewing, Nanomanufacturing: A Perspective by J. Alexander Liddle and Gregg M. Gallatin. ACS Nano, 2016, 10 (3), pp 2995–3014 DOI: 10.1021/acsnano.5b03299 Publication Date (Web): February 10, 2016 Copyright This article not subject to U.S. Copyright. Published 2016 by the American Chemical Society This paper is behind a paywall. Luckily for those who’d like a little more information before purchase, Berger’s review provides some insight into the study additional to what you’ll find in the abstract, Nanomanufacturing, as the authors define it in their article, therefore, has the salient characteristic of being a source of money, while nanofabrication is often a sink. To supply some background and indicate the scale of the nanomanufacturing challenge, the figure below shows the selling price ($·m-2) versus the annual production (m2) for a variety of nanoenabled or potentially nanoenabled products. The overall global market sizes are also indicated. It is interesting to note that the selling price spans 5 orders of magnitude, the production six, and the market size three. Although there is no strong correlation between the variables, market price and size nanoenabled product Log-log plot of the approximate product selling price ($·m-2) versus global annual production (m2) for a variety of nanoenabled, or potentially nanoenabled products. Approximate market sizes (2014) are shown next to each point. (Reprinted with permission by American Chemical Society) Log-log plot of the approximate product selling price ($·m-2) versus global annual production (m2) for a variety of nanoenabled, or potentially nanoenabled products. Approximate market sizes (2014) are shown next to each point. (Reprinted with permission by American Chemical Society) I encourage anyone interested in nanomanufacturing to read Berger’s article in its entirety as there is more detail and there are more figures to illustrate the points being made. He ends his review with this, “Perhaps the most exciting prospect is that of creating dynamical nanoscale systems that are capable of exhibiting much richer structures and functionality. Whether this is achieved by learning how to control and engineer biological systems directly, or by building systems based on the same principles, remains to be seen, but will undoubtedly be disruptive and quite probably revolutionary.” I find the reference to biological systems quite interesting especially in light of the recent launch of DARPA’s (US Defense Advanced Research Projects Agency) Engineered Living Materials (ELM) program (see my Aug. 9, 2016 posting). A Jan. 6, 2015 news item on Nanowerk features a proposal by US scientists for a Unified Microbiome Initiative (UMI), In October , an interdisciplinary group of scientists proposed forming a Unified Microbiome Initiative (UMI) to explore the world of microorganisms that are central to life on Earth and yet largely remain a mystery. An article in the journal ACS Nano (“Tools for the Microbiome: Nano and Beyond”) describes the tools scientists will need to understand how microbes interact with each other and with us. Microbes live just about everywhere: in the oceans, in the soil, in the atmosphere, in forests and in and on our bodies. Research has demonstrated that their influence ranges widely and profoundly, from affecting human health to the climate. But scientists don’t have the necessary tools to characterize communities of microbes, called microbiomes, and how they function. Rob Knight, Jeff F. Miller, Paul S. Weiss and colleagues detail what these technological needs are. The researchers are seeking the development of advanced tools in bioinformatics, high-resolution imaging, and the sequencing of microbial macromolecules and metabolites. They say that such technology would enable scientists to gain a deeper understanding of microbiomes. Armed with new knowledge, they could then tackle related medical and other challenges with greater agility than what is possible today. Here’s a link to and a citation for the paper, Tools for the Microbiome: Nano and Beyond by Julie S. Biteen, Paul C. Blainey, Zoe G. Cardon, Miyoung Chun, George M. Church, Pieter C. Dorrestein, Scott E. Fraser, Jack A. Gilbert, Janet K. Jansson, Rob Knight, Jeff F. Miller, Aydogan Ozcan, Kimberly A. Prather, Stephen R. Quake, Edward G. Ruby, Pamela A. Silver, Sharif Taha, Ger van den Engh, Paul S. Weiss, Gerard C. L. Wong, Aaron T. Wright, and Thomas D. Young. ACS Nano, Article ASAP DOI: 10.1021/acsnano.5b07826 Publication Date (Web): December 22, 2015 I sped through very quickly and found a couple of references to ‘nano’, Ocean Microbiomes and Nanobiomes Life in the oceans is supported by a community of extremely small organisms that can be called a “nanobiome.” These nanoplankton particles, many of which measure less than 0.001× the volume of a white blood cell, harvest solar and chemical energy and channel essential elements into the food chain. A deep network of larger life forms (humans included) depends on these tiny microbes for its energy and chemical building blocks. The importance of the oceanic nanobiome has only recently begun to be fully appreciated. Two dominant forms, Synechococcus and Prochlorococcus, were not discovered until the 1980s and 1990s.(32-34) Prochloroccus has now been demonstrated to be so abundant that it may account for as much as 10% of the world’s living organic carbon. The organism divides on a diel cycle while maintaining constant numbers, suggesting that about 5% of the world’s biomass flows through this species on a daily basis.(35-37) Metagenomic studies show that many other less abundant life forms must exist but elude direct observation because they can neither be isolated nor grown in culture. The small sizes of these organisms (and their genomes) indicate that they are highly specialized and optimized. Metagenome data indicate a large metabolic heterogeneity within the nanobiome. Rather than combining all life functions into a single organism, the nanobiome works as a network of specialists that can only exist as a community, therein explaining their resistance to being cultured. The detailed composition of the network is the result of interactions between the organisms themselves and the local physical and chemical environment. There is thus far little insight into how these networks are formed and how they maintain steady-state conditions in the turbulent natural ocean environment. Rather than combining all life functions into a single organism, the nanobiome works as a network of specialists that can only exist as a community The serendipitous discovery of Prochlorococcus happened by applying flow cytometry (developed as a medical technique for counting blood cells) to seawater.(34) With these medical instruments, the faint signals from nanoplankton can only be seen with great difficulty against noisy backgrounds. Currently, a small team is adapting flow cytometric technology to improve the capabilities for analyzing individual nanoplankton particles. The latest generation of flow cytometers enables researchers to count and to make quantitative observations of most of the small life forms (including some viruses) that comprise the nanobiome. To our knowledge, there are only two well-equipped mobile flow cytometry laboratories that are regularly taken to sea for real-time observations of the nanobiome. The laboratories include equipment for (meta)genome analysis and equipment to correlate the observations with the local physical parameters and (nutrient) chemistry in the ocean. Ultimately, integration of these measurements will be essential for understanding the complexity of the oceanic microbiome. The ocean is tremendously undersampled. Ship time is costly and limited. Ultimately, inexpensive, automated, mobile biome observatories will require methods that integrate microbiome and nanobiome measurements, with (meta-) genomics analyses, with local geophysical and geochemical parameters.(38-42) To appreciate how the individual components of the ocean biome are related and work together, a more complete picture must be established. The marine environment consists of stratified zones, each with a unique, characteristic biome.(43) The sunlit waters near the surface are mixed by wind action. Deeper waters may be mixed only occasionally by passing storms. The dark deepest layers are stabilized by temperature/salinity density gradients. Organic material from the photosynthetically active surface descends into the deep zone, where it decomposes into nutrients that are mixed with compounds that are released by volcanic and seismic action. These nutrients diffuse upward to replenish the depleted surface waters. The biome is stratified accordingly, sometimes with sudden transitions on small scales. Photo-autotrophs dominate near the surface. Chemo-heterotrophs populate the deep. The makeup of the microbial assemblages is dictated by the local nutrient and oxygen concentrations. The spatiotemporal interplay of these systems is highly relevant to such issues as the carbon budget of the planet but remains little understood. And then, there was this, Nanoscience and Nanotechnology Opportunities The great advantage of nanoscience and nanotechnology in studying microbiomes is that the nanoscale is the scale of function in biology. It is this convergence of scales at which we can “see” and at which we can fabricate that heralds the contributions that can be made by developing new nanoscale analysis tools.(159-168) Microbiomes operate from the nanoscale up to much larger scales, even kilometers, so crossing these scales will pose significant challenges to the field, in terms of measurement, stimulation/response, informatics, and ultimately understanding. Some progress has been made in creating model systems(143-145, 169-173) that can be used to develop tools and methods. In these cases, the tools can be brought to bear on more complex and real systems. Just as nanoscience began with the ability to image atoms and progressed to the ability to manipulate structures both directly and through guided interactions,(162, 163, 174-176) it has now become possible to control structure, materials, and chemical functionality from the submolecular to the centimeter scales simultaneously. Whereas substrates and surface functionalization have often been tailored to be resistant to bioadhesion, deliberate placement of chemical patterns can also be used for the growth and patterning of systems, such as biofilms, to be put into contact with nanoscale probes.(177-180) Such methods in combination with the tools of other fields (vide infra) will provide the means to probe and to understand microbiomes. Key tools for the microbiome will need to be miniaturized and made parallel. These developments will leverage decades of work in nanotechnology in the areas of nanofabrication,(181) imaging systems,(182, 183) lab-on-a-chip systems,(184) control of biological interfaces,(185) and more. Commercialized and commoditized tools, such as smart phone cameras, can also be adapted for use (vide infra). By guiding the development and parallelization of these tools, increasingly complex microbiomes will be opened for study.(167) Imaging and sensing, in general, have been enjoying a Renaissance over the past decades, and there are various powerful measurement techniques that are currently available, making the Microbiome Initiative timely and exciting from the broad perspective of advanced analysis techniques. Recent advances in various -omics technologies, electron microscopy, optical microscopy/nanoscopy and spectroscopy, cytometry, mass spectroscopy, atomic force microscopy, nuclear imaging, and other techniques, create unique opportunities for researchers to investigate a wide range of questions related to microbiome interactions, function, and diversity. We anticipate that some of these advanced imaging, spectroscopy, and sensing techniques, coupled with big data analytics, will be used to create multimodal and integrated smart systems that can shed light onto some of the most important needs in microbiome research, including (1) analyzing microbial interactions specifically and sensitively at the relevant spatial and temporal scales; (2) determining and analyzing the diversity covered by the microbial genome, transcriptome, proteome, and metabolome; (3) managing and manipulating microbiomes to probe their function, evaluating the impact of interventions and ultimately harnessing their activities; and (4) helping us identify and track microbial dark matter (referring to 99% of micro-organisms that cannot be cultured). In this broad quest for creating next-generation imaging and sensing instrumentation to address the needs and challenges of microbiome-related research activities comprehensively, there are important issues that need to be considered, as discussed below. The piece is extensive and quite interesting, if you have the time. The US Air Force wants to merge classical and quantum physics for practical purposes according to a May 5, 2014 news item on Azonano, The Air Force Office of Scientific Research has selected the Harvard School of Engineering and Applied Sciences (SEAS) to lead a multidisciplinary effort that will merge research in classical and quantum physics and accelerate the development of advanced optical technologies. Federico Capasso, Robert L. Wallace Professor of Applied Physics and Vinton Hayes Senior Research Fellow in Electrical Engineering, will lead this Multidisciplinary University Research Initiative [MURI] with a world-class team of collaborators from Harvard, Columbia University, Purdue University, Stanford University, the University of Pennsylvania, Lund University, and the University of Southampton. The grant is expected to advance physics and materials science in directions that could lead to very sophisticated lenses, communication technologies, quantum information devices, and imaging technologies. “This is one of the world’s strongest possible teams,” said Capasso. “I am proud to lead this group of people, who are internationally renowned experts in their fields, and I believe we can really break new ground.” The premise of nanophotonics is that light can interact with matter in unusual ways when the material incorporates tiny metallic or dielectric features that are separated by a distance shorter than the wavelength of the light. Metamaterials are engineered materials that exploit these phenomena, producing strange effects, enabling light to bend unnaturally, twist into a vortex, or disappear entirely. Yet the fabrication of thick, or bulk, metamaterials—that manipulate light as it passes through the material—has proven very challenging. Recent research by Capasso and others in the field has demonstrated that with the right device structure, the critical manipulations can actually be confined to the very surface of the material—what they have dubbed a “metasurface.” These metasurfaces can impart an instantaneous shift in the phase, amplitude, and polarization of light, effectively controlling optical properties on demand. Importantly, they can be created in the lab using fairly common fabrication techniques. At Harvard, the research has produced devices like an extremely thin, flat lens, and a material that absorbs 99.75% of infrared light. But, so far, such devices have been built to order—brilliantly suited to a single task, but not tunable. This project, however,is focused on the future (Note: Links have been removed), “Can we make a rapidly configurable metasurface so that we can change it in real time and quickly? That’s really a visionary frontier,” said Capasso. “We want to go all the way from the fundamental physics to the material building blocks and then the actual devices, to arrive at some sort of system demonstration.” The proposed research also goes further. A key thrust of the project involves combining nanophotonics with research in quantum photonics. By exploiting the quantum effects of luminescent atomic impurities in diamond, for example, physicists and engineers have shown that light can be captured, stored, manipulated, and emitted as a controlled stream of single photons. These types of devices are essential building blocks for the realization of secure quantum communication systems and quantum computers. By coupling these quantum systems with metasurfaces—creating so-called quantum metasurfaces—the team believes it is possible to achieve an unprecedented level of control over the emission of photons. “Just 20 years ago, the notion that photons could be manipulated at the subwavelength scale was thought to be some exotic thing, far fetched and of very limited use,” said Capasso. “But basic research opens up new avenues. In hindsight we know that new discoveries tend to lead to other technology developments in unexpected ways.” The research team includes experts in theoretical physics, metamaterials, nanophotonic circuitry, quantum devices, plasmonics, nanofabrication, and computational modeling. Co-principal investigator Marko Lončar is the Tiantsai Lin Professor of Electrical Engineering at Harvard SEAS. Co-PI Nanfang Yu, Ph.D. ’09, developed expertise in metasurfaces as a student in Capasso’s Harvard laboratory; he is now an assistant professor of applied physics at Columbia. Additional co-PIs include Alexandra Boltasseva and Vladimir Shalaev at Purdue, Mark Brongersma at Stanford, and Nader Engheta at the University of Pennsylvania. Lars Samuelson (Lund University) and Nikolay Zheludev (University of Southampton) will also participate. The bulk of the funding will support talented graduate students at the lead institutions. The project, titled “Active Metasurfaces for Advanced Wavefront Engineering and Waveguiding,” is among 24 planned MURI awards selected from 361 white papers and 88 detailed proposals evaluated by a panel of experts; each award is subject to successful negotiation. The anticipated amount of the Harvard-led grant is up to $6.5 million for three to five years. For anyone who’s not familiar (that includes me, anyway) with MURI awards, there’s this from Wikipedia (Note: links have been removed), Multidisciplinary University Research Initiative (MURI) is a basic research program sponsored by the US Department of Defense (DoD). Currently each MURI award is about $1.5 million a year for five years. I gather that in addition to the Air Force, the Army and the Navy also award MURI funds. Another Chad Mirkin, Northwestern University (Chicago, Illinois, US), research breakthrough has been announced (this man, with regard to research, is as prolific as a bunny) in a July 19, 2013 news item on ScienceDaily, A new low-cost, high-resolution tool is primed to revolutionize how nanotechnology is produced from the desktop, according to a new study by Northwestern University researchers. Currently, most nanofabrication is done in multibillion-dollar centralized facilities called foundries. This is similar to printing documents in centralized printing shops. Consider, however, how the desktop printer revolutionized the transfer of information by allowing individuals to inexpensively print documents as needed. This paradigm shift is why there has been community-wide ambition in the field of nanoscience to create a desktop nanofabrication tool. “With this breakthrough, we can construct very high-quality materials and devices, such as processing semiconductors over large areas, and we can do it with an instrument slightly larger than a printer,” said Chad A. Mirkin, senior author of the study. The July 19, 2013 Northwestern University news release (on EurekAlert), which originated the news item, provides details, The tool Mirkin’s team has created produces working devices and structures at the nanoscale level in a matter of hours, right at the point of use. It is the nanofabrication equivalent of a desktop printer. Without requiring millions of dollars in instrumentation costs, the tool is poised to prototype a diverse range of functional structures, from gene chips to protein arrays to building patterns that control how stem cells differentiate to making electronic circuits. “Instead of needing to have access to millions of dollars, in some cases billions of dollars of instrumentation, you can begin to build devices that normally require that type of instrumentation right at the point of use,” Mirkin said. The paper details the advances Mirkin’s team has made in desktop nanofabrication based upon easily fabricated beam-pen lithography (BPL) pen arrays, structures that consist of an array of polymeric pyramids, each coated with an opaque layer with a 100 nanometer aperture at the tip. Using a digital micromirror device, the functional component of a projector, a single beam of light is broken up into thousands of individual beams, each channeled down the back of different pyramidal pens within the array and through the apertures at the tip of each pen. The nanofabrication tool allows one to rapidly process substrates coated with photosensitive materials called resists and generate structures that span the macro-, micro- and nanoscales, all in one experiment. Key advances made by Mirkin’s team include developing the hardware, writing the software to coordinate the direction of light onto the pen array and constructing a system to make all of the pieces of this instrument work together in synchrony. This approach allows each pen to write a unique pattern and for these patterns to be stitched together into functional devices. “There is no need to create a mask or master plate every time you want to create a new structure,” Mirkin said. “You just assign the beams of light to go in different places and tell the pens what pattern you want generated.” Because the materials used to make the desktop nanofabrication tool are easily accessible, commercialization may be as little as two years away, Mirkin said. In the meantime, his team is working on building more devices and prototypes. In the paper, Mirkin explains how his lab produced a map of the world, with nanoscale resolution that is large enough to see with the naked eye, a feat never before achieved with a scanning probe instrument. Not only that, but closer inspection with a microscope reveals that this image is actually a mosaic of individual chemical formulae made up of nanoscale points. Making this pattern showcases the instrument’s capability of simultaneously writing centimeter-scale patterns with nanoscale resolution. Here’s a link to and a citation for the published paper, This paper is behind a paywall. As an alternative of sorts, you might like to check out this March 22, 2012 video of Mirkin’s presentation entitled, A Chemist’s Approach to Nanofabrication: Towards a “Desktop Fab” for the US Air Force Office of Scientific Research. 30 graduate students from across Canada came to the University of Toronto (U of T) this month (June 2011) to spend nine days learning how to make nano-sized devices. From the June 22, 2011 news item on Nanowerk, The summer institute was conceived by Professor Stewart Aitchison of electrical and computer engineering, and was hosted by U of T’s ECTI (Emerging Communications Technology Institute), which provides open research facilities for micro- and nanofabrication. Funding was received from the University’s Connaught Fund to foster connections and collaborations among students, postdoctoral fellows and other scholars. In six three-hour lab sessions, students learned how to operate equipment and perform the processes crucial to fabricating nano-scale devices. Aju Jugessur, a senior research associate with the ECTI, was part of the planning committee for the summer institute, and helped develop the training sessions. The unique nature of the training is what attracted Rahul Lodha, a doctoral student in materials engineering from the University of British Columbia. “I’m currently working with both micro- and nano-size particles, and what I’ve been doing is to add the nano-particles to micro-structures. What I’ve learned here is how to combine the two,” said Lodha. “What’s of great interest to me is how the properties of a material change when you get to the nano scale. Nano-titanium dioxide can be used for water purification, because when regular light hits it, ultra-violet rays are emitted in the range required to purify water. But regular sized titanium dioxide by itself doesn’t do this.” It’s exciting when discoveries and innovations are coming fast and furious but it can be difficult to figure out exactly how to proceed. I just read about a new table-top technique for nanofabrication that doesn’t require ultra-violet light. This stands in contrast to the proposed new maskwriting facility for nanofrabrication at Simon Fraser University (SFU). The processes described in the SFU release and in the article about the table-top technique for lithographic patterning seem very similar except one uses ultra violet-light and the other does not. At this pace it seems as if the SFU facility is likely to beocme obsolete soon. Still, it’s a long way from experiments in a laboratory to industrial use as planned at SFU and I don’t imagine that it makes much sense to wait for the new process. After all by the time that’s ready for ‘prime time’ use, there’ll probably be another discovery.
Determining how much power your home electronics take will help you efficiently calculate your monthly energy bill. If you have ever bought an electronic appliance, chances are you may have come across terms such as voltage (volts), wattage (watts), and amperage (amps). But what do watts and amps mean? And why should they matter? Having a better understanding of volts, watts, and amps is the key to minimizing your monthly utility bills. Want to know more about them and how to convert watts to amps and vice versa? Read on Understanding Watts & Amps Both volt-amperes and watts are measurement units for electrical energy. Watts indicate real-power, while volts-amperes indicate apparent-power. Typically, electronic products such as air conditioners and heat pumps display both these values to inform consumers about their energy requirements. The real-power in watts is the power that generates heat or performs work. It’s used to measure the rate of energy transfer or power flow in your appliance. Watt or Watts is a unit of power and is classified by the “W” symbol. The equation to derive watts is: W = V x A Amps or Amperes is the SI system’s base unit. It measures the volume of electrons in an electrical circuit. The capitalized “A” is a symbol for amps or amperes. Amperes measure electricity flow as the electric current. To better understand this, think of electric current as the water flowing through a hosepipe; the more it flows, the bigger the current is. The formula of amps is: A = W/V How To Convert Watts To Amps You have an air conditioner powered by 800 wattages. Do you know how many amperes that amounts to? It’s 5 amperes (or amps)! For many people living in different parts of the world, it may be beneficial to learn how to make this conversion. Therefore, here are three helpful ways you can use to convert watts to amperes: To convert power (watts) to current (amps), use the following electrical power formula: P = I x V Where P means power (in watts), I represents amperage or electrical current (in amperes or amps), and V signifies voltage or electrical potential (in volts). Since we have to find amperes, the equation will be: I = P/V Most electrical units have a standard voltage of 110 to 120 volts, whereas upgraded electric units use 220 volts. By using this formula, you can convert watts to amps directly if you know the voltage. For example: let’s suppose you have a 500 watts AC unit plugged into 120 volts voltage. Put these values into the amperes’ equation: I = P/V I = 500/120 = 4.17 Amps Watts To Amps Table If you don’t want to waste time doing all the computations, use the handy watts to amps table. One major benefit of this conversion table is that it’s much easier to read and displays conversions from 100 watts to amperes, 600 watts to amps, 3000 watts to amps, or more. So, if you want to know how many amps is 600 watts, how many amps is 1200 watts, or even how many amps is 1500 watts, you won’t need to calculate anything. All you have to do is refer to the table: \|Watts:\|\|Amps (at 120V):\| \|100 Watts to amps\|\|0.83 Amps\| \|200 Watts to amps\|\|1.67 Amps\| \|300 Watts to amps\|\|2.50 Amps\| \|400 Watts to amps\|\|3.33 Amps\| \|500 Watts to amps\|\|4.17 Amps\| \|600 Watts to amps\|\|5.00 Amps\| \|700 Watts to amps\|\|5.83 Amps\| \|800 Watts to amps\|\|6.67 Amps\| \|900 Watts to amps\|\|7.50 Amps\| \|1000 Watts to amps\|\|8.33 Amps\| \|1100 Watts to amps\|\|9.17 Amps\| \|1200 Watts to amps\|\|10.00 Amps\| \|1300 Watts to amps\|\|10.83 Amps\| \|1400 Watts to amps\|\|11.67 Amps\| \|1500 Watts to amps\|\|12.17 Amps\| \|1800 Watts to amps\|\|15.00 Amps\| \|2000 Watts to amps\|\|16.67 Amps\| \|2500 Watts to amps\|\|20.83 Amps\| \|3000 Watts to amps\|\|25.00 Amps\| If you want to convert watts to amps by yourself but do not want to do the maths, you can use an online converter. An online conversion calculator is more helpful if you are rummaging through the market purchasing a heat pump or an air conditioner for your house. It’s excellent for on-the-spot results! The watts to amps online converter is simple to use: input the watts (W) and volts (V), and you’ll get amps. Various Methods For Watts To Amps Calculation Fixed Voltage Calculation You can either use the formula I (A) = W / V or use an online converter calculator to convert watts to amps. However, if you want to calculate through a table, here are steps: - .Find a watts to amps conversion table. The table above works too. - .Search the power (watts) value you would like to convert. - .Once you pick a value, look for the corresponding electrical current (amperes) Here’s how you can calculate amps using watts and direct current (DC) voltage: - .Know your circuits’ power (measured in watts) - .Locate the voltage value on the device. You can find this at the same place you found the power value. - .Put these values into the ampere equation, which is I (A) = P (W) / V (v), and you’ll get amperes. AC Single Phase Calculation To calculate watts to amps for a single-phase alternative current (AC) circuit, follow the steps below: - .Know your power factor (ratio of real power to apparent power) - .Use the single-phase equation that is I (A) = P (W) / V (v) x PF where I signifies amps, P indicates watts, V implies volts, and PF means power factor. - .Input the values in the above equation, and you’ll have the answer. AC Three-Phase Calculation To calculate watts to amps using three-phase AC voltage, follow the steps below: - .Know your power factor. Find it on the schematic or circuit label. - .If you’re using line-to-line voltage, you can use the following equation to convert watts to amperes: (I (A) = P (W) / VL-L(V) x PF x √3) - .But if you use line-to-neutral voltage for three-phase alternative current circuits, than the equation is: I (A) = P (W) / V L-N(v) x PF x 3 - .Now, solve the equations to get amperes. The Relationship Between Watts, Amps & Energy Efficiency Each month your power company sends you an electricity bill, detailed in kW (one kilowatt = 1000 watts). Therefore, the more volts and amps your HVAC system and other electronic appliances use, the higher your energy bills will be — It’s as simple as that! It’s also important to know that even when your appliances are shut, they may draw some power (watts) if plugged in. This phenomenon is known as phantom load or vampire power. In short, more watts and amps indicate less energy efficiency and more energy cost. People Also Ask (FAQ) Who invented the watt unit? The watt unit was named after the famous eighteenth-century Scottish inventor, James Watt. It was first proposed by William Siemens in 1882. How many amps are in a watt? One watt has one ampere. How many amps is a 3000-watt generator? On 120 volts, a 3000-watt generator usually puts out 25 Amps. Do heaters and air conditioners use the same conversion metrics? Yes, air conditioners and heaters use the same conversion metrics such as EER, SEER, COP, etc. Do most home HVAC devices come in 120v or 240v? Though many everyday electrical appliances come in 120 and 240 volts, 120-volt outlets take a slight edge over the 240-volt ones. What is an amp breaker and when is it used? Amp breaker carries the amperage needed by the unit. When there’s more current in the system than it’s meant for, chances are it may start a fire. However, the amp breaker senses this and automatically interrupts the power flow. It’s essential to know how many watts and amps your electrical home appliance consumes. Being aware of how much you’re consuming will help you strategize your overall electricity usage. If your devices use excessive power, you’ll have to pay hefty bills. To avoid this situation, you should consider the watts and amps of a unit before investing in it. Last Updated on July 14, 2022 - Levoit 131 Air Purifier Won’t Turn On (Troubleshooting) - January 29, 2023 - How To Troubleshoot A Winix Air Purifier (Solved!) - January 29, 2023 - How To Make A DIY Air Purifier (5 Easy Steps!) - January 29, 2023
Graphic depiction of Pellet-Beam Propulsion for Breakthrough Space Exploration. Today, multiple space agencies are investigating cutting-edge propulsion ideas that will allow for rapid transits to other bodies in the Solar System. These include NASA’s Nuclear-Thermal or Nuclear-Electric Propulsion (NTP/NEP) concepts that could enable transit times to Mars in 100 days (or even 45) and a nuclear-powered Chinese spacecraft that could explore Neptune and its largest moon, Triton. While these and other ideas could allow for interplanetary exploration, getting beyond the Solar System presents some major challenges. As we explored in a previous article, it would take spacecraft using conventional propulsion anywhere from 19,000 to 81,000 years to reach even the nearest star, Proxima Centauri (4.25 light-years from Earth). To this end, engineers have been researching proposals for uncrewed spacecraft that rely on beams of directed energy (lasers) to accelerate light sails to a fraction of the speed of light. A new idea proposed by researchers from UCLA envisions a twist on the beam-sail idea: a pellet-beam concept that could accelerate a 1-ton spacecraft to the edge of the Solar System in less than 20 years. The concept, titled “Pellet-Beam Propulsion for Breakthrough Space Exploration,” was proposed by Artur Davoyan, an Assistant Professor of Mechanical and Aerospace Engineering at the University of California, Los Angeles (UCLA). The proposal was one of fourteen proposals chosen by the NASA Innovative Advanced Concepts (NIAC) program as part of their 2023 selections, which awarded a total of $175,000 in grants to develop the technologies further. Davoyan’s proposal builds on recent work with directed-energy propulsion (DEP) and light sail technology to realize a Solar Gravitational Lens.Continue reading… “A Novel Propulsion System Would Hurl Hypervelocity Pellets at a Spacecraft to Speed it up”
Ta-Nehisi Coates' landmark Atlantic article, The Case for Reparations , helps explain how this segregated society came to be: > The American real-estate industry believed segregation to be a moral principle. As late as 1950, the National Association of Real Estate Boards’ code of ethics warned that “a Realtor should never be instrumental in introducing into a neighborhood … any race or nationality, or any individuals whose presence will clearly be detrimental to property values.” A 1943 brochure specified that such potential undesirables might include madams, bootleggers, gangsters—and “a colored man of means who was giving his children a college education and thought they were entitled to live among whites.” The federal government concurred. It was the Home Owners’ Loan Corporation, not a private trade association, that pioneered the practice of redlining, selectively granting loans and insisting that any property it insured be covered by a restrictive covenant—a clause in the deed forbidding the sale of the property to anyone other than whites. Millions of dollars flowed from tax coffers into segregated white neighborhoods. “For perhaps the first time, the federal government embraced the discriminatory attitudes of the marketplace,” the historian Kenneth T. Jackson wrote in his 1985 book, Crabgrass Frontier, a history of suburbanization. “Previously, prejudices were personalized and individualized; FHA exhorted segregation and enshrined it as public policy. Whole areas of cities were declared ineligible for loan guarantees.” Redlining was not officially outlawed until 1968, by the Fair Housing Act. By then the damage was done—and reports of redlining by banks have continued. The federal government is premised on equal fealty from all its citizens, who in return are to receive equal treatment. But as late as the mid-20th century, this bargain was not granted to black people, who repeatedly paid a higher price for citizenship and received less in return. Plunder had been the essential feature of slavery, of the society described by Calhoun. But practically a full century after the end of the Civil War and the abolition of slavery, the plunder—quiet, systemic, submerged—continued even amidst the aims and achievements of New Deal liberals. Wait, wouldn't it be the other way around? Inflating property values would increase tax revenue. Even if they were subsidizing white home ownership they may have come out ahead. It's one of the driving forces of gentrification: if investing X gets the city X + Y in tax revenues then it's an economically sound decision. So the subsidy argument falls apart. If it doesn't cost the city money overall and white people end up paying more both for housing and in taxes then the problem with redlining lies elsewhere. (I am not trying to defend redlining, by the way.) So, no I don't think the subsidy argument falls apart. You still have the problem that subsidies are generally thought to cost money. If redlining makes the city money it goes from "this is evil and doesn't work economically" to "this is evil but it makes money." I'm starting to interpret the "don't complain about downvotes" guideline as "don't shed light on how this community misuses downvotes to quietly marginalize contrary views while maintaining the illusion of civil discourse." Really? Where are these videos. I think I only saw one video making the rounds where this was the case. The rest was speculation and mob mentality. "Hands up Don't shoot", for instance, never happened. "We’ve seen a community devastated by a terrorist attack that can only be described as pure, premeditated evil" This sort of "evil" happens almost every day in the inner city. Chicago, for instance, had 7+ shootings in only one weekend. Why are we focusing on the one rare nutcase and someone making it into proof that an entire community of people are racist (ironic that this is exactly what we are trying to stop: judging an entire group of people on one person's actions). How about the college event in Ohio that stated that only "African Americans" can attend and the guy (who was not African American" filming was pushed around and bullied?? How about the trans-gendered guest on the Dr. Drew HLN show that not only put his hand around the another guest's throat he was supposed to be debating, but threatened him with violence?? "It was only recently, when White-on-Black police brutality and terrorism began to surface in the news," How can you possibly call this "terrorism"?? In nearly all cases I've seen so far, the police offers asked the person in question to stop or comply..and they resisted, which resulted in a use of justified force. "that I was turned on to a stream of different voices. Reading the #drivingwhileblack tweets" Which is bullshit. I'm not black and have gotten stopped multiple times in my life for things I considered bullshit. If you give the cop an attitude, you will suffer the consequences. If you comply and are cool about everything the officer asks, he will let you go or write you a ticket. You need to think about it from his/her perspective: If you overpower the officer, they could lose their life. "I think we need to readily acknowledge that we are racist," Speak for yourself. I give everyone an equal chance, regardless of race. It's their actions later that determine whether I like them or not. I'm sick and tired of the thought police somehow trying to convince me that I'm racist. If the majority of people in this country were really racist, we wouldn't have people of color in pretty much every position of power and occupation..including the presidency. Check out the Implicit Association Test (https://en.wikipedia.org/wiki/Implicit-association_test) for an introduction to this line of research. You can still be doing/saying racist things while meaning well. The only solution is self-awareness and humility. Funny. I take the exact same anecdotes and conclude, "Wow, black Americans are pretty resilient." >Federal troops withdrew from the South in 1877. The dream of Reconstruction died. For the next century, political violence was visited upon blacks wantonly, with special treatment meted out toward black people of ambition. Black schools and churches were burned to the ground. Black voters and the political candidates who attempted to rally them were intimidated, and some were murdered. At the end of World War I, black veterans returning to their homes were assaulted for daring to wear the American uniform. The demobilization of soldiers after the war, which put white and black veterans into competition for scarce jobs, produced the Red Summer of 1919: a succession of racist pogroms against dozens of cities ranging from Longview, Texas, to Chicago to Washington, D.C. Organized white violence against blacks continued into the 1920s—in 1921 a white mob leveled Tulsa’s “Black Wall Street,” and in 1923 another one razed the black town of Rosewood, Florida—and virtually no one was punished. >Having been enslaved for 250 years, black people were not left to their own devices. They were terrorized. In the Deep South, a second slavery ruled. In the North, legislatures, mayors, civic associations, banks, and citizens all colluded to pin black people into ghettos, where they were overcrowded, overcharged, and undereducated. Businesses discriminated against them, awarding them the worst jobs and the worst wages. Police brutalized them in the streets. And the notion that black lives, black bodies, and black wealth were rightful targets remained deeply rooted in the broader society. Now we have half-stepped away from our long centuries of despoilment, promising, “Never again.” But still we are haunted. It is as though we have run up a credit-card bill and, having pledged to charge no more, remain befuddled that the balance does not disappear. The effects of that balance, interest accruing daily, are all around us. I disagree with some things you've said here but will just say 2 things: 1. I'm grateful you give everyone an equal chance. I thought I did too until I uncovered what I now believe to be an ingrained sort of bias. If you're free from that, more power to you! Far be it from me to tell you who you are. 2. I do believe that racism is one of the hidden engines of society, and inhabits each of us more than we know for that reason. That's why I was proposing to move the dialogue from an existential proof of racism to a question of how exactly it has shaped us. It's not (or doesn't feel like) "pseudoempathy" as another commenter put it. It feels like moving past denial to a more productive mode of engagement with this gnarled issue. Time and time again, studies demonstrate that we are all a little bit racist. Another commenter pointed out that the Implicit Association Test is a nice introduction to this research. You can take a test here: https://implicit.harvard.edu/implicit/takeatest.html Unconscious discrimination is a serious source of hardship for minorities and it's important to be aware of our bias. This is what the author of the article is getting at, and he is correct in the central point. However, we live in a culture where racists are the scum of the earth, fired from their jobs, ostracized, hated universally. You can even be fired from your job if you defend someone that's a racist Given how hated racism is in our culture right now, debate about racial issues is skewed in three ways. First, we might not take the side of the privileged in an issue because we fear we are being unconsciously racist. Second, we might not take the side of the privileged in an issue because we fear we might be called a racist, and, if not immediately fired from ours jobs, at least shunned. Finally, we might not take the side of the privileged in an issue, because even if taking their side would be technically correct, the privileged already have enough privilege, so to say, and by speaking out in favor of them we might be weakening the forces which are working hard to eliminate racism from society as much as possible. These biases can be just as unconscious. And they obscure the truth. Parent is also speaking out of fear. He has come to believe that acknowledging the existence of implicit racism, is the same as always siding with the minority in every case. Even in cases where the minority is clearly in the wrong. If you value truth, this is an abomination. If you value truth enough, it's something to get extremely angry about. By heavily downvoting parent's post, you are confirming these exact fears, while ignoring the true criticism hidden within. You are turning people away from the movement to eliminate racism, or at least making them less enthusiastic. And therefore you are doing more to slow the eradication of racism than posts like parent's ever would. Can we upvote parent for his bravery in speaking out against the bias our culture currently has? And calmly and rationally debate his concerns? That would be infinitely more convincing than the downvote button. (PaulHaugis does make some good points about lynchmods and bullying and it's weird that those posts get so heavily downvoted.) You should know that what you've said is considered totally racist these days and you'll have to write an article like the one you just criticized if you ever want to clear your name. I think people should be able to speak freely, but I won't lament systemic racism's demise. Would you mind quoting the part of his post where he says that racism doesn't exist? Dillon Taylor, Gilbert Collar, Christopher Roupe. My criticism is about placing small, isolated incidents under a microscope. A seemingly large amount of evidence gets national media coverage - so it appears to be a bigger problem than it is. Ebola fear-mongering is a good example of that. There are local pandemics of much more immediate danger that receive far less coverage for far less time than ebola did. It's confirmation bias at best and media propaganda at worst. The media is a business, people seem to forget that. They have no issues towing lines if it brings in more revenue. That also means they'll tug political ideologies that align closely with their viewers. I also have no issue admitting that a problem likely does exist. But it's much smaller than the media would have you believe: they just put it under a microscope. So to you, it seems much larger. That's the problem with microscopes. The 1,217 deadly police shootings from 2010 to 2012 captured in the federal data show that blacks, age 15 to 19, were killed at a rate of 31.17 per million, while just 1.47 per million white males in that age range died at the hands of police. One way of appreciating that stark disparity, ProPublica's analysis shows, is to calculate how many more whites over those three years would have had to have been killed for them to have been at equal risk. The number is jarring – 185, more than one per week. ProPublica's risk analysis on young males killed by police certainly seems to support what has been an article of faith in the African American community for decades: Blacks are being killed at disturbing rates when set against the rest of the American population. Our examination involved detailed accounts of more than 12,000 police homicides stretching from 1980 to 2012 contained in the FBI's Supplementary Homicide Report. The data, annually self-reported by hundreds of police departments across the country, confirms some assumptions, runs counter to others, and adds nuance to a wide range of questions about the use of deadly police force. Colin Loftin, University at Albany professor and co-director of the Violence Research Group, said the FBI data is a minimum count of homicides by police, and that it is impossible to precisely measure what puts people at risk of homicide by police without more and better records. Still, what the data shows about the race of victims and officers, and the circumstances of killings, are "certainly relevant," Loftin said. "No question, there are all kinds of racial disparities across our criminal justice system," he said. "This is one example." "21 times greater" is a great sound-bite but I honestly don't know what you'd expect. Take white males, make them 10 times as likely to be killed in general, 5-10 times as likely to be murderers, make them stronger, more likely to come from extreme poverty, give them a 50% high-school graduation rate, increase their rate of illiteracy, increase the rates at which they carry deadly weapons, increase how often they are violent in general, increase their sense of despair and hopelessness, break their family structure so many of them turn to street gangs for acceptance and give them a culture that openly glorifies violence against the police. Now they're still white males, how much would their chances of being on the losing end of a violent confrontation with the police increase? In other words there are many other causes and conditions that are at play here and assuming it's because cops are racist is absurd. The fact that so called "racists" are unable to freely express even a moderate opposition to the mainstream narrative on racism, is the best proof that this narrative is at best incomplete. e.g. without fear of losing ones job. If HN let us delete our names and/or comments it would be different.
debt slavery, also called debt servitude, debt bondage, or debt peonage, a state of indebtedness to landowners or merchant employers that limits the autonomy of producers and provides the owners of capital with cheap labour. Examples of debt slavery, indentured servitude, peonage, and other forms of forced labour exist around the world and throughout history, but the boundaries between them can be difficult to define (seeslavery). It is instructive to consider one prevalent system of debt slavery as a means of identifying the characteristics typical of the condition. This article therefore describes the system that existed among sharecroppers and landowners in the American South from the 1860s until World War II. After the end of the American Civil War and the abolition of slavery, many African Americans and some whites in the rural South made a living by renting small plots of land from large landowners who were usually white and pledging a percentage of their crops to the landowners at harvest—a system known as sharecropping. Landowners provided sharecroppers with land, seeds, tools, clothing, and food. Charges for the supplies were deducted from the sharecroppers’ portion of the harvest, leaving them with substantial debt to landowners in bad years. Sharecroppers would become caught in continual debt, especially during weak harvests or periods of low prices, such as when cotton prices fell in the 1880s and ’90s. Once in debt, sharecroppers were forbidden by law to leave the landowner’s property until their debt was paid, effectively putting them in a state of slavery to the landowner. Between 1880 and 1930 the proportion of Southern farms operated by the tenants increased from 36 to 55 percent. Indebted sharecroppers faced limited options. Racism and the legacy of slavery in the South made prospects for African Americans difficult after the Civil War, particularly because they represented the bulk of Southern sharecroppers. To gain freedom from their debt, farmers tried to make extra money in various ways, such as working on neighbouring farms and selling the eggs, milk, and vegetables they produced in addition to their main crop. Banks generally refused to lend money to sharecroppers, leaving them further dependent on landowners. An indebted sharecropper could continue to work for the same landowner and try to pay off the debt with the next year’s harvest or could begin farming for a different landowner with the debt built into the new contract. Finding themselves deeply enmeshed in that system of debt slavery and faced with limited opportunities to eliminate their debt, many farming families ran away or moved frequently in search of better employment opportunities. In response, landowners employed armed riders to supervise and discipline the farmers working on their land. Contracts between landowners and sharecroppers were typically harsh and restrictive. Many contracts forbade sharecroppers from saving cotton seeds from their harvest, forcing them to increase their debt by obtaining seeds from the landowner. Landowners also charged extremely high interest rates. Landowners often weighed harvested crops themselves, which presented further opportunities to deceive or extort sharecroppers. Immediately following the Civil War, financially distressed landowners could rent land to African American sharecroppers, secure their debt and labour, and then drive them away just before it was time to harvest the crops. Southern courts were unlikely to rule in favour of Black sharecroppers against white landowners. Despite the limited options it offered, sharecropping did provide more autonomy than did slavery for African Americans. Sharecropping also enabled families to stay together rather than face the possibility that a parent or child might be sold and forced to work on a different plantation. Those advantages, however, were meagre compared with the poverty and other hardships generated by debt slavery. Get a Britannica Premium subscription and gain access to exclusive content. The Great Depression had devastating effects on sharecroppers, as did the South’s continued overproduction and overemphasis on cotton production. Cotton prices fell dramatically after the stock market crash of 1929, and the ensuing downturn bankrupted farmers. The Agricultural Adjustment Act of 1933 offered farmers money to produce less cotton in order to raise prices. Many white landowners kept the money and allowed the land previously worked by African American sharecroppers to remain empty. Landowners also often invested the money in mechanization, reducing the need for labour and leaving more farming families, Black and white, underemployed and in poverty. That system of debt slavery continued in the South until after World War II, when it gradually died out as the mechanization of farming became widespread. So too, African Americans left the system as they moved to better-paying industrial jobs in the North during the Great Migration.
The center of a groupG, denoted Z(G), is the set of those group elements that commute with all elements of G, that is, the set of all h ∈ G such that hg = gh for all g ∈ G. Z(G) is always a normal subgroup of G. A group G is abelian if and only if Z(G) = G. The commutator of two elements g and h of a group G is the element [g, h] = g−1h−1gh. Some authors define the commutator as [g, h] = ghg−1h−1 instead. The commutator of two elements g and h is equal to the group's identity if and only if g and h commutate, that is, if and only if gh = hg. with strict inclusions, such that each Hi is a maximal strict normal subgroup of Hi+1. Equivalently, a composition series is a subnormal series such that each factor groupHi+1 / Hi is simple. The factor groups are called composition factors. Two elements x and y of a group G are conjugate if there exists an element g ∈ G such that g−1xg = y. The element g−1xg, denoted xg, is called the conjugate of x by g. Some authors define the conjugate of x by g as gxg−1. This is often denoted gx. Conjugacy is an equivalence relation. Its equivalence classes are called conjugacy classes. Two subgroups H1 and H2 of a group G are conjugate subgroups if there is a g ∈ G such that gH1g−1 = H2. A cyclic group is a group that is generated by a single element, that is, a group such that there is an element g in the group such that every other element of the group may be obtained by repeatedly applying the group operation to g or its inverse. The direct product of two groups G and H, denoted G × H, is the cartesian product of the underlying sets of G and H, equipped with a component-wise defined binary operation (g1, h1) · (g2, h2) = (g1 ⋅ g2, h1 ⋅ h2). With this operation, G × H itself forms a group. A finite group is a group of finite order, that is, a group with a finite number of elements. finitely generated group A group G is finitely generated if there is a finite generating set, that is, if there is a finite set S of elements of G such that every element of G can be written as the combination of finitely many elements of S and of inverses of elements of S. A generating set of a group G is a subset S of G such that every element of G can be expressed as a combination (under the group operation) of finitely many elements of S and inverses of elements of S. Given two groups (G, ∗) and (H, ·), a homomorphism from G to H is a functionh : G → H such that for all a and b in G, h(a∗b) = h(a) · h(b). index of a subgroup The index of a subgroupH of a group G, denoted \|G : H\| or [G : H] or (G : H), is the number of cosets of H in G. For a normal subgroupN of a group G, the index of N in G is equal to the order of the quotient groupG / N. For a finite subgroup H of a finite group G, the index of H in G is equal to the quotient of the orders of G and H. Given two groups (G, ∗) and (H, ·), an isomorphism between G and H is a bijectivehomomorphism from G to H, that is, a one-to-one correspondence between the elements of the groups in a way that respects the given group operations. Two groups are isomorphic if there exists a group isomorphism mapping from one to the other. Isomorphic groups can be thought of as essentially the same, only with different labels on the individual elements. For a subset S of a group G, the normalizer of S in G, denoted NG(S), is the subgroup of G defined by A normal series of a group G is a sequence of normal subgroups of G such that each element of the sequence is a normal subgroup of the next element: A subgroupN of a group G is normal in G (denoted ) if the conjugation of an element n of N by an element g of G is always in N, that is, if for all g ∈ G and n ∈ N, gng−1 ∈ N. A normal subgroup N of a group G can be used to construct the quotient groupG/N (G mod N). The order of an elementg of a group G is the smallest positiveintegern such that gn = e. If no such integer exists, then the order of g is said to be infinite. The order of a finite group is divisible by the order of every element. An element g of a group G is called a real element of G if it belongs to the same conjugacy class as its inverse, that is, if there is a h in Gwith , where is defined as h−1gh. An element of a group G is real if and only if for all representations of G the trace of the corresponding matrix is a real number. A subgroup of a group G is a subsetH of the elements of G that itself forms a group when equipped with the restriction of the group operation of G to H×H. A subset H of a group G is a subgroup of G if and only if it is nonempty and closed under products and inverses, that is, if and only if for every a and b in H, ab and a−1 are also in H. A subgroup series of a group G is a sequence of subgroups of G such that each element in the series is a subgroup of the next element: A subgroupH of a group G is a subnormal subgroup of G if there is a finite chain of subgroups of the group, each one normal in the next, beginning at H and ending at G. Isomorphic groups. Two groups are isomorphic if there exists a group isomorphism mapping from one to the other. Isomorphic groups can be thought of as essentially the same, only with different labels on the individual elements. One of the fundamental problems of group theory is the classification of groupsup to isomorphism. Simple group. Simple groups are those groups having only and themselves as normal subgroups. The name is misleading because a simple group can in fact be very complex. An example is the monster group, whose order is about 1054. Every finite group is built up from simple groups via group extensions, so the study of finite simple groups is central to the study of all finite groups. The finite simple groups are known and classified. The structure of any finite abelian group is relatively simple; every finite abelian group is the direct sum of cyclic p-groups. This can be extended to a complete classification of all finitely generated abelian groups, that is all abelian groups that are generated by a finite set. The situation is much more complicated for the non-abelian groups. Free group. Given any set , one can define a group as the smallest group containing the free semigroup of . The group consists of the finite strings (words) that can be composed by elements from , together with other elements that are necessary to form a group. Multiplication of strings is defined by concatenation, for instance Every group is basically a factor group of a free group generated by . Please refer to presentation of a group for more explanation. One can then ask algorithmic questions about these presentations, such as: Do these two presentations specify isomorphic groups?; or Does this presentation specify the trivial group? The general case of this is the word problem, and several of these questions are in fact unsolvable by any general algorithm. Group representation (not to be confused with the presentation of a group). A group representation is a homomorphism from a group to a general linear group. One basically tries to "represent" a given abstract group as a concrete group of invertible matrices which is much easier to study.
What Is Schizophrenia? Schizophrenia is a chronic brain disorder that affects about one percent of the population. When schizophrenia is active, symptoms can include delusions, hallucinations, trouble with thinking and concentration, and lack of motivation. However, when these symptoms are treated, most people with schizophrenia will greatly improve over time. Schizophrenia is a chronic brain disorder that is usually progressively debilitating without medical treatment. According to the National Institute of Mental Health, about 1 percent of the population currently suffers from schizophrenia. While there is no known cure for this severe mental illness, new medications can help alleviate many of the disease’s severe symptoms with fewer motor side effects than older medications. Schizophrenia is a serious mental illness that interferes with a person’s ability to think clearly, manage emotions, make decisions and relate to others. It is a complex, long-term medical illness, affecting about 1% of Americans. Although schizophrenia can occur at any age, the average age of onset tends to be in the late teens to the early 20s for men, and the late 20s to early 30s for women. It is uncommon for schizophrenia to be diagnosed in a person younger than 12 or older than 40. It is possible to live well with schizophrenia. The number of reported cases is split evenly between men and women, although schizophrenia tends to appear earlier for men—usually in the late teens or early 20s—compared to women, who generally begin to display symptoms in their 20s or early 30s. Onset of schizophrenia is rare before puberty and uncommon after age 45. While there is no cure for schizophrenia, research is leading to new, safer treatments. Experts also are unraveling the causes of the disease by studying genetics, conducting behavioral research, and by using advanced imaging to look at the brain’s structure and function. These approaches hold the promise of new, more effective therapies. The complexity of schizophrenia may help explain why there are misconceptions about the disease. Schizophrenia does not mean split personality or multiple-personality. Most people with schizophrenia are not dangerous or violent. They also are not homeless nor do they live in hospitals. Most people with schizophrenia live with family, in group homes or on their own. Research has shown that schizophrenia affects men and women about equally but may have an earlier onset in males. Rates are similar in all ethnic groups around the world. Schizophrenia is considered a group of disorders where causes and symptoms vary considerable between individuals. When the disease is active, it can be characterized by episodes in which the patient is unable to distinguish between real and unreal experiences. As with any illness, the severity, duration and frequency of symptoms can vary; however, in persons with schizophrenia, the incidence of severe psychotic symptoms often decreases during a patient’s lifetime. Not taking medications as prescribed, use of alcohol or illicit drugs, and stressful situations tend to increase symptoms. Symptoms fall into several categories: - Positive psychotic symptoms: Hallucinations, such as hearing voices, paranoid delusions and exaggerated or distorted perceptions, beliefs and behaviors. - Negative symptoms: A loss or a decrease in the ability to initiate plans, speak, express emotion or find pleasure. - Disorganization symptoms: Confused and disordered thinking and speech, trouble with logical thinking and sometimes bizarre behavior or abnormal movements. - Impaired cognition: Problems with attention, concentration, memory and declining educational performance. Symptoms usually first appear in early adulthood. Men often experience symptoms in their early 20s and women often first show signs in their late 20s and early 30s. More subtle signs may be present earlier, including troubled relationships, poor school performance and reduced motivation. It is rarely diagnosed in children or adolescents. Before a diagnosis can be made, however, a psychiatrist should conduct a thorough medical examination to rule out substance misuse or other medical illnesses whose symptoms mimic schizophrenia. Schizophrenia presents differently in different people. Symptoms tend to appear gradually and can easily go unnoticed by friends and family in the beginning. However, in some cases, symptoms of schizophrenia occur suddenly and can be quite dramatic. As the illness advances, the symptoms can become more bizarre and severe. People with schizophrenia tend to have psychotic symptoms, such as hearing voices when no one is speaking or insisting that other people are listening to their thoughts or attempting to control them. Many people with schizophrenia have active psychotic episodes, a state where hallucinations and/or delusions occur and they lose touch with reality. Most people with schizophrenia experience at least one relapse after their first such episode. Other early signs of the disease include increasing social withdrawal and loss of interest in normal pursuits, unusual behavior or a decrease in overall functioning, often before the delusions and hallucinations begin. These are often the first warning signs that alert friends and family to a problem. As the illness progresses, a person’s speech and behavior tend to become progressively disorganized and confused, and their work performance usually deteriorates. Eventually, the symptoms become more extreme, appearing as if the person has undergone a dramatic personality change. If these and other symptoms persist for six months or longer and no external cause such as the effects of illicit drug use or a medical illness is detected, the person is usually diagnosed with schizophrenia. People who have schizophrenia are more likely to commit suicide than people in the general population, with an estimated 10 percent of all people diagnosed with schizophrenia ending their life this way. Young adult males are most likely to commit suicide. Role of Genetics Genetics appear to play a role in schizophrenia. However, genetics alone do not explain the disease. An identical twin of someone with schizophrenia has a 40 percent to 65 percent chance of developing the illness, while children who have a first-degree relative with the disease have about 10 times the risk of developing it than that of someone who does not have a family member with the illness. People with a second-degree relative, such as an aunt, grandparent or cousin with schizophrenia, also have an increased risk. Researchers believe multiple genes are involved in the risk for schizophrenia but that no single gene causes the disease by itself. Recent research shows certain gene mutations occur among families in which several members have the illness, but that these abnormalities are not found in other families. This suggests that mutations may occur in any of a number of genes that might result in schizophrenia. Affected genes have been linked to various aspects of brain functioning that could account for the symptoms of schizophrenia and could affect a patient’s ability to function. Future research may be able to identify who is at risk for developing the disease based on genetic profiles. Other factors, such as prenatal difficulties (including viral infections and complications around the time of birth), also appear to influence the development of the disease. In addition, some illicit drugs, such as marijuana and stimulants like cocaine and amphetamines, may make schizophrenia symptoms worse. Research has found increasing evidence of a link between marijuana use at a young age and a greater risk of developing schizophrenia. Role of Brain Abnormalities Schizophrenia is a brain disorder, with many abnormalities of the brain structure, function and chemistry. For example, several studies find people with schizophrenia have enlarged ventricles, cavities in the brain filled with cerebrospinal fluid. In addition, some studies find that people with schizophrenia tend to have specific areas of the brain that are smaller compared to people without schizophrenia, and that some of these areas have lower metabolic activity. However, scientists are careful to note that these and other abnormalities are subtle, are not found in all cases and could be present in people who never develop schizophrenia. In addition, studies of brain tissue following death have revealed changes in the distribution or characteristics of brain cells in people with schizophrenia that may have taken place before birth as well as during other times of change in brain development. Considerable brain restructuring occurs during adolescence and may be further altered in schizophrenia, resulting in the characteristic onset of symptoms during this crucial developmental stage in life. Scientists are working to better determine exactly how schizophrenia develops. A challenging part of diagnosing schizophrenia is that there is no way to confirm it with laboratory studies, so clinicians rely on a pattern of psychotic symptoms and functional deterioration. Many of the symptoms can be found in other mental disorders, which can present further challenges. For example, some individuals with schizophrenia have prolonged periods of elation or depression, which can be confused with bipolar disorder (also called manic depression) or major depressive disorder. People with bipolar disorder and major depression can also experience psychotic symptoms. These conditions need to be ruled out before diagnosing schizophrenia. A mental health professional such as a psychologist or psychiatrist typically diagnoses schizophrenia. The clinician begins with a complete medical history and physical examination followed by blood and urine tests to rule out other medical causes for the symptoms. For instance, commonly abused drugs such as cocaine, methamphetamines or LSD can cause symptoms that mimic schizophrenia (including hallucinations or paranoia). Interestingly, people who have schizophrenia tend to abuse drugs and alcohol at a higher rate than the general population. So just because someone is abusing drugs doesn’t mean the person doesn’t also have schizophrenia. Psychiatrists often diagnose schizophrenia when someone has had at least two active symptoms of the disorder, such as a psychotic episode that includes delusions and hallucinations, for at least a month, with other symptoms, such as a decline in functioning and disturbed thoughts lasting six months or longer. Schizophrenia appears to improve and worsen over the course of the illness. When it improves, the person suffering from the disease may appear perfectly normal. Unfortunately, this is when many people decide to stop taking their medication and relapse. During an acute psychotic episode, patients often lose their ability to think logically or may lose their perception of who they are or of others around them. Most people with schizophrenia also have social and occupational problems, including problems in the workplace, with interpersonal relationships and in the way they care for themselves. Symptoms of schizophrenia are usually split into positive, negative and neurocognitive categories. Positive symptoms are unusual thoughts, perceptions or distortion of normal functions. They include: - Delusions. These are firmly held erroneous beliefs that result from distortions or exaggerations of reasoning or misinterpretations of a person’s perceptions or experiences. Common delusions include unrealistic beliefs that the person is being watched or followed (e.g. paranoia). - Hallucinations. These are abnormalities of perception that can occur in any of the senses, although auditory hallucinations (hearing voices even though no one is speaking) are most common. These voices often insult the person, comment on his or her behavior or give commands. Visual hallucinations are the second most common type. - Thought disorders. These are dysfunctional or unusual ways of thinking. “Disorganized thinking” is when a person can’t organize or connect his or her thoughts. Speech may be garbled and hard to understand. “Thought blocking” is when a person stops talking in the middle of a thought. Another form of thought disorders may cause a person to make up meaningless words. Negative symptoms relate to disruptions of normal emotions, motivation and drive. Symptoms to look for include: - “Flat affect,” when a person’s emotional expressions go “flat,” and there is little change in their facial expressions, voice or body language. The person may avoid eye contact. - Lack of pleasure in everyday life and/or needing help with everyday activities. May include a neglect of basic personal hygiene. - Speaking little, even when spoken to, or giving only disinterested replies. - Disinterest in social interaction and retreat into an “inner world.” Neurocognitive symptoms of schizophrenia are symptoms that have to do with the person’s ability to think and reason. They include: - Problems with attention - Trouble with certain types of memory - Problems with functions that allow one to plan and organize Some patients with schizophrenia also experience abnormal movements, such as twitching, repetitive gestures or catatonia (for example, maintaining unusual positions or not moving or responding at all). For reasons that are not understood, more severe forms of catatonia were more common before the availability of antipsychotic medications. On the other hand, certain motor movements, such as tremor, rigidity and restlessness, commonly occur as side effects to antipsychotic medications. Several subtypes of schizophrenia have been suggested, based on a person’s range and intensity of symptoms. There several recognized types of schizophrenia, including the following: - Paranoid schizophrenia. A person experiences predominantly positive symptoms (delusions and hallucinations), without a lot of disorganization or negative symptoms. The person may feel suspicious, persecuted and/or grandiose. - Disorganized schizophrenia (also called hebephrenic schizophrenia). People with disorganized schizophrenia have difficulty with logical, coherent thinking and speech. They also sometimes lack motivation, emotion and the ability to feel pleasure. - Catatonic schizophrenia. People with catatonic schizophrenia exhibit extreme inactivity or activity that’s disconnected from his or her environment or encounters with other people. These episodes can last for minutes to hours. - Undifferentiated schizophrenia. People with undifferentiated schizophrenia meet diagnostic criteria for schizophrenia, but not the paranoid, disorganized or catatonic subtypes. - Residual schizophrenia. People with residual schizophrenia have a history of schizophrenic episodes characterized by negative symptoms or mild positive symptoms. People with this form of schizophrenia differ from those with other forms in that they lack prominent psychotic symptoms. Although schizophrenia is usually a lifelong illness, some people develop all the symptoms of schizophrenia that resolve spontaneously. When the symptoms last less than one month, a diagnosis of brief psychotic disorder is given. When symptoms last less than six months, the diagnosis schizophreniform disorder is used. Unfortunately, schizophreniform disorder is rare, and most people progress to chronic schizophrenia The best treatment for any individual suffering from schizophrenia blends a combination of antipsychotic medications with psychosocial interventions. Psychosocial interventions include supportive psychotherapy, illness management skills, integrated treatment for any coexisting substance abuse, family participation in therapy and psychosocial and vocational rehabilitation. People with schizophrenia who need a high degree of social services should receive assistance from an interdisciplinary treatment team. Antipsychotic medications for schizophrenia can eliminate or reduce the hallucinations and delusions of the disorder. These drugs, which help restore biochemical imbalances, may also help people regain their coherent thinking abilities. The older “conventional” or “typical” antipsychotic drugs were introduced in the 1950s. Over the years, studies have found that these drugs are very effective in treating acute episodes of delusions or hallucinations and can provide long-term maintenance and prevention of future schizophrenic relapses. However, these drugs can cause unpleasant side effects such as dry mouth, constipation, blurred vision and difficulty urinating. These types of side effects are called “anticholinergic.” These medications can also cause extrapyramidal side effects (EPS), which affect how the body moves. For example, restlessness, tremors and slowing of normal gestures and movements can occur after days to weeks of treatment. Some patients report muscle spasms and cramps in the head and neck area, as well as stiff muscles throughout their body. Tardive dyskinesia (TD) is a type of EPS that can occur after months or years of treatment with antipsychotic medications. The risk of TD increases the longer antipsychotic medications are taken. This condition is more common among older patients. It involves small involuntary movements of the fingers, tongue, lips, face or jaw. The symptoms tend to get worse and turn into thrusting and rolling motions of the tongue, lip smacking, grimacing or uncontrollable sucking motions. Involuntary movements of the hands, feet, neck and shoulders can also occur. Tardive dyskinesia can be a permanent, irreversible side effect. These medications can also interfere with reproductive hormones, affecting a woman’s menstrual cycles and fertility or causing breast enlargement, milk secretion or sexual side effects in both men and women. Sedation and dizziness are also relatively common side effects. Because of the potential side effects associated with these medications, it is important that any medication regimen is tailored to the individual. You should work closely with your doctor to achieve the most benefit with the fewest problems from the medication. Sometimes adding another drug can help reduce certain antipsychotic-related side effects and possibly improve their effectiveness. Examples of older “typical” antipsychotic medications include chlorpromazine (Thorazine), haloperidol (Haldol), perphenazine (Trilafon) and fluphenazine (Prolixin). Over the past 20 years, pharmaceutical manufacturers have introduced a newer generation of antipsychotic drugs known as novel or “atypical” antipsychotics. The major advantage of these medications is a decreased risk of some side effects, such as EPS. These medications include clozapine (Clozaril), olanzapine (Zyprexa), quetiapine (Seroquel), risperidone (Risperdal), ziprasidone (Geodon), paliperidone (Invega) and aripiprazole (Abilify). Clozapine is unique in that it is the most effective antipsychotic medication and is not typically associated with EPS or TD. However, patients taking clozapine must be monitored closely with regular blood tests because the medicine can cause a blood disorder called agranulocytosis, a disorder in which there are an insufficient number of white blood cells. Although it only occurs in a very small percentage of those taking clozapine, it can prove fatal if not caught and treated immediately. Studies find the atypical antipsychotics are about as effective as the older conventional medications but have fewer extrapyramidal side effects. It has also been suggested that the atypical antipsychotics may improve anxiety, depression and cognitive symptoms. As a result, these newer drugs have replaced older drugs as “first line” therapy in the United States. However, this new generation of medications has its own potential side effects, including sedation, significant weight gain and sexual dysfunction. Some are associated with a higher incidence of diabetes or high cholesterol, particularly in those who gain weight. While they don’t typically interfere with menstruation as much as the typical antipsychotics, there is little information about the safety or impact of antipsychotic treatment during pregnancy and breastfeeding. If you are taking these medications and considering getting pregnant, talk to your health care professional first. Perhaps the biggest challenge facing people with schizophrenia and their families is the high rate at which many stop taking their medication. Some stop treatment because they don’t really believe they are ill. Others have such extreme disorganized thinking they can’t remember to take their regular medication doses. Injectable medications that last for several weeks can sometimes help in these situations. Patients also stop taking their medication because of difficulties with side effects. Substance abuse can also interfere with the efficacy of the medication, influencing patients’ compliance. Finally, uninformed family members may suggest patients stop taking their medication because the symptoms seem to have disappeared. That’s why it’s important for a health care professional to stay involved in the treatment of someone with schizophrenia, even if they seem to be doing fine. In unusual circumstances, electroconvulsive therapy (ECT) can be used to treat schizophrenia. During ECT, an electrical current passes through the patient’s brain inducing a seizure. This treatment may be used if the person hasn’t responded to antipsychotic medication or, in some circumstances, for those in catatonic states. Once the delusions and hallucinations of schizophrenia subside, patients also can benefit from psychosocial therapies that help them improve their social skills and teach them how to live independently. These sessions can be provided in group, family or individual settings. Many therapists use behavioral learning techniques, including coaching, modeling and positive reinforcement, all of which can make a big difference in helping patients cope with other stresses in their lives that could contribute to relapses. Psychoeducational family therapy is another segment of treatment that many psychiatrists see as necessary to help prevent relapses. These family education training sessions teach family members and close friends how to recognize the early warning signs of a relapse and what to do before the situation worsens. Improving communication and problem-solving skills among family members and the person with schizophrenia can help reduce the potential for relapse. For individuals suffering from schizophrenia who need community services for support, clinical case managers can coordinate the necessary services and make sure medical and psychiatric treatments are addressed. These case managers can also play a key role in crisis management if the person doesn’t have a support network of family and friends. Typically, a health care provider will prescribe antipsychotics to relieve symptoms of psychosis, such as delusions and hallucinations. Due to lack of awareness of having an illness and the serious side effects of medication used to treat schizophrenia, people who have been prescribed them are often hesitant to take them. First Generation (typical) Antipsychotics These medications can cause serious movement problems that can be short (dystonia) or long term (called tardive dyskinesia), and also muscle stiffness. Other side effects can also occur. - Chlorpromazine (Thorazine) - Fluphenazine (Proxlixin) - Haloperidol (Haldol) - Loxapine (Loxitane) - Perphenazine (Trilafon) - Thiothixene (Navane) - Trifluoperazine (Stelazine) Second Generation (atypical) Antipsychotics These medications are called atypical because they are less likely to block dopamine and cause movement disorders. They do, however, increase the risk of weight gain and diabetes. Changes in nutrition and exercise, and possibly medication intervention, can help address these side effects. - Aripiprazole (Abilify) - Asenapine (Saphris) - Clozapine (Clozaril) - Iloperidone (Fanapt) - Lurasidone (Latuda) - Olanzapine (Zyprexa) - Paliperidone (Invega) - Risperidone (Risperdal) - Quetiapine (Seroquel) - Ziprasidone (Geodon) One unique second generation antipsychotic medication is called clozapine. It is the only FDA approved antipsychotic medication for the treatment of refractory schizophrenia and has been the only one indicated to reduce thoughts of suicide. However, it does have multiple medical risks in addition to these benefits. Read a more complete discussion of these risk and benefits. Cognitive behavioral therapy Cognitive behavioral therapy (CBT) is an effective treatment for some people with affective disorders. With more serious conditions, including those with psychosis, additional cognitive therapy is added to basic CBT (CBTp). CBTp helps people develop coping strategies for persistent symptoms that do not respond to medicine. Supportive psychotherapy is used to help a person process his experience and to support him in coping while living with schizophrenia. It is not designed to uncover childhood experiences or activate traumatic experiences, but is rather focused on the here and now. Cognitive Enhancement Therapy (CET) Cognitive Enhancement Therapy (CET) works to promote cognitive functioning and confidence in one’s cognitive ability. CET involves a combination of computer based brain training and group sessions. This is an active area of research in the field at this time. People who engage in therapeutic interventions often see improvement, and experience greater mental stability. Psychosocial treatments enable people to compensate for or eliminate the barriers caused by their schizophrenia and learn to live successfully. If a person participates in psychosocial rehabilitation, she is more likely to continue taking their medication and less likely to relapse. Some of the more common psychosocial treatments include: - Assertive Community Treatment (ACT) provides comprehensive treatment for people with serious mental illnesses, such as schizophrenia. Unlike other community-based programs that connect people with mental health or other services, ACT provides highly individualized services directly to people with mental illness. Professionals work with people with schizophrenia and help them meet the challenges of daily life. ACT professionals also address problems proactively, prevent crises, and ensure medications are taken. - Peer support groups like NAMI Peer-to-Peer encourage people’s involvement in their recovery by helping them work on social skills with others. Complementary Health Approaches Omega-3 fatty acids, commonly found in fish oil, have shown some promise for treating and managing schizophrenia. Some researchers believe that omega-3 may help treat mental illness because of its ability to help replenish neurons and connections in affected areas of the brain. Physical Health. People with schizophrenia are subject to many medical risks, including diabetes and cardiovascular problems, and also smoking and lung disease. For this reason, coordinated and active attention to medical risks is essential. Substance Abuse. About 25% of people with schizophrenia also abuse substances such as drugs or alcohol. Substance abuse can make the treatments for schizophrenia less effective, make people less likely to follow their treatment plans, and even worsen their symptoms. Researchers believe that a number of genetic and environmental factors contribute to causation, and life stresses may play a role in the disorder’s onset and course. Since multiple factors may contribute, scientists cannot yet be specific about the exact cause in individual cases. Since the term schizophrenia embraces several different disorders, variation in cause between cases is expected. Recovery and Rehabilitation Treatment can help many people with schizophrenia lead highly productive and rewarding lives. As with other chronic illnesses, some patients do extremely well while others continue to be symptomatic and need support and assistance. After the symptoms of schizophrenia are controlled, various types of therapy can continue to help people manage the illness and improve their lives. Therapy and supports can help people learn social skills, cope with stress, identify early warning signs of relapse and prolong periods of remission. Because schizophrenia typically strikes in early adulthood, individuals with the disorder often benefit from rehabilitation to help develop life-management skills, complete vocational or educational training, and hold a job. For example, supported-employment programs have been found to help persons with schizophrenia obtain self-sufficiency. These programs provide people with severe mental illness with competitive jobs in the community. Many people living with schizophrenia receive emotional and material support from their family. Therefore, it is important that families be provided with education, assistance and support. Such assistance has been shown to help prevent relapses and improve the overall mental health of the family members as well as the person with schizophrenia. Living With Schizophrenia Optimism is important and patients, family members and mental health professionals need to be mindful that many patients have a favorable course of illness, that challenges can often be addressed, and that patients have many personal strengths that can be recognized and supported. - Schizoaffective disorder - Delusional disorder - Brief psychotic disorder - Schizophreniform disorder Facts to Know - About 1 percent of the population has schizophrenia, according to the National Institute of Mental Health. - The number of reported cases is split between men and women, although schizophrenia tends to appear earlier for men—usually in the late teens or early 20s—compared to women, who generally begin to show signs of trouble in their 20s or early 30s. Onset of schizophrenia is rare before puberty and uncommon after age 45. - People with schizophrenia tend to have psychotic symptoms, such as hearing voices when no one is speaking or insisting that other people are listening to their thoughts or attempting to control them. Many people with schizophrenia have active psychotic episodes, a state where hallucinations and/or delusions occur and they lose touch with reality. Most people with schizophrenia experience at least one relapse after their first such episode. Other early signs of the disease include increasing social withdrawal and loss of interest in normal pursuits, unusual behavior or a decrease in overall functioning, often before the delusions and hallucinations begin. These are often the first warning signs that alert friends and family to a problem. - Genetics appears to play a role in schizophrenia. However, genetics alone does not explain the disease. An identical twin of someone with schizophrenia has a 40 percent to 65 percent chance of developing the illness, while children who have a first-degree relative with the disease have about a 10 percent risk of developing it themselves. People with a second-degree relative, such as an aunt, grandparent or cousin, also have an increased risk. - Researchers find that multiple genes are involved in the risk for schizophrenia, but they are not the only cause. Other factors, such as prenatal difficulties (including viral infections and complications around the time of birth), also appear to influence the development of the disease. Researchers suspect that the disease may be the result of inappropriate connections between neurons in the brain that form during fetal development or puberty, times of significant changes in the brain. - There is no way to definitively diagnose schizophrenia with laboratory studies, so clinicians rely on a pattern of psychotic symptoms and functional deterioration, as well as eliminating other possible causes of symptoms, to make a diagnosis. Psychiatrists often diagnose schizophrenia when someone has had active symptoms of the disorder, such as a psychotic episode that includes delusions and hallucinations, for at least a month, with other symptoms, such as decline in functioning and disturbed thought, lasting six months or longer. Many other conditions can resemble schizophrenia, so diagnosis should be performed by an experienced mental health professional. - Schizophrenia appears to improve and worsen in cycles. When it improves, the person suffering from the disease may appear perfectly normal. Unfortunately, this is when many people decide to stop taking their medication and relapse. However, during the acute or psychotic phase, individuals with schizophrenia think without logical reasoning and may lose perception of who they or others around them are. - In most cases, schizophrenia is a chronic condition requiring lifelong treatment. The best treatment blends a combination of antipsychotic medications with psychosocial interventions such as supportive psychotherapy, family participation in therapy and psychosocial and vocational rehabilitation. During crisis periods or times of severe symptoms, hospitalization may be required. Schizophrenia treatment is usually guided by an experienced psychiatrist, but it may also involve psychologists, social workers, psychiatric nurses and possibly a case manager. - What is schizophrenia? Schizophrenia is a chronic brain disorder that is often progressively debilitating for individuals unless they seek intervention through medications, psychosocial treatments and other types of care. - Are women at greater risk of developing the disorder compared with men? The number of reported cases is split rather evenly between men and women, although schizophrenia tends to present itself at different ages for the two sexes. Onset of the disorder tends to occur earlier for men—usually in the late teens or early 20s—compared to women, who generally begin to show signs of trouble in their 20s or early 30s. An identical twin of someone with schizophrenia has about a 40 percent to 65 percent chance of developing the illness. Interestingly, researchers have found there is a further heightened risk for a female identical twin to develop schizophrenia if her twin has the illness. Women tend to have a less severe form of the disorder and respond better to treatment. - Am I at greater risk of developing schizophrenia if I have a close relative who has been diagnosed with the disorder? If you have a close relative with the disease, you are more likely to develop it compared with someone who has no close relatives with schizophrenia. Your risk is also slightly elevated if you have a secondary family member with the disease, such as an aunt, uncle, grandparent or cousin. - What are the early warning signs of schizophrenia? Most people who develop schizophrenia begin having delusions and hallucinations. Other early signs include increasing social withdrawal, loss of pleasure in everyday life, unusual behavior or decreases in overall functioning before the delusions and hallucinations begin. Speech and behavior tend to become progressively disorganized and confused, and work performance often deteriorates. - What are my treatment options if I am diagnosed with the disorder? The primary mode of treatment for schizophrenia is a regimen of antipsychotic medications that make a significant difference in eliminating or significantly reducing the hallucinations and delusions. These drugs, which help restore biochemical imbalances to normal levels, also help the patient regain coherent thinking abilities. However, a major drawback to these medications is a wide array of side effects, some of them quite severe for some patients. In addition to medications, health care professionals strongly recommend patients with schizophrenia supplement their drug regimen with an array of psychosocial interventions. - What are my chances for a relapse once I am taking medications and following a treatment plan? When taken as directed, antipsychotic medications can make a huge difference in the long-term potential for minimizing relapses and hospitalizations. Relapses usually happen when people stop taking their medication or take it only occasionally. People often stop their medication because they feel better and don’t think they need it anymore. However, you should never stop taking an antipsychotic medication without first checking with your doctor. And even if your doctor gives you the OK, you should taper the dose of your medication gradually and not stop it suddenly. - Is there any way to prevent myself from developing schizophrenia? Current research is being done to answer this question, and there are several clinics around the world devoted to identifying and helping “at risk” individuals. It does appear that the onset of schizophrenia can be triggered by stress or by using certain drugs such as marijuana. If a person has a family history of schizophrenia, avoiding illicit drug use is advisable, as well as reducing stress, getting adequate sleep and starting antipsychotic medications as soon as necessary. For more information visit us our website: http://www.healthinfi.com
A UK team of astronomers report the first detection of matter falling into a black hole at 30% of the speed of light, located in the center of the billion-light-year distant galaxy PG211+143. The team, led by Professor Ken Pounds of the University of Leicester, used data from the European Space Agency’s X-ray observatory XMM-Newton to observe the black hole. Their results appear in a new paper in Monthly Notices of the Royal Astronomical Society. Black holes are objects with such strong gravitational fields that not even light travels quickly enough to escape their grasp, hence the description ‘black’. They are hugely important in astronomy because they offer the most efficient way of extracting energy from matter. As a direct result, gas in-fall – accretion – onto black holes must be powering the most energetic phenomena in the Universe. The center of almost every galaxy – like our own Milky Way – contains a so-called supermassive black hole, with masses of millions to billions of times the mass of our Sun. With sufficient matter falling into the hole, these can become extremely luminous, and are seen as a quasar or active galactic nucleus (AGN). However black holes are so compact that gas is almost always rotating too much to fall in directly. Instead, it orbits the hole, approaching gradually through an accretion disc – a sequence of circular orbits of decreasing size. As gas spirals inwards, it moves faster and faster and becomes hot and luminous, turning gravitational energy into the radiation that astronomers observe. The orbit of the gas around the black hole is often assumed to be aligned with the rotation of the black hole, but there is no compelling reason for this to be the case. In fact, the reason we have summer and winter is that the Earth’s daily rotation does not line up with its yearly orbit around the Sun. Until now it has been unclear how misaligned rotation might affect the in-fall of gas. This is particularly relevant to the feeding of supermassive black holes since matter (interstellar gas clouds or even isolated stars) can fall in from any direction. Using data from XMM-Newton, Prof. Pounds and his collaborators looked at X-ray spectra (where X-rays are dispersed by wavelength) from the galaxy PG211+143. This object lies more than one billion light-years away in the direction of the constellation Coma Berenices, and is a Seyfert galaxy, characterized by a very bright AGN resulting from the presence of the massive black hole at its nucleus. The researchers found the spectra to be strongly red-shifted, showing the observed matter to be falling into the black hole at the enormous speed of 30 percent of the speed of light, or around 100,000 kilometers per second. The gas has almost no rotation around the hole, and is detected extremely close to it in astronomical terms, at a distance of only 20 times the hole’s size (its event horizon, the boundary of the region where escape is no longer possible). The observation agrees closely with recent theoretical work, also at Leicester and using the UK’s Dirac supercomputer facility simulating the ‘tearing’ of misaligned accretion discs. This work has shown that rings of gas can break off and collide with each other, canceling out their rotation and leaving gas to fall directly toward the black hole. Prof. Pounds, from the University of Leicester’s Department of Physics and Astronomy, said: “The galaxy we were observing with XMM-Newton has a 40 million solar mass black hole which is very bright and evidently well fed. Indeed some 15 years ago we detected a powerful wind indicating the hole was being over-fed. While such winds are now found in many active galaxies, PG1211+143 has now yielded another ‘first’, with the detection of matter plunging directly into the hole itself.” He continues: “We were able to follow an Earth-sized clump of matter for about a day, as it was pulled towards the black hole, accelerating to a third of the velocity of light before being swallowed up by the hole. A further implication of the new research is that ‘chaotic accretion’ from misaligned discs is likely to be common for supermassive black holes. Such black holes would then spin quite slowly, being able to accept far more gas and grow their masses more rapidly than generally believed, providing an explanation for why black holes which formed in the early Universe quickly gained very large masses. Reference: “An ultrafast inflow in the luminous Seyfert PG1211+143” by K A Pounds, C J Nixon, A Lobban and A R King, 3 September 2018, Monthly Notices of the Royal Astronomical Society.
Have you ever stood around a cocktail party discussing statistics? I didn't think so. But we hear about them all the time, especially when we're absorbing clinical trial results -- or election year polls. Understanding the basics of statistics is not that hard to do, despite how it seemed in school! There are a handful of concepts that serve as the building blocks for learning statistics. I'm jumping ahead of mean, median, mode; those will not be covered here (see sidebar). We will look first at standard deviation, standard error, and confidence interval, and how they all tie in to p-value. The standard deviation is simply a measure of the amount of variability in your particular sample. Because we can't practically measure everyone in a population that we are interested in studying, we have to take a sample of the population. The standard deviation describes the variation in measurements from individual to individual data point within the sample. Below is a picture of what the standard deviation (SD) tells us. The mean, μ, which is the average, is the highest point in the center of the bell-shaped curve. The area between plus or minus (±) 1 standard deviation (1σ) of the mean captures 68% of all measurements in your sample; the area between ± 2 standard deviations (2σ) captures 95% of all measurements in your sample. In other words, not very many data points -- approximately 5% -- will lie more than 2 standard deviations from the mean. The standard error (SE) is important in describing how well the sample mean represents the true population mean. Remember, because we can't practically measure everyone in the population, we take a random sample. Every random sample will give a slightly different estimation of the whole population. The standard error gives you a measure of how precise your sample mean is compared to the true population mean. It is calculated by the standard deviation divided by the square root of the mean. So it depends on the size of your sample. As the sample size gets larger, then variability gets smaller and we get a more precise measurement of the truth. If we measure every member of the population, then it is no longer a sample. There is only one value that can be computed by measuring every member of the population, thus there is no variability and the truth is known. Since every random sample will give a slightly different estimation of the whole population, it makes sense to try to describe what the true population looks like with more than a single number. The confidence interval (CI) estimates a range of values within which we are pretty sure the truth lies. The confidence interval depends on the standard error. It is calculated by the sample mean you have measured in your sample plus or minus approximately 2 times the standard error. For example, the 95% CI gives us the range of values within which we are confident that the true population mean falls 95% of the time. Every point outside of the confidence interval is very unlikely to occur by chance alone. If we have a 95% CI, then it means that there is a 5% chance that the true mean of the population is outside of that interval. In other words, we're pretty confident of the value of our confidence interval! This area outside the confidence area corresponds to a parameter called alpha, α. And usually we split α so that half is in the upper tail (2.5%) and half is in the lower tail (2.5%). This is what we mean by a two-tailed confidence interval. The CI tells us a lot about our sample. We can draw conclusions about statistical significance based on the location of the CI. For example, suppose we have a CI that estimates the difference between two groups: a value of zero corresponds to no difference (that is, the null value). Therefore a CI that excludes zero denotes a statistically significant finding. Beware, though, that the null value is not always zero! It depends upon your null hypothesis, which will be described below. Before moving on to new concepts, let's put the three summary statistics of standard deviation, standard error, and confidence interval together by considering an example from blood pressure measurements on 50 individuals. The scatter plot in the picture below shows each of the 50 individual measurements from this hypothetical sample. Our sample mean is represented by the large dot in the center of the 4 vertical lines beside the scatter plot. In the first green line, we can see that about 2/3 of our sample results are contained within +/- 1 standard deviation. In the second green line, 95% of our data points are covered by +/- 2 standard deviations. Once we know the standard error, we can construct the confidence interval. The 95% CI, depicted by the second blue line, gives us the range within which we are 95% confident that the true population mean lies. The first step of the experiment is to state your hypothesis. The null hypothesis, H0, is pre-defined and represents a statement which is the reverse of what we hope the experiment will show. It is named the null hypothesis because it is the statement that we want the data to reject. The alternative hypothesis, Ha, is also predefined and represents a statement of what we hope the experiment will show. Ha is the hypothesis that there is a real effect. Suppose we design a study to test if Optimized Background Treatment (OBT) + New Drug are better than just OBT alone. Our null hypothesis is that there is no difference between the groups. Our alternative hypothesis is that the two groups are not the same. (We hope that OBT + New Drug is better!) Depending on the data gathered from the study, we will either reject the null hypothesis or not. The next step is to design your experiment and select the test statistic. The test statistic defines the method that will be used to compare the two groups and help interpret the outcome at the end of the study. Sometimes the comparison may be based on the differences in means, and use continuous data analysis methods. Sometimes the comparison may be based on proportions, and use categorical data analysis methods. There are many possibilities. For our example from Step 1, the test statistic will be based on the comparison of the proportion of patients with HIV viral load (VL) less than (<) 50 copies/mL in each treatment group of our study sample. Many other important decisions go into designing the experiment besides selecting the test statistic. We also calculate the sample size, agree on the power of the study, and establish parameters like α and β (described below). After we generate a random study sample, we conduct the study and collect the data. The third step is to investigate the hypotheses stated in Step 1 and compare the groups. In our hypothetical example, we find that 75% of subjects in the OBT + New Drug group achieve VL <50 copies/mL compared to 35% of patients in the control group. This produces a p-value <0.0001. The p-value (the "p" stands for "probability") helps us decide whether the data from the random study sample supports the null hypothesis or the alternative hypothesis. P-value is the probability that these results would occur if there was truly no difference between the groups -- that is, how likely the results would have been observed purely by chance. The closer the p-value is to 0, the greater the likelihood that the observed difference in viral load is real and not due to chance, thus the more reason we have to reject the null hypothesis in favor of the alternative hypothesis. We look for a p-value of 0.05 or smaller. This represents a 5-in-100 probability -- a very small chance indeed! The last step is to compare the p-value with α and interpret the finding. Alpha is called the significance level. As described above in the section on CI, it is the area outside of the confidence area. It is most commonly defined as α=0.05. If the p-value is less than or equal to α, then the null hypothesis is rejected and we declare a statistically significant finding has been observed. If the p-value is greater than α, then the null hypothesis is not rejected. Remember, our hypothetical example produced a p-value <0.0001. This is well below α=0.05, so we reject the null hypothesis and conclude that OBT + New Drug and OBT alone are different. We can even take it one step further and conclude that OBT + New Drug are better than OBT. The results of a study are often described by both the p-value and the 95% CI. The p-value is a single number that guides whether or not to reject the null hypothesis. The 95% CI provides a range of plausible values for describing the underlying population. \|Ho: no fire\|\|Ha: fire\| \|Accept Ho: no alarm\|\|No error\|\|Type II\| \|Reject Ho: alarm\|\|Type I\|\|No error\| Three more terms that we often hear or read about are called Type I error, Type II error, and power. They are inter-related and are important in the design stage and in the interpretation stage as well. One way to think about them is to consider the relationship between a smoke detector and a house fire. (Reference: Larry Gonick & Woollcott Smith; The Cartoon Guide to Statistics; 1993; pp151-152). The purpose of the smoke detector, of course, is to warn us in case of a fire. However, it is possible to have a fire without an alarm, as well as an alarm without a fire. Those are situations or errors that we do not ideally want, but they are possible events nevertheless. So the "true state" can be either no fire (Ho) or house fire (Ha). Ideally, we want the alarm to alert us if there is a fire and we want the alarm to remain silent when there is no fire. If we have an alarm without a fire, then a Type I error has been committed. This corresponds to α, which is the probability of claiming a difference/rejecting Ho. Alpha is normally pre-set to 0.05. In other words, we accept a 5% chance of a "false alarm." If we have a fire but it does not cause an alarm, then a Type II error has been committed. This corresponds to beta, β, which is the probability of missing a difference when one truly exists/not rejecting Ho. Beta is normally pre-set to 10% or 20%. In other words, we accept a 10% or 20% chance of a "failed alarm." Power is defined by 1-β, which is the probability of a real fire when there is an alarm. It is normally pre-set to 80% or 90%. It controls the probability of observing a true difference, or a "true alarm." In other words, with power=80%, we accept that eight trials out of 10 will correctly declare a true difference and that two trials out of 10 will incorrectly miss a true difference. β is a risk that we would want to minimize; and it is a risk to minimize as much as possible but it comes with a price: a larger study, plus more time to recruit subjects, measure, and report. A p-value greater than α=0.05 could be non-significant because there is truly no difference between the groups. Or it could be non-significant because the study is not large enough to detect a true underlying difference. Determining the optimal sample size for a study requires a great deal of thought in the beginning at the planning stage. A sample size that is unnecessarily large is a waste of resources. But a sample size that is too small has a higher likelihood of not representing the underlying population and consequently missing a "true alarm." The small study has a wider confidence interval because the standard error is large, or less precise. As we said above in Building Block #2, when the sample size gets larger, the variability gets smaller and we get a more precise measurement of the truth. The optimal sample size depends on all of the various assumptions that go into its calculation. For instance, to plan a superiority study as in Step 2 above, we need to make decisions/assumptions on the following parameters: α (generally 0.05), whether the hypothesis is one-sided or two-sided (generally two-sided), power (generally 80-90%), the response rate in the test arm, and the response rate in the control arm. These assumptions are directly tied to the study being designed -- so different types of studies require different sets of information for the sample size calculation. Changing any one of the decisions/assumptions will change the sample size calculation. Understanding the basics of statistics is helpful in evaluating the messages that arise out of research. Good research follows clearly articulated steps and serious planning. The goal of research is to answer a question. In order to do so, it comes down to establishing: In conclusion, study designs are chosen depending on the questions that are being studied. Study endpoints are selected according to the hypothesis under investigation and the study population being enrolled. And study interpretations depend on the hypotheses being tested. Statistics can help weigh the evidence and draw conclusions from the data. The Median, the Mean, and the Mode Before you can begin to understand statistics, there are four terms you will need to fully understand. The first term, "average," is something we have been familiar with from a very early age when we start analyzing our marks on report cards. We add together all of our test results and then divide it by the sum of the total number of marks there are. We often call it the average. However, statistically it's the mean! The median is the "middle value" in your list. When the totals of the list are odd, the median is the middle entry in the list aft er sorting the list into increasing order. When the totals of the list are even, the median is equal to the sum of the two middle (after sorting the list into increasing order) numbers divided by two. Thus, remember to line up your values, the middle number is the median! Be sure to remember the odd and even rule. The mode in a list of numbers refers to the list of numbers that occur most frequently. A trick to remembering this one is to remember that mode starts with the same first two letters that most does. Most frequently -- mode. You'll never forget that one! It is important to note that there can be more than one mode. If no number occurs more than once in the set, then there is no mode for that set of numbers. Occasionally in statistics you'll be asked for the "range" in a set of numbers. The range is simply the smallest number subtracted from the largest number in your set. Thus, if your set is 9, 3, 44, 15, and 6, the range would be 44-3=41. Your range is 41. A natural progression once the three terms in statistics are understood is the concept of probability. Probability is the chance of an event happening and is usually expressed as a fraction. But that's another topic! Amy Cutrell resides in Chapel Hill, NC, and has worked at GlaxoSmithKline for twenty years. She received a MS in biostatistics from the UNC School of Public Health.
Formulas in Excel perform calculations such as addition, subtraction and multiplication. They use the familiar arithmetic operators (+, – etc) however, formulas in Excel always begin with an equals sign (=). Arithmetic Operators in Excel An example of a formula in Excel might be =2+2, which of course will return the answer 4. However, this would be a very restricted formula as it only returns one possible value. In practice, when we input formulas into an Excel spreadsheet we substitute raw data for cell references. So an example formula might be =A1+B1. If the values in A1 and B1 are both 2 then the formula will return the answer 4 as before. However, we can now change the values in cells A1 and B1 and get different results without having to edit the formula. As a general rule, we should try never to insert raw data into Excel formulas; it is almost always better to reference cells instead. Here are some examples of Excel formulas: - Subtract B1 from A1: =A1-B1 - Multiply A1 and B1: =A1B1 - Divide A1 and B1: = A1/B1 Formulas can be edited in the cell by double-clicking with the mouse. They can also be edited in the formula bar by selecting the cell, then clicking inside the formula bar. Combining Arithmetic Operators If we wish to combine operators in the same formula it is sometimes necessary to separate them with brackets. this is especially true if we mix multiple & divide with addition and subtraction. This is because the operators of multiply and divide take precedence. Consider the following example: We wish to add A1 and B1 then multiply the result by 20%. If we enter =A1+B120% we get the result 2.4. But this is incorrect, we should get 0.8. The reason we don’t is that because multiplication takes precedence over addition, Excel will first multiply B1 by 20% and then add A1 to the product. In order to add A1+B1 first we need to wrap them in brackets, so our formula becomes =(A1+B1)*20%. This gives the correct result of 0.8. - First enter the data shown into cells A1 and B1. - Next add, subtract, multiply & divide the data in separate cells in column C. - Finally, in C5 add the data and calculate 10% of the product. Attending a Microsoft Excel Training Course Our 1 day Foundation Microsoft Excel course covers formulas and many other essential skills. It is suitable for people with no previous experience of using Excel and also those self-taught users who would benefit from a structured training course to ‘fill in the gaps’ and extend their working knowledge of the application. We run onsite Microsoft Excel training courses throughout the UK, please call free on 0800 2922842 to discuss your IT training needs. Alternatively you can email us on email@example.com.
In radio-frequency engineering, a transmission line is a specialized cable or other structure designed to conduct alternating current of radio frequency, that is, currents with a frequency high enough that their wave nature must be taken into account. Transmission lines are used for purposes such as connecting radio transmitters and receivers with their antennas (they are then called feed lines or feeders), distributing cable television signals, trunklines routing calls between telephone switching centres, computer network connections and high speed computer data buses. This article covers two-conductor transmission line such as parallel line (ladder line), coaxial cable, stripline, and microstrip. Some sources also refer to waveguide, dielectric waveguide, and even optical fibre as transmission line, however these lines require different analytical techniques and so are not covered by this article; see Waveguide (electromagnetism). - 1 Overview - 2 History - 3 Applicability - 4 The four terminal model - 5 Telegrapher's equations - 6 Input impedance of transmission line - 7 Practical types - 8 General applications - 9 See also - 10 References - 11 Further reading - 12 External links Ordinary electrical cables suffice to carry low frequency alternating current (AC), such as mains power, which reverses direction 100 to 120 times per second, and audio signals. However, they cannot be used to carry currents in the radio frequency range, above about 30 kHz, because the energy tends to radiate off the cable as radio waves, causing power losses. Radio frequency currents also tend to reflect from discontinuities in the cable such as connectors and joints, and travel back down the cable toward the source. These reflections act as bottlenecks, preventing the signal power from reaching the destination. Transmission lines use specialized construction, and impedance matching, to carry electromagnetic signals with minimal reflections and power losses. The distinguishing feature of most transmission lines is that they have uniform cross sectional dimensions along their length, giving them a uniform impedance, called the characteristic impedance, to prevent reflections. Types of transmission line include parallel line (ladder line, twisted pair), coaxial cable, and planar transmission lines such as stripline and microstrip. The higher the frequency of electromagnetic waves moving through a given cable or medium, the shorter the wavelength of the waves. Transmission lines become necessary when the transmitted frequency's wavelength is sufficiently short that the length of the cable becomes a significant part of a wavelength. At microwave frequencies and above, power losses in transmission lines become excessive, and waveguides are used instead, which function as "pipes" to confine and guide the electromagnetic waves. Some sources define waveguides as a type of transmission line; however, this article will not include them. At even higher frequencies, in the terahertz, infrared and visible ranges, waveguides in turn become lossy, and optical methods, (such as lenses and mirrors), are used to guide electromagnetic waves. The theory of sound wave propagation is very similar mathematically to that of electromagnetic waves, so techniques from transmission line theory are also used to build structures to conduct acoustic waves; and these are called acoustic transmission lines. Mathematical analysis of the behaviour of electrical transmission lines grew out of the work of James Clerk Maxwell, Lord Kelvin and Oliver Heaviside. In 1855 Lord Kelvin formulated a diffusion model of the current in a submarine cable. The model correctly predicted the poor performance of the 1858 trans-Atlantic submarine telegraph cable. In 1885 Heaviside published the first papers that described his analysis of propagation in cables and the modern form of the telegrapher's equations. In many electric circuits, the length of the wires connecting the components can for the most part be ignored. That is, the voltage on the wire at a given time can be assumed to be the same at all points. However, when the voltage changes in a time interval comparable to the time it takes for the signal to travel down the wire, the length becomes important and the wire must be treated as a transmission line. Stated another way, the length of the wire is important when the signal includes frequency components with corresponding wavelengths comparable to or less than the length of the wire. A common rule of thumb is that the cable or wire should be treated as a transmission line if the length is greater than 1/10 of the wavelength. At this length the phase delay and the interference of any reflections on the line become important and can lead to unpredictable behaviour in systems which have not been carefully designed using transmission line theory. The four terminal model For the purposes of analysis, an electrical transmission line can be modelled as a two-port network (also called a quadripole), as follows: In the simplest case, the network is assumed to be linear (i.e. the complex voltage across either port is proportional to the complex current flowing into it when there are no reflections), and the two ports are assumed to be interchangeable. If the transmission line is uniform along its length, then its behaviour is largely described by a single parameter called the characteristic impedance, symbol Z0. This is the ratio of the complex voltage of a given wave to the complex current of the same wave at any point on the line. Typical values of Z0 are 50 or 75 ohms for a coaxial cable, about 100 ohms for a twisted pair of wires, and about 300 ohms for a common type of untwisted pair used in radio transmission. When sending power down a transmission line, it is usually desirable that as much power as possible will be absorbed by the load and as little as possible will be reflected back to the source. This can be ensured by making the load impedance equal to Z0, in which case the transmission line is said to be matched. Some of the power that is fed into a transmission line is lost because of its resistance. This effect is called ohmic or resistive loss (see ohmic heating). At high frequencies, another effect called dielectric loss becomes significant, adding to the losses caused by resistance. Dielectric loss is caused when the insulating material inside the transmission line absorbs energy from the alternating electric field and converts it to heat (see dielectric heating). The transmission line is modelled with a resistance (R) and inductance (L) in series with a capacitance (C) and conductance (G) in parallel. The resistance and conductance contribute to the loss in a transmission line. The total loss of power in a transmission line is often specified in decibels per metre (dB/m), and usually depends on the frequency of the signal. The manufacturer often supplies a chart showing the loss in dB/m at a range of frequencies. A loss of 3 dB corresponds approximately to a halving of the power. High-frequency transmission lines can be defined as those designed to carry electromagnetic waves whose wavelengths are shorter than or comparable to the length of the line. Under these conditions, the approximations useful for calculations at lower frequencies are no longer accurate. This often occurs with radio, microwave and optical signals, metal mesh optical filters, and with the signals found in high-speed digital circuits. The telegrapher's equations (or just telegraph equations) are a pair of linear differential equations which describe the voltage () and current () on an electrical transmission line with distance and time. They were developed by Oliver Heaviside who created the transmission line model, and are based on Maxwell's Equations. The transmission line model is an example of the distributed element model. It represents the transmission line as an infinite series of two-port elementary components, each representing an infinitesimally short segment of the transmission line: - The distributed resistance of the conductors is represented by a series resistor (expressed in ohms per unit length). - The distributed inductance (due to the magnetic field around the wires, self-inductance, etc.) is represented by a series inductor (in henries per unit length). - The capacitance between the two conductors is represented by a shunt capacitor (in farads per unit length). - The conductance of the dielectric material separating the two conductors is represented by a shunt resistor between the signal wire and the return wire (in siemens per unit length). The model consists of an infinite series of the elements shown in the figure, and the values of the components are specified per unit length so the picture of the component can be misleading. , , , and may also be functions of frequency. An alternative notation is to use , , and to emphasize that the values are derivatives with respect to length. These quantities can also be known as the primary line constants to distinguish from the secondary line constants derived from them, these being the propagation constant, attenuation constant and phase constant. The line voltage and the current can be expressed in the frequency domain as Special case of a lossless line When the elements and are negligibly small the transmission line is considered as a lossless structure. In this hypothetical case, the model depends only on the and elements which greatly simplifies the analysis. For a lossless transmission line, the second order steady-state Telegrapher's equations are: These are wave equations which have plane waves with equal propagation speed in the forward and reverse directions as solutions. The physical significance of this is that electromagnetic waves propagate down transmission lines and in general, there is a reflected component that interferes with the original signal. These equations are fundamental to transmission line theory. General case of a line with losses In the general case the loss terms, and , are both included, and the full form of the Telegrapher's equations become: where is the (complex) propagation constant. These equations are fundamental to transmission line theory. They are also wave equations, and have solutions similar to the special case, but which are a mixture of sines and cosines with exponential decay factors. Solving for the propagation constant in terms of the primary parameters , , , and gives: and the characteristic impedance can be expressed as The solutions for and are: The constants must be determined from boundary conditions. For a voltage pulse , starting at and moving in the positive direction, then the transmitted pulse at position can be obtained by computing the Fourier Transform, , of , attenuating each frequency component by , advancing its phase by , and taking the inverse Fourier Transform. The real and imaginary parts of can be computed as the right-hand expressions holding when neither , nor , nor is zero, and with where atan2 is the everywhere-defined form of two-parameter arctangent function, with arbitrary value zero when both arguments are zero. Special, low loss case For small losses and high frequencies, the general equations can be simplified: If and then Noting that an advance in phase by is equivalent to a time delay by , can be simply computed as Input impedance of transmission line The characteristic impedance of a transmission line is the ratio of the amplitude of a single voltage wave to its current wave. Since most transmission lines also have a reflected wave, the characteristic impedance is generally not the impedance that is measured on the line. The impedance measured at a given distance from the load impedance may be expressed as where is the propagation constant and is the voltage reflection coefficient measured at the load end of the transmission line. Alternatively, the above formula can be rearranged to express the input impedance in terms of the load impedance rather than the load voltage reflection coefficient: Input impedance of lossless transmission line For a lossless transmission line, the propagation constant is purely imaginary, , so the above formulas can be rewritten as where is the wavenumber. In calculating the wavelength is generally different inside the transmission line to what it would be in free-space. Consequently, the velocity constant of the material the transmission line is made of needs to be taken into account when doing such a calculation. Special cases of lossless transmission lines Half wave length For the special case where where n is an integer (meaning that the length of the line is a multiple of half a wavelength), the expression reduces to the load impedance so that for all This includes the case when , meaning that the length of the transmission line is negligibly small compared to the wavelength. The physical significance of this is that the transmission line can be ignored (i.e. treated as a wire) in either case. Quarter wave length For the case where the length of the line is one quarter wavelength long, or an odd multiple of a quarter wavelength long, the input impedance becomes Another special case is when the load impedance is equal to the characteristic impedance of the line (i.e. the line is matched), in which case the impedance reduces to the characteristic impedance of the line so that for all and all . For the case of a shorted load (i.e. ), the input impedance is purely imaginary and a periodic function of position and wavelength (frequency) For the case of an open load (i.e. ), the input impedance is once again imaginary and periodic Stepped transmission line A stepped transmission line is used for broad range impedance matching. It can be considered as multiple transmission line segments connected in series, with the characteristic impedance of each individual element to be . The input impedance can be obtained from the successive application of the chain relation where is the wave number of the -th transmission line segment and is the length of this segment, and is the front-end impedance that loads the -th segment. Because the characteristic impedance of each transmission line segment is often different from that of the input cable , the impedance transformation circle is off-centred along the axis of the Smith Chart whose impedance representation is usually normalized against . The stepped transmission line is an example of a distributed element circuit. A large variety of other circuits can also be constructed with transmission lines including filters, power dividers and directional couplers. Coaxial lines confine virtually all of the electromagnetic wave to the area inside the cable. Coaxial lines can therefore be bent and twisted (subject to limits) without negative effects, and they can be strapped to conductive supports without inducing unwanted currents in them. In radio-frequency applications up to a few gigahertz, the wave propagates in the transverse electric and magnetic mode (TEM) only, which means that the electric and magnetic fields are both perpendicular to the direction of propagation (the electric field is radial, and the magnetic field is circumferential). However, at frequencies for which the wavelength (in the dielectric) is significantly shorter than the circumference of the cable other transverse modes can propagate. These modes are classified into two groups, transverse electric (TE) and transverse magnetic (TM) waveguide modes. When more than one mode can exist, bends and other irregularities in the cable geometry can cause power to be transferred from one mode to another. The most common use for coaxial cables is for television and other signals with bandwidth of multiple megahertz. In the middle 20th century they carried long distance telephone connections. A microstrip circuit uses a thin flat conductor which is parallel to a ground plane. Microstrip can be made by having a strip of copper on one side of a printed circuit board (PCB) or ceramic substrate while the other side is a continuous ground plane. The width of the strip, the thickness of the insulating layer (PCB or ceramic) and the dielectric constant of the insulating layer determine the characteristic impedance. Microstrip is an open structure whereas coaxial cable is a closed structure. A stripline circuit uses a flat strip of metal which is sandwiched between two parallel ground planes. The insulating material of the substrate forms a dielectric. The width of the strip, the thickness of the substrate and the relative permittivity of the substrate determine the characteristic impedance of the strip which is a transmission line. A coplanar waveguide consists of a center strip and two adjacent outer conductors, all three of them flat structures that are deposited onto the same insulating substrate and thus are located in the same plane ("coplanar"). The width of the center conductor, the distance between inner and outer conductors, and the relative permittivity of the substrate determine the characteristic impedance of the coplanar transmission line. A balanced line is a transmission line consisting of two conductors of the same type, and equal impedance to ground and other circuits. There are many formats of balanced lines, amongst the most common are twisted pair, star quad and twin-lead. Twisted pairs are commonly used for terrestrial telephone communications. In such cables, many pairs are grouped together in a single cable, from two to several thousand. The format is also used for data network distribution inside buildings, but the cable is more expensive because the transmission line parameters are tightly controlled. Star quad is a four-conductor cable in which all four conductors are twisted together around the cable axis. It is sometimes used for two circuits, such as 4-wire telephony and other telecommunications applications. In this configuration each pair uses two non-adjacent conductors. Other times it is used for a single, balanced line, such as audio applications and 2-wire telephony. In this configuration two non-adjacent conductors are terminated together at both ends of the cable, and the other two conductors are also terminated together. When used for two circuits, crosstalk is reduced relative to cables with two separate twisted pairs. When used for a single, balanced line, magnetic interference picked up by the cable arrives as a virtually perfect common mode signal, which is easily removed by coupling transformers. The combined benefits of twisting, balanced signalling, and quadrupole pattern give outstanding noise immunity, especially advantageous for low signal level applications such as microphone cables, even when installed very close to a power cable. The disadvantage is that star quad, in combining two conductors, typically has double the capacitance of similar two-conductor twisted and shielded audio cable. High capacitance causes increasing distortion and greater loss of high frequencies as distance increases. Twin-lead consists of a pair of conductors held apart by a continuous insulator. By holding the conductors a known distance apart, the geometry is fixed and the line characteristics are reliably consistent. It is lower loss than coaxial cable because the characteristic impedance of twin-lead is generally higher than coaxial cable, leading to lower resistive losses due to the reduced current. However, it is more susceptible to interference. Lecher lines are a form of parallel conductor that can be used at UHF for creating resonant circuits. They are a convenient practical format that fills the gap between lumped components (used at HF/VHF) and resonant cavities (used at UHF/SHF). Unbalanced lines were formerly much used for telegraph transmission, but this form of communication has now fallen into disuse. Cables are similar to twisted pair in that many cores are bundled into the same cable but only one conductor is provided per circuit and there is no twisting. All the circuits on the same route use a common path for the return current (earth return). There is a power transmission version of single-wire earth return in use in many locations. Electrical transmission lines are very widely used to transmit high frequency signals over long or short distances with minimum power loss. One familiar example is the down lead from a TV or radio aerial to the receiver. Transmission lines are also used as pulse generators. By charging the transmission line and then discharging it into a resistive load, a rectangular pulse equal in length to twice the electrical length of the line can be obtained, although with half the voltage. A Blumlein transmission line is a related pulse forming device that overcomes this limitation. These are sometimes used as the pulsed power sources for radar transmitters and other devices. If a short-circuited or open-circuited transmission line is wired in parallel with a line used to transfer signals from point A to point B, then it will function as a filter. The method for making stubs is similar to the method for using Lecher lines for crude frequency measurement, but it is 'working backwards'. One method recommended in the RSGB's radiocommunication handbook is to take an open-circuited length of transmission line wired in parallel with the feeder delivering signals from an aerial. By cutting the free end of the transmission line, a minimum in the strength of the signal observed at a receiver can be found. At this stage the stub filter will reject this frequency and the odd harmonics, but if the free end of the stub is shorted then the stub will become a filter rejecting the even harmonics. - Artificial transmission line - Longitudinal electromagnetic wave - Propagation velocity - Radio frequency power transmission - Time domain reflectometer Part of this article was derived from Federal Standard 1037C. - Jackman, Shawn M.; Matt Swartz; Marcus Burton; Thomas W. Head (2011). CWDP Certified Wireless Design Professional Official Study Guide: Exam PW0-250. John Wiley & Sons. pp. Ch. 7. ISBN 978-1118041611. - Oklobdzija, Vojin G.; Ram K. Krishnamurthy (2006). High-Performance Energy-Efficient Microprocessor Design. Springer Science & Business Media. p. 297. ISBN 978-0387340470. - Guru, Bhag Singh; Hüseyin R. Hızıroğlu (2004). Electromagnetic Field Theory Fundamentals, 2nd Ed. Cambridge Univ. Press. pp. 422–423. ISBN 978-1139451925. - Schmitt, Ron Schmitt (2002). Electromagnetics Explained: A Handbook for Wireless/ RF, EMC, and High-Speed Electronics. Newnes. p. 153. ISBN 978-0080505237. - Carr, Joseph J. (1997). Microwave & Wireless Communications Technology. USA: Newnes. pp. 46–47. ISBN 978-0750697071. - Raisanen, Antti V.; Arto Lehto (2003). Radio Engineering for Wireless Communication and Sensor Applications. Artech House. pp. 35–37. ISBN 978-1580536691. - Ernst Weber and Frederik Nebeker, The Evolution of Electrical Engineering, IEEE Press, Piscataway, New Jersey USA, 1994 ISBN 0-7803-1066-7 - Qian, Chunqi; Brey, William W. (2009). "Journal of Magnetic Resonance – Impedance matching with an adjustable segmented transmission line". Journal of Magnetic Resonance. 199 (1): 104–110. Bibcode:2009JMagR.199..104Q. doi:10.1016/j.jmr.2009.04.005. PMID 19406676. - Syed V. Ahamed, Victor B. Lawrence, Design and engineering of intelligent communication systems, pp.130–131, Springer, 1997 ISBN 0-7923-9870-X. - The Importance of Star-Quad Microphone Cable - Evaluating Microphone Cable Performance & Specifications - The Star Quad Story - What's Special About Star-Quad Cable? - How Starquad Works - Lampen, Stephen H. (2002). Audio/Video Cable Installer's Pocket Guide. McGraw-Hill. pp. 32, 110, 112. ISBN 978-0071386210. - Rayburn, Ray (2011). Eargle's The Microphone Book: From Mono to Stereo to Surround – A Guide to Microphone Design and Application (3 ed.). Focal Press. pp. 164–166. ISBN 978-0240820750. - Steinmetz, Charles Proteus (August 27, 1898), "The Natural Period of a Transmission Line and the Frequency of lightning Discharge Therefrom", The Electrical World: 203–205 - Grant, I. S.; Phillips, W. R. (1991-08-26), Electromagnetism (2nd ed.), John Wiley, ISBN 978-0-471-92712-9 - Ulaby, F. T. (2004), Fundamentals of Applied Electromagnetics (2004 media ed.), Prentice Hall, ISBN 978-0-13-185089-7 - "Chapter 17", Radio communication handbook, Radio Society of Great Britain, 1982, p. 20, ISBN 978-0-900612-58-9 - Naredo, J. L.; Soudack, A. C.; Marti, J. R. (Jan 1995), "Simulation of transients on transmission lines with corona via the method of characteristics", IEE Proceedings. Generation, Transmission and Distribution., Morelos: Institution of Electrical Engineers, 142 (1), ISSN 1350-2360 \|Wikimedia Commons has media related to Transmission lines.\| - Annual Dinner of the Institute at the Waldorf-Astoria. Transactions of the American Institute of Electrical Engineers, New York, January 13, 1902. (Honoring of Guglielmo Marconi, January 13, 1902) - Avant! software, Using Transmission Line Equations and Parameters. Star-Hspice Manual, June 2001. - http://www.iop.org/EJ/abstract/0022-3727/23/2/001. Missing or empty \|title=(help) (Concept of inhomogeneous waves propagation — Show the importance of the telegrapher's equation with Heaviside's condition.) - Farlow, S.J., Partial differential equations for scientists and engineers. J. Wiley and Sons, 1982, p. 126. ISBN 0-471-08639-8. - Kupershmidt, Boris A., Remarks on random evolutions in Hamiltonian representation. Math-ph/9810020. J. Nonlinear Math. Phys. 5 (1998), no. 4, 383–395. - Transmission line matching. EIE403: High Frequency Circuit Design. Department of Electronic and Information Engineering, Hong Kong Polytechnic University. (PDF format) - Wilson, B. (2005, October 19). Telegrapher's Equations. Connexions. - John Greaton Wöhlbier, ""Fundamental Equation" and "Transforming the Telegrapher's Equations". Modeling and Analysis of a Traveling Wave Under Multitone Excitation. - Keysight Technologies. Educational Resources. Wave Propagation along a Transmission Line. May need to add "http://www.keysight.com" to your Java Exception Site list. Educational Java Applet. - Qian, Chunqi; Brey, William W. (2009). "Impedance matching with an adjustable segmented transmission line". Journal of Magnetic Resonance. 199 (1): 104–110. Bibcode:2009JMagR.199..104Q. doi:10.1016/j.jmr.2009.04.005. PMID 19406676.
Subtraction is really another way of showing that you're adding the additive inverse. In Subtractionland, it's always opposite day. Or is it? For example, 4 – 3 is just another way of writing 4 + (-3). Subtraction exists so that instead of writing a plus sign, a negative sign, and parentheses, we can just write a minus sign. Because mathematicians are generally lazy, and they don't want to have to go writing all those extra symbols if they can help it. In fact, the symbol "₳" means "please bring me a donut so I don't have to get up from the couch." On the number line, subtraction means walking to the first number, then walking in the opposite direction specified by the second number. Told you it was opposite day. Or did we? What does it mean to subtract a negative number? 4 – (-18) = ? Well, adding (-18) would mean we walk 18 to the left, so subtracting (-18) means we walk 18 to the right. So 4 – (-18) really means 4 + 18 = 22. Think of it this way: if you take the minus sign and the negative sign and cross them, you get a plus sign. If you found the preceding sentence helpful, please check this box: □. Another way to approach this problem is to remember what subtraction is abbreviating, then rewrite the whole thing as an addition problem: 4 – (-18) = 4 + (-(-18)) Since the negative of a negative is positive, -(-18) = 18. 4 – (-18) = 4 + 18 = 22 Be Careful: Honestly, the notation here can get really confusing. So take off your confused cap and put on your unbefuddled derby. A minus sign and a negative sign look similar, but mean different things. The trick is to see whether the little horizontal line has to do with one number or two. A negative sign is a horizontal line in front of just one number, and it tells us to reflect the number across zero on a number line: A minus sign is a horizontal sign in between two numbers, and it tells us to walk to the first number, then walk in the opposite direction of the second number: 4 – 5 = -1 To help avoid uncertainty, you can put parentheses around negative numbers. For example, write (-4) instead of -4. Hopefully you don't use a lot of emoticons when doing your math homework, because something like this can get awfully confusing: (-:3 - 7;-0):-) You can also make your negative signs smaller and higher up than minus signs. Don't put them so high up that you can't get them back down when you need them, though. Be Careful: Subtraction does not commute! (It works from home.) This is because subtraction changes the direction we're walking on the number line for the second number only. 8 – 10 = -2 10 – 8 = 2 So 8 – 10 ≠ 10 – 8. Subtraction is also not associative. The order in which we perform multiple subtractions changes the final answer. (3 – 4) – 2 = -3 3 – (4 – 2) = 1 You're always going to want to perform subtraction from left to right: 3 – 4 – 2 = -3. This should be easy to remember, because that's also the direction in which you read, as well as the direction in which you open the chocolates on your Advent calendar. Or, if you're Jewish, the direction in which you light the candles of your menorah. Or, if you're Buddhist, the direction in which you align your chakras. Another way to think about this is that subtraction is really just the addition of a negative. This way, you can rewrite the problem as: 3 + (-4) + (-2) Now it's an addition problem, so it doesn't matter what order you add them in! If we're subtracting a bigger number from a smaller number (for example, 13 – 25), one way to find the answer is to pretend the problem is structured in reverse: evaluate 25 – 13 to get 12. Since we know 13 – 25 will be to the left of zero, stick a negative sign onto the front of it to get -12. Make sure you use Gorilla Glue so that thing really stays on there. The reason this method works is that whether you go 13 to the right and 25 to the left, or 25 to the right and 13 to the left, you'll end up the same distance from zero. To give the correct final answer, use common sense to figure out which side of zero the answer is on. If you're lacking in the common sense department, then maybe don't use this method. Also, don't rest your palm on one of the eyes of a stove when it's glowing orange.
Stellar evolution is the process by which a star changes during its lifetime. Depending on the mass of the star, this lifetime ranges from a few million years for the most massive to trillions of years for the least massive, which is considerably longer than the age of the universe. The table shows the lifetimes of stars as a function of their masses. All stars are born from collapsing clouds of gas and dust, often called nebulae or molecular clouds. Over the course of millions of years, these protostars settle down into a state of equilibrium, becoming what is known as a main-sequence star. Nuclear fusion powers a star for most of its life. Initially the energy is generated by the fusion of hydrogen atoms at the core of the main-sequence star. Later, as the preponderance of atoms at the core becomes helium, stars like the Sun begin to fuse hydrogen along a spherical shell surrounding the core. This process causes the star to gradually grow in size, passing through the subgiant stage until it reaches the red giant phase. Stars with at least half the mass of the Sun can also begin to generate energy through the fusion of helium at their core, whereas more-massive stars can fuse heavier elements along a series of concentric shells. Once a star like the Sun has exhausted its nuclear fuel, its core collapses into a dense white dwarf and the outer layers are expelled as a planetary nebula. Stars with around ten or more times the mass of the Sun can explode in a supernova as their inert iron cores collapse into an extremely dense neutron star or black hole. Although the universe is not old enough for any of the smallest red dwarfs to have reached the end of their lives, stellar models suggest they will slowly become brighter and hotter before running out of hydrogen fuel and becoming low-mass white dwarfs. Stellar evolution is not studied by observing the life of a single star, as most stellar changes occur too slowly to be detected, even over many centuries. Instead, astrophysicists come to understand how stars evolve by observing numerous stars at various points in their lifetime, and by simulating stellar structure using computer models. In June 2015, astronomers reported evidence for Population III stars in the Cosmos Redshift 7 galaxy at z = 6.60. Such stars are likely to have existed in the very early universe (i.e., at high redshift), and may have started the production of chemical elements heavier than hydrogen that are needed for the later formation of planets and life as we know it. - 1 Birth of a star - 2 Mature stars - 3 Stellar remnants - 4 Models - 5 See also - 6 Further reading - 7 External links - 8 References Birth of a star Stellar evolution starts with the gravitational collapse of a giant molecular cloud. Typical giant molecular clouds are roughly 100 light-years (9.5×1014 km) across and contain up to 6,000,000 solar masses (1.2×1037 kg). As it collapses, a giant molecular cloud breaks into smaller and smaller pieces. In each of these fragments, the collapsing gas releases gravitational potential energy as heat. As its temperature and pressure increase, a fragment condenses into a rotating sphere of superhot gas known as a protostar. A protostar continues to grow by accretion of gas and dust from the molecular cloud, becoming a pre-main-sequence star as it reaches its final mass. Further development is determined by its mass. (Mass is compared to the mass of the Sun: 1.0 M☉ (2.0×1030 kg) means 1 solar mass.) Protostars are encompassed in dust, and are thus more readily visible at infrared wavelengths. Observations from the Wide-field Infrared Survey Explorer (WISE) have been especially important for unveiling numerous Galactic protostars and their parent star clusters. Brown dwarfs and sub-stellar objects Protostars with masses less than roughly 0.08 M☉ (1.6×1029 kg) never reach temperatures high enough for nuclear fusion of hydrogen to begin. These are known as brown dwarfs. The International Astronomical Union defines brown dwarfs as stars massive enough to fuse deuterium at some point in their lives (13 Jupiter masses (MJ), 2.5 × 1028 kg, or 0.0125 M☉). Objects smaller than 13 MJ are classified as sub-brown dwarfs (but if they orbit around another stellar object they are classified as planets). Both types, deuterium-burning and not, shine dimly and die away slowly, cooling gradually over hundreds of millions of years. For a more-massive protostar, the core temperature will eventually reach 10 million kelvin, initiating the proton–proton chain reaction and allowing hydrogen to fuse, first to deuterium and then to helium. In stars of slightly over 1 M☉ (2.0×1030 kg), the carbon–nitrogen–oxygen fusion reaction (CNO cycle) contributes a large portion of the energy generation. The onset of nuclear fusion leads relatively quickly to a hydrostatic equilibrium in which energy released by the core exerts a "radiation pressure" balancing the weight of the star's matter, preventing further gravitational collapse. The star thus evolves rapidly to a stable state, beginning the main-sequence phase of its evolution. A new star will sit at a specific point on the main sequence of the Hertzsprung–Russell diagram, with the main-sequence spectral type depending upon the mass of the star. Small, relatively cold, low-mass red dwarfs fuse hydrogen slowly and will remain on the main sequence for hundreds of billions of years or longer, whereas massive, hot O-type stars will leave the main sequence after just a few million years. A mid-sized yellow dwarf star, like the Sun, will remain on the main sequence for about 10 billion years. The Sun is thought to be in the middle of its main sequence lifespan. Eventually the core exhausts its supply of hydrogen and the star begins to evolve off of the main sequence. Without the outward pressure generated by the fusion of hydrogen to counteract the force of gravity the core contracts until either electron degeneracy pressure becomes sufficient to oppose gravity or the core becomes hot enough (around 100 MK) for helium fusion to begin. Which of these happens first depends upon the star's mass. What happens after a low-mass star ceases to produce energy through fusion has not been directly observed; the universe is around 13.8 billion years old, which is less time (by several orders of magnitude, in some cases) than it takes for fusion to cease in such stars. Recent astrophysical models suggest that red dwarfs of 0.1 M☉ may stay on the main sequence for some six to twelve trillion years, gradually increasing in both temperature and luminosity, and take several hundred billion more to collapse, slowly, into a white dwarf. Such stars will not become red giants as they are fully convective and will not develop a degenerate helium core with a shell burning hydrogen. Instead, hydrogen fusion will proceed until almost the whole star is helium. Slightly more massive stars do expand into red giants, but their helium cores are not massive enough to reach the temperatures required for helium fusion so they never reach the tip of the red giant branch. When hydrogen shell burning finishes, these stars move directly off the red giant branch like a post AGB star, but at lower luminosity, to become a white dwarf. A star of about 0.5 M☉ will be able to reach temperatures high enough to fuse helium, and these "mid-sized" stars go on to further stages of evolution beyond the red giant branch. Stars of roughly 0.5–10 M☉ become red giants, which are large non-main-sequence stars of stellar classification K or M. Red giants lie along the right edge of the Hertzsprung–Russell diagram due to their red color and large luminosity. Examples include Aldebaran in the constellation Taurus and Arcturus in the constellation of Boötes. Red giants all have inert cores with hydrogen-burning shells: concentric layers atop the core that are still fusing hydrogen into helium. Mid-sized stars are red giants during two different phases of their post-main-sequence evolution: red-giant-branch stars, whose inert cores are made of helium, and asymptotic-giant-branch stars, whose inert cores are made of carbon. Asymptotic-giant-branch stars have helium-burning shells inside the hydrogen-burning shells, whereas red-giant-branch stars have hydrogen-burning shells only. In either case, the accelerated fusion in the hydrogen-containing layer immediately over the core causes the star to expand. This lifts the outer layers away from the core, reducing the gravitational pull on them, and they expand faster than the energy production increases. This causes the outer layers of the star to cool, which causes the star to become redder than it was on the main sequence. The red-giant-branch phase of a star's life follows the main sequence. Initially, the cores of red-giant-branch stars collapse, as the internal pressure of the core is insufficient to balance gravity. This gravitational collapse releases energy, heating concentric shells immediately outside the inert helium core so that hydrogen fusion continues in these shells. The core of a red-giant-branch star of up to a few solar masses stops collapsing when it is dense enough to be supported by electron degeneracy pressure. Once this occurs, the core reaches hydrostatic equilibrium: the electron degeneracy pressure is sufficient to balance gravitational pressure. The core's gravity compresses the hydrogen in the layer immediately above it, causing it to fuse faster than hydrogen would fuse in a main-sequence star of the same mass. This in turn causes the star to become more luminous (from 1,000–10,000 times brighter) and expand; the degree of expansion outstrips the increase in luminosity, causing the effective temperature to decrease. The expanding outer layers of the star are convective, with the material being mixed by turbulence from near the fusing regions up to the surface of the star. For all but the lowest-mass stars, the fused material has remained deep in the stellar interior prior to this point, so the convecting envelope makes fusion products visible at the star's surface for the first time. At this stage of evolution, the results are subtle, with the largest effects, alterations to the isotopes of hydrogen and helium, being unobservable. The effects of the CNO cycle appear at the surface, with lower 12C/13C ratios and altered proportions of carbon and nitrogen. These are detectable with spectroscopy and have been measured for many evolved stars. As the hydrogen in the shell around the core is consumed, the helium core grows. Eventually, the electrons in the helium core of stars less than about 2.5 M☉ become degenerate, preventing the helium core from contracting further. Later in the red giant phase, the cores of stars more massive than 0.5 M☉ get hot enough to start helium fusion by the triple-alpha process. In stars of approximately one solar mass, it can take a billion years or more for the core to reach helium ignition temperatures. If the core is largely supported by electron degeneracy pressure, helium fusion will ignite on a timescale of days in a helium flash. In more massive stars, the ignition of helium fusion occurs relatively slowly with no flash. The nuclear power released during the helium flash is very large, on the order of 108 times the luminosity of the Sun for a few days and 1011 times the luminosity of the Sun (roughly the luminosity of the Milky Way Galaxy) for a few seconds. However, the energy is absorbed by the stellar envelope and thus cannot be seen from outside the star. The energy released by helium fusion causes the core to expand, so that hydrogen fusion in the overlying layers slows and total energy generation decreases. The star contracts, although not all the way to the main sequence, and it migrates to the horizontal branch on the Hertzsprung–Russell diagram, gradually shrinking in radius and increasing its surface temperature. Core helium flash stars evolve to the red end of the horizontal branch but do not migrate to higher temperatures before they gain a degenerate carbon-oxygen core and start helium shell burning. These stars are often observed as a red clump of stars in the colour-magnitude diagram of a cluster, hotter and less luminous than the red giants. Higher-mass stars with larger helium cores move along the horizontal branch to higher temperatures, some becoming unstable pulsating stars in the yellow instability strip (RR Lyrae variables), whereas some become even hotter and can form a blue tail or blue hook to the horizontal branch. The exact morphology of the horizontal branch depends on parameters such as metallicity, age, and helium content, but the exact details are still being modelled. After a star has consumed the helium at the core, hydrogen and helium fusion continues in shells around a hot core of carbon and oxygen. The star follows the asymptotic giant branch on the Hertzsprung–Russell diagram, paralleling the original red giant evolution, but with even faster energy generation (which lasts for a shorter time). Although helium is being burnt in a shell, the majority of the energy is produced by hydrogen burning in a shell further from the core of the star. Helium from these hydrogen burning shells drops towards the center of the star and periodically the energy output from the helium shell increases dramatically. This is known as a thermal pulse and they occur towards the end of the asymptotic-giant-branch phase, sometimes even into the post-asymptotic-giant-branch phase. Depending on mass and composition, there may be several to hundreds of thermal pulses. There is a phase on the ascent of the asymptotic-giant-branch where a deep convective zone forms and can bring carbon from the core to the surface. This is known as the second dredge up, and in some stars there may even be a third dredge up. In this way a carbon star is formed, very cool and strongly reddened stars showing strong carbon lines in their spectra. A process known as hot bottom burning may convert carbon into oxygen and nitrogen before it can be dredged to the surface, and the interaction between these processes determines the observed luminosities and spectra of carbon stars in particular clusters. Another well known class of asymptotic-giant-branch stars are the Mira variables, which pulsate with well-defined periods of tens to hundreds of days and large amplitudes up to about 10 magnitudes (in the visual, total luminosity changes by a much smaller amount). In more-massive stars the stars become more luminous and the pulsation period is longer, leading to enhanced mass loss, and the stars become heavily obscured at visual wavelengths. These stars can be observed as OH/IR stars, pulsating in the infra-red and showing OH maser activity. These stars are clearly oxygen rich, in contrast to the carbon stars, but both must be produced by dredge ups. These mid-range stars ultimately reach the tip of the asymptotic-giant-branch and run out of fuel for shell burning. They are not sufficiently massive to start full-scale carbon fusion, so they contract again, going through a period of post-asymptotic-giant-branch superwind to produce a planetary nebula with an extremely hot central star. The central star then cools to a white dwarf. The expelled gas is relatively rich in heavy elements created within the star and may be particularly oxygen or carbon enriched, depending on the type of the star. The gas builds up in an expanding shell called a circumstellar envelope and cools as it moves away from the star, allowing dust particles and molecules to form. With the high infrared energy input from the central star, ideal conditions are formed in these circumstellar envelopes for maser excitation. It is possible for thermal pulses to be produced once post-asymptotic-giant-branch evolution has begun, producing a variety of unusual and poorly understood stars known as born-again asymptotic-giant-branch stars. These may result in extreme horizontal-branch stars (subdwarf B stars), hydrogen deficient post-asymptotic-giant-branch stars, variable planetary nebula central stars, and R Coronae Borealis variables. In massive stars, the core is already large enough at the onset of the hydrogen burning shell that helium ignition will occur before electron degeneracy pressure has a chance to become prevalent. Thus, when these stars expand and cool, they do not brighten as much as lower-mass stars; however, they were much brighter than lower-mass stars to begin with, and are thus still brighter than the red giants formed from less-massive stars. These stars are unlikely to survive as red supergiants; instead they will destroy themselves as type II supernovas. Extremely massive stars (more than approximately 40 M☉), which are very luminous and thus have very rapid stellar winds, lose mass so rapidly due to radiation pressure that they tend to strip off their own envelopes before they can expand to become red supergiants, and thus retain extremely high surface temperatures (and blue-white color) from their main-sequence time onwards. The largest stars of the current generation are about 100-150 M☉ because the outer layers would be expelled by the extreme radiation. Although lower-mass stars normally do not burn off their outer layers so rapidly, they can likewise avoid becoming red giants or red supergiants if they are in binary systems close enough so that the companion star strips off the envelope as it expands, or if they rotate rapidly enough so that convection extends all the way from the core to the surface, resulting in the absence of a separate core and envelope due to thorough mixing. The core grows hotter and denser as it gains material from fusion of hydrogen at the base of the envelope. In all massive stars, electron degeneracy pressure is insufficient to halt collapse by itself, so as each major element is consumed in the center, progressively heavier elements ignite, temporarily halting collapse. If the core of the star is not too massive (less than approximately 1.4 M☉, taking into account mass loss that has occurred by this time), it may then form a white dwarf (possibly surrounded by a planetary nebula) as described above for less-massive stars, with the difference that the white dwarf is composed chiefly of oxygen, neon, and magnesium. Above a certain mass (estimated at approximately 2.5 M☉ and whose star's progenitor was around 10 M☉), the core will reach the temperature (approximately 1.1 gigakelvins) at which neon partially breaks down to form oxygen and helium, the latter of which immediately fuses with some of the remaining neon to form magnesium; then oxygen fuses to form sulfur, silicon, and smaller amounts of other elements. Finally, the temperature gets high enough that any nucleus can be partially broken down, most commonly releasing an alpha particle (helium nucleus) which immediately fuses with another nucleus, so that several nuclei are effectively rearranged into a smaller number of heavier nuclei, with net release of energy because the addition of fragments to nuclei exceeds the energy required to break them off the parent nuclei. A star with a core mass too great to form a white dwarf but insufficient to achieve sustained conversion of neon to oxygen and magnesium, will undergo core collapse (due to electron capture) before achieving fusion of the heavier elements. Both heating and cooling caused by electron capture onto minor constituent elements (such as aluminum and sodium) prior to collapse may have a significant impact on total energy generation within the star shortly before collapse. This may produce a noticeable effect on the abundance of elements and isotopes ejected in the subsequent supernova. Once the nucleosynthesis process arrives at iron-56, the continuation of this process consumes energy (the addition of fragments to nuclei releases less energy than required to break them off the parent nuclei). If the mass of the core exceeds the Chandrasekhar limit, electron degeneracy pressure will be unable to support its weight against the force of gravity, and the core will undergo sudden, catastrophic collapse to form a neutron star or (in the case of cores that exceed the Tolman-Oppenheimer-Volkoff limit), a black hole. Through a process that is not completely understood, some of the gravitational potential energy released by this core collapse is converted into a Type Ib, Type Ic, or Type II supernova. It is known that the core collapse produces a massive surge of neutrinos, as observed with supernova SN 1987A. The extremely energetic neutrinos fragment some nuclei; some of their energy is consumed in releasing nucleons, including neutrons, and some of their energy is transformed into heat and kinetic energy, thus augmenting the shock wave started by rebound of some of the infalling material from the collapse of the core. Electron capture in very dense parts of the infalling matter may produce additional neutrons. Because some of the rebounding matter is bombarded by the neutrons, some of its nuclei capture them, creating a spectrum of heavier-than-iron material including the radioactive elements up to (and likely beyond) uranium. Although non-exploding red giants can produce significant quantities of elements heavier than iron using neutrons released in side reactions of earlier nuclear reactions, the abundance of elements heavier than iron (and in particular, of certain isotopes of elements that have multiple stable or long-lived isotopes) produced in such reactions is quite different from that produced in a supernova. Neither abundance alone matches that found in the Solar System, so both supernovae and ejection of elements from red giants are required to explain the observed abundance of heavy elements and isotopes thereof. The energy transferred from collapse of the core to rebounding material not only generates heavy elements, but provides for their acceleration well beyond escape velocity, thus causing a Type Ib, Type Ic, or Type II supernova. Note that current understanding of this energy transfer is still not satisfactory; although current computer models of Type Ib, Type Ic, and Type II supernovae account for part of the energy transfer, they are not able to account for enough energy transfer to produce the observed ejection of material. Some evidence gained from analysis of the mass and orbital parameters of binary neutron stars (which require two such supernovae) hints that the collapse of an oxygen-neon-magnesium core may produce a supernova that differs observably (in ways other than size) from a supernova produced by the collapse of an iron core. The most-massive stars that exist today may be completely destroyed by a supernova with an energy greatly exceeding its gravitational binding energy. This rare event, caused by pair-instability, leaves behind no black hole remnant. In the past history of the universe, some stars were even larger than the largest that exists today, and they would immediately collapse into a black hole at the end of their lives, due to photodisintegration. After a star has burned out its fuel supply, its remnants can take one of three forms, depending on the mass during its lifetime. White and black dwarfs For a star of 1 M☉, the resulting white dwarf is of about 0.6 M☉, compressed into approximately the volume of the Earth. White dwarfs are stable because the inward pull of gravity is balanced by the degeneracy pressure of the star's electrons, a consequence of the Pauli exclusion principle. Electron degeneracy pressure provides a rather soft limit against further compression; therefore, for a given chemical composition, white dwarfs of higher mass have a smaller volume. With no fuel left to burn, the star radiates its remaining heat into space for billions of years. A white dwarf is very hot when it first forms, more than 100,000 K at the surface and even hotter in its interior. It is so hot that a lot of its energy is lost in the form of neutrinos for the first 10 million years of its existence, but will have lost most of its energy after a billion years. The chemical composition of the white dwarf depends upon its mass. A star of a few solar masses will ignite carbon fusion to form magnesium, neon, and smaller amounts of other elements, resulting in a white dwarf composed chiefly of oxygen, neon, and magnesium, provided that it can lose enough mass to get below the Chandrasekhar limit (see below), and provided that the ignition of carbon is not so violent as to blow the star apart in a supernova. A star of mass on the order of magnitude of the Sun will be unable to ignite carbon fusion, and will produce a white dwarf composed chiefly of carbon and oxygen, and of mass too low to collapse unless matter is added to it later (see below). A star of less than about half the mass of the Sun will be unable to ignite helium fusion (as noted earlier), and will produce a white dwarf composed chiefly of helium. In the end, all that remains is a cold dark mass sometimes called a black dwarf. However, the universe is not old enough for any black dwarfs to exist yet. If the white dwarf's mass increases above the Chandrasekhar limit, which is 1.4 M☉ for a white dwarf composed chiefly of carbon, oxygen, neon, and/or magnesium, then electron degeneracy pressure fails due to electron capture and the star collapses. Depending upon the chemical composition and pre-collapse temperature in the center, this will lead either to collapse into a neutron star or runaway ignition of carbon and oxygen. Heavier elements favor continued core collapse, because they require a higher temperature to ignite, because electron capture onto these elements and their fusion products is easier; higher core temperatures favor runaway nuclear reaction, which halts core collapse and leads to a Type Ia supernova. These supernovae may be many times brighter than the Type II supernova marking the death of a massive star, even though the latter has the greater total energy release. This inability to collapse means that no white dwarf more massive than approximately 1.4 M☉ can exist (with a possible minor exception for very rapidly spinning white dwarfs, whose centrifugal force due to rotation partially counteracts the weight of their matter). Mass transfer in a binary system may cause an initially stable white dwarf to surpass the Chandrasekhar limit. If a white dwarf forms a close binary system with another star, hydrogen from the larger companion may accrete around and onto a white dwarf until it gets hot enough to fuse in a runaway reaction at its surface, although the white dwarf remains below the Chandrasekhar limit. Such an explosion is termed a nova. When a stellar core collapses, the pressure causes electron capture, thus converting the great majority of the protons into neutrons. The electromagnetic forces keeping separate nuclei apart are gone (proportionally, if nuclei were the size of dust mites, atoms would be as large as football stadiums), and most of the core of the star becomes a dense ball of contiguous neutrons (in some ways like a giant atomic nucleus), with a thin overlying layer of degenerate matter (chiefly iron unless matter of different composition is added later). The neutrons resist further compression by the Pauli Exclusion Principle, in a way analogous to electron degeneracy pressure, but stronger. These stars, known as neutron stars, are extremely small—on the order of radius 10 km, no bigger than the size of a large city—and are phenomenally dense. Their period of rotation shortens dramatically as the stars shrink (due to conservation of angular momentum); observed rotational periods of neutron stars range from about 1.5 milliseconds (over 600 revolutions per second) to several seconds. When these rapidly rotating stars' magnetic poles are aligned with the Earth, we detect a pulse of radiation each revolution. Such neutron stars are called pulsars, and were the first neutron stars to be discovered. Though electromagnetic radiation detected from pulsars is most often in the form of radio waves, pulsars have also been detected at visible, X-ray, and gamma ray wavelengths. If the mass of the stellar remnant is high enough, the neutron degeneracy pressure will be insufficient to prevent collapse below the Schwarzschild radius. The stellar remnant thus becomes a black hole. The mass at which this occurs is not known with certainty, but is currently estimated at between 2 and 3 M☉. Black holes are predicted by the theory of general relativity. According to classical general relativity, no matter or information can flow from the interior of a black hole to an outside observer, although quantum effects may allow deviations from this strict rule. The existence of black holes in the universe is well supported, both theoretically and by astronomical observation. Because the core-collapse supernova mechanism itself is imperfectly understood, it is still not known whether it is possible for a star to collapse directly to a black hole without producing a visible supernova, or whether some supernovae initially form unstable neutron stars which then collapse into black holes; the exact relation between the initial mass of the star and the final remnant is also not completely certain. Resolution of these uncertainties requires the analysis of more supernovae and supernova remnants. A stellar evolutionary model is a mathematical model that can be used to compute the evolutionary phases of a star from its formation until it becomes a remnant. The mass and chemical composition of the star are used as the inputs, and the luminosity and surface temperature are the only constraints. The model formulae are based upon the physical understanding of the star, usually under the assumption of hydrostatic equilibrium. Extensive computer calculations are then run to determine the changing state of the star over time, yielding a table of data that can be used to determine the evolutionary track of the star across the Hertzsprung–Russell diagram, along with other evolving properties. Accurate models can be used to estimate the current age of a star by comparing its physical properties with those of stars along a matching evolutionary track. - Astronomy 606 (Stellar Structure and Evolution) lecture notes, Cole Miller, Department of Astronomy, University of Maryland - Astronomy 162, Unit 2 (The Structure & Evolution of Stars) lecture notes, Richard W. Pogge, Department of Astronomy, Ohio State University - Hansen, Carl J.; Kawaler, Steven D.; Trimble, Virginia (2004). Stellar interiors: physical principles, structure, and evolution (2nd ed.). Springer-Verlag. ISBN 0-387-20089-4 - Prialnik, Dina (2000). An Introduction to the Theory of Stellar Structure and Evolution. Cambridge University Press. ISBN 0-521-65065-8. - Ryan, Sean G.; Norton, Andrew J. (2010). Stellar Evolution and Nucleosynthesis. Cambridge University Press. p. 125. ISBN 0521133203. \|Wikiversity has learning materials about Stellar evolution\| - Bertulani, Carlos A. (2013). Nuclei in the Cosmos. World Scientific. ISBN 978-981-4417-66-2. - Laughlin, Gregory; Bodenheimer, Peter; Adams, Fred C. (1997). "The End of the Main Sequence". The Astrophysical Journal 482: 420–432. Bibcode:1997ApJ...482..420L. doi:10.1086/304125. - Sobral, David; Matthee, Jorryt; Darvish, Behnam; Schaerer, Daniel; Mobasher, Bahram; Röttgering, Huub J. A.; Santos, Sérgio; Hemmati, Shoubaneh (4 June 2015). "Evidence For POPIII-Like Stellar Populations In The Most Luminous LYMAN-α Emitters At The Epoch Of Re-Ionisation: Spectroscopic Confirmation" (PDF). The Astrophysical Journal. doi:10.1088/0004-637x/808/2/139. Retrieved 17 June 2015. - Overbye, Dennis (17 June 2015). "Astronomers Report Finding Earliest Stars That Enriched Cosmos". New York Times. Retrieved 17 June 2015. - Prialnik (2000, Chapter 10) - "Wide-field Infrared Survey Explorer Mission". NASA. - Majaess, D. (2013). Discovering protostars and their host clusters via WISE, ApSS, 344, 1 (VizieR catalog) - "Working Group on Extrasolar Planets: Definition of a "Planet"". IAU position statement. 2003-02-28. Archived from the original on February 4, 2012. Retrieved 2012-05-30. - Prialnik (2000, Fig. 8.19, p. 174) - "Why the Smallest Stars Stay Small". Sky & Telescope (22). November 1997. - Adams, F. C.; P. Bodenheimer; G. Laughlin (2005). "M dwarfs: planet formation and long term evolution". Astronomische Nachrichten 326 (10): 913–919. Bibcode:2005AN....326..913A. doi:10.1002/asna.200510440. - Ryan & Norton (2010, p. 114) - Hansen, Kawaler & Trimble (2004, pp. 55–56) - Hansen, Kawaler & Trimble (2004, pp. 62–63) - Ryan & Norton (2010, p. 115) - Prialnik (2000, p. 155, Table 8.4) - Ryan & Norton (2010, p. 125) - Prialnik (2000, p. 151) - Gratton, R. G.; Carretta, E.; Bragaglia, A.; Lucatello, S.; d'Orazi, V. (2010). "The second and third parameters of the horizontal branch in globular clusters". Astronomy and Astrophysics 517: A81. arXiv:1004.3862. Bibcode:2010A&A...517A..81G. doi:10.1051/0004-6361/200912572. - Sackmann, I. -J.; Boothroyd, A. I.; Kraemer, K. E. (1993). "Our Sun. III. Present and Future". The Astrophysical Journal 418: 457. Bibcode:1993ApJ...418..457S. doi:10.1086/173407. - van Loon; Zijlstra; Whitelock; Peter te Lintel Hekkert; Chapman; Cecile Loup; Groenewegen; Waters; Trams (1998). "Obscured Asymptotic Giant Branch stars in the Magellanic Clouds IV. Carbon stars and OH/IR stars". Astronomy and Astrophysics 329: 169–85. arXiv:astro-ph/9709119v1. CiteSeerX: 10 .1 .1 .389 .3269. - Bibcode: 1991IAUS..145..363H - D. Vanbeveren; De Loore, C.; Van Rensbergen, W. (1998). "Massive stars" (PDF). The Astronomy and Astrophysics Review 9 (1–2): 63–152. Bibcode:1998A&ARv...9...63V. doi:10.1007/s001590050015. Archived from the original (PDF) on 2009-03-27. - Ken'ichi Nomoto (1987). "Evolution of 8–10 M☉ stars toward electron capture supernovae. II – Collapse of an O + Ne + Mg core". Astrophysical Journal. 322. Part 1: 206–214. Bibcode:1987ApJ...322..206N. doi:10.1086/165716. - Claudio Ritossa; et al. (1999). "On the Evolution of Stars that Form Electron-degenerate Cores Processed by Carbon Burning. V. Shell Convection Sustained by Helium Burning, Transient Neon Burning, Dredge-out, URCA Cooling, and Other Properties of an 11 M_solar Population I Model Star". The Astrophysical Journal 515 (1): 381–397. Bibcode:1999ApJ...515..381R. doi:10.1086/307017. - How do Massive Stars Explode? - Robert Buras; et al. (June 2003). "Supernova Simulations Still Defy Explosions". Research Highlights. Max-Planck-Institut für Astrophysik. - E. P. J. van den Heuvel (2004). "X-Ray Binaries and Their Descendants: Binary Radio Pulsars; Evidence for Three Classes of Neutron Stars?". Proceedings of the 5th INTEGRAL Workshop on the INTEGRAL Universe (ESA SP-552) 552: 185–194. arXiv:astro-ph/0407451. Bibcode:2004inun.conf..185V. - Pair Instability Supernovae and Hypernovae., Nicolay J. Hammer, (2003), accessed May 7, 2007. Archived June 8, 2012 at the Wayback Machine - Fossil Stars (1): White Dwarfs - Ken'ichi Nomoto (1984). "Evolution of 8–10 M☉ stars toward electron capture supernovae. I – Formation of electron-degenerate O + Ne + Mg cores". Astrophysical Journal. Part 1 277: 791–805. Bibcode:1984ApJ...277..791N. doi:10.1086/161749. - Ken'ichi Nomoto & Yoji Kondo (1991). "Conditions for accretion-induced collapse of white dwarfs". Astrophysical Journal. 367. Part 2: L19–L22. Bibcode:1991ApJ...367L..19N. doi:10.1086/185922. - D'Amico, N.; Stappers, B. W.; Bailes, M.; Martin, C. E.; Bell, J. F.; Lyne, A. G.; Manchester, R. N (1998). "The Parkes Southern Pulsar Survey - III. Timing of long-period pulsars". Monthly Notices of the Royal Astronomical Society 297: 28–40. Bibcode:1998MNRAS.297...28D. doi:10.1046/j.1365-8711.1998.01397.x. - Courtland, Rachel (17 October 2008). "Pulsar Detected by Gamma Waves Only". New Scientist. Archived from the original on April 2, 2013. - Demarque, P.; Guenther, D. B.; Li, L. H.; Mazumdar, A.; Straka, C. W. (August 2008). "YREC: the Yale rotating stellar evolution code". Astrophysics and Space Science 316 (1–4): 31–41. arXiv:0710.4003. Bibcode:2008Ap&SS.316...31D. doi:10.1007/s10509-007-9698-y. ISBN 9781402094408. - Ryan, Seán; Norton, Andrew J. (2010). "Assigning ages from hydrogen-burning timescales". Stellar Evolution and Nucleosynthesis. Cambridge University Press. p. 79. ISBN 0-521-13320-3.
Word problems help develop different skills sets for young math students. Learn how to create fourth grade level word problems to help your child understand math better.See Transcript Transcript:Tips for Creating 4th Grade Level Word Problems Hi, I’m Scott for About.com, today I have a few tips for you on how to create word problems from Math.About.com. Word problems are a great way to teach children how the math they are learning in school applies to everyday practical situations. More specifically, word problems show students that math is not just about dry number calculations, but about real life problems. Word problems or story problems help children develop critical thinking skills. Review Basic Concepts in the Word Problems > Tip 1: Start by becoming familiar with the general concepts your child is learning in math. Students in the fourth grade should be learning how to understand basic patterns and algebra, data management and probability, number concepts and basic geometry concepts and types of measurement. For an overview of fourth grade math skills, go to: Math.About.com. Word Problems Should Relate to the Student's Life Tip 2: Once you’ve decided the type of word problem you’re going to create, relate the problem to a real-life situation. For example, Children in the 4th grade should be able to understand basic patterns and algebra, data management and probability, number concepts and basic geometry concepts and types of measurement. Fourth grade word problems should test these specific skills, grounding abstract math concepts in practical situations that third graders can relate to such as classroom or play situations. When creating word problems for fourth graders, use people, objects, places, or concepts that they are familiar with. In the following word problem, familiar every circumstances such as preparing to go to school help the student relate to abstract fourth grade number concepts.Here is a sample problem: Kerri has to be to school by 8:30. It takes her 5 minutes to brush her teeth, 10 minutes to shower, 20 minutes to dry her hair, 10 minutes to eat breakfast and 25 minutes to walk to school. What time will she need to get up? Create a Strategy to Solve the Word Problem Tip 3: Math is all about problem solving. One of the best ways to help children learn math is to present them with a problem in which they have to devise their own strategies to find the solution(s). There is usually more than 1 way to solve many math problems, so try to devise a problem that can be solved in two or more different ways using math concepts familiar to the child. Here is the sample problem: You and two friends are ready to share your Birthday cake. Just before you cut the cake, a 4th friend comes to join you. Show and explain what you will do.Here, the question can solved using the concept of fractions. At first, the child must cut the cake into thirds (as there were three total students). But in the end there were four total students so they must cut it into fourths.The answer could be arrived at by using geometry concepts just as well. Since in the end there were four students, you could cut the cake in two half circles, then cut each half circle into quarter circles to get four equal pieces. Show How the Math Problem is Solved Tip 4: Have the students justify their solutions. You can find word problem worksheets according to each grade on Math.About.com along with more practical problem solving tips. Thank you for watching. For more information, visit: Math.About.com About videos are made available on an "as is" basis, subject to the User Agreement
Franklin D. Roosevelt was the 32nd president of the United States. He served from 1933-1945. Roosevelt helped the American people regain hope during the hardest of times. He brought confidence when he promised motivating, powerful action, and added in his inaugural address, “the only thing we have left to fear is fear itself”(Franklin D. Roosevelt). During the toughest times of the Great Depression, he introduced the New Deal. The New Deal resorted hope and provided programs to help the people during the Great Depression. The Great Depression was an economic slump in North America, Europe, and other industrialized areas of the world that began in 1929 and lasted until about 1939. It was the longest and most severe depression ever experienced by the industrialized Western world. ” Even though it is said the U. S. economy had gone into depression six months earlier, the Great Depression may be said to have begun with the collapse of stock market prices in the New York Stock Exchange. Stock prices in the United States continued to fall during the next three years. Other than ruining many thousands of individual investors, the abrupt decline in the value of assets greatly damaged banks and other financial institutions (About the Great Depression). The Great Depression had important consequences in the political territory. Economic distress led to the election of Franklin D. Roosevelt. Roosevelt introduced Lerner 2 many major changes in the American economy. He used increased government regulation and massive public-works projects to promote recovery. In spite of this active intervention, mass unemployment and economic decline continued (About the Great Depression). To help, Franklin D. Roosevelt came up with the idea of the New Deal. The term New Deal was coined during Roosevelt’s nomination acceptance speech (The New Deal). When launching the New Deal, Roosevelt’s intent was to address the Country’s needs. “Roosevelt promised relief for the poor and more public works programs to provide jobs. He attacked Hoover and the Republicans for their response to the Great Depression. ” The New Deal offered new roles for women, too. Although some women served as leaders in several New Deal agencies, most still experienced challenges and discrimination. They experienced lower wages, less opportunities, and hostility in the workplace (Chapter 22). The New Deal also offered new roles for African Americans. A group of African Americans hired to fill government posts were known as the Black Cabinet. They served as unofficial advisers to the president. African Americans still continued to face tremendous hardships during the 1930’s. For example, New Deal programs did not help thousands of African American sharecroppers and tenant farmers (Chapter 22). The New Deal promised the three R’s. They were relief, recovery, and reform. The first R, relief, helped millions of Americans enjoy some form of help (Chapter 22). Early programs that provided food, shelter, and water helped people tremendously. Lerner 3 executing these programs at a local level was no simple matter. Federal officials encountered customs and laws that led to injustice. These programs included the Federal Emergency Relief Administration, the Work Progress Administration, the National Youth Administration and many more (Bondi 319). The second R, recovery, wasn’t as successful as it should have been. Unemployment remained high and the idea of recovery did not work as well as what Roosevelt said. Some critics said that Roosevelt needed the support of big businesses. Others said that the New Deal didn’t spend enough money. The third R, reform, was more successful and long lasting. The Federal Deposit Insurance Corporation restored people’s confidence in the nation’s banks. The reform part of the New Deal left thousands of roadways, bridges, dams, and public buildings (Chapter 22). “Floods change the course of history. ” The flood that happened in the spring of 1927 is no exception to this statement. When the waters of the Mississippi broke through banks and levees the disaster was tremendous. A wall of water rushed into an area where nearly one million people lived. The Secretary of Commerce, Herbert Hoover hurried to Memphis to take charge (Shlaes 15). Hoover served on a commission entrusted with finding a fair way to divide the waters of the Colorado River among seven basin states (Hoover Dam History). The building of the Hoover Dam gave thousands of jobs, as it was the largest man-made structures at the time of its construction. It prevents flooding as well as provides much needed irrigation and hydroelectric power to arid regions of states (Hoover Dam). Weakening support of pro-New Deal senators and the election of 1938 caused the end of the New Deal. “Setbacks such as the court-packing fight and the 1937 economic Lerner 4 downturn gave power to anti-New Deal senators. ” The oppositions in Congress made passing New Deal legislations more difficult. During the 1938 elections, Roosevelt tried to influence voters in the South, however his candidates lost. The republicans benefited in both houses. As a result, Roosevelt lacked the congressional support he needed to pass New Deal laws. At the end of the New Deal in 1938, Americans turned their attention to the start of World War II (Chapter 22).
Mathematical equations, from the formulas of special and general relativity, to the pythagorean theorem, are both powerful and pleasing in their beauty to many scientists here are experts' . Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more khan academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Here are the terms used in equations for addition, subtraction, multiplication, and division these terms include augend, addend, sum, subtrahend, minuend, difference . Which represents a well-defined algorithm that can be used to solve any quadratic equation: 207 starting with a quadratic equation in standard form, ax 2 + bx + c = 0 divide each side by a, the coefficient of the squared term. Area using parametric equations area using polar coordinates mathematical model matrix matrix addition mathwords: terms and formulas from algebra i to . In this lesson, you'll get a refresher on number sentences you will then learn what equations are and how they can be useful in finding out. In an equation, the quantities on both sides of the equal sign are equal that's the mathematical meaning of equation, but equation can also be used in any number of situations, challenges, or efforts to solve a problem. A mathematical notation indicating the number of times a quantity is multiplied by itself base the value that is raised to a power when a number is written in exponential notation in the term 5³, 5 is the base. Equation rules, inequality, equation of a line, solution set, verify a solution this page updated 19-jul-17 mathwords: terms and formulas from algebra i to calculus. Linear format equations using unicodemath and latex in word you can also create math equations using on the keyboard using a combination of keywords and math . An equation is a mathematical statement that two things are equal it consists of two expressions, one on each side of an 'equals' sign for example: this equation states that 12 is equal to the sum of 7 and 5, which is obviously true. Definition of mathematical model: method of simulating real-life situations with mathematical equations to forecast their future behavior mathematical modeling uses tools such as decision-theory, queuing theory, and linear . An equation says that two things are equal it will have an equals sign = like this: 7 + 2 = 10 − 1 that equation says: what is on the left (7 + 2) is equal to what is on the right (10 − 1). Term: in an algebraic expression or equation, either a single number or variable, or the product of several numbers and variables separated from another term by a + or - sign, eg in the expression 3 + 4x + 5yzw, the 3, the 4x and the 5yzw are all separate terms. Mathematical formulae algebra 1 the roots of the quadratic equationax2+bx+c=0 constant term coe of x2 36 the quadratic equation whose roots are and is . First off, this is a badly titled question because i'm unsure of how to word the problem please suggest a better title the sum of $55,555$ and $33,333$ is $88,888$. A function is an equation for which any $x$ that can be plugged into the equation will yield exactly one $y$ out of the equation there it is that is the definition of functions that we’re going to use and will probably be easier to decipher just what it means. As you see, the way the equations are displayed depends on the delimiter, in this case \[ \] and open an example in sharelatex mathematical modesl a t e x allows two writing modes for mathematical expressions: the inline mode and the display mode. The term polynomial equation is usually preferred to algebraic equation a differential equation is a mathematical equation that relates some function with its . Definition of formula a formula is an expression or equation that expresses the relationship between certain quantities for example, a = pr 2 is the formula to find the area of a circle of radius r units. O write an equation, using mathematical operators and 3, x, y, 9, and b o write a one-term expression, using any mathematical operator and 4, a , and b o write a two-term expression, using any mathematical operator and 4, a , and b . Hence, we need some mathematical tools for solving equations combine like terms in each member of an equation using the addition or subtraction property . The word term is used in mathematical equations to describe either a single number, or numbers and variables multiplied together numerical terms are then grouped into expressions to come up with a definitive answer to the equation math terms are commonly seen in algebra equations using . This is a glossary of common math terms used in arithmetic, geometry, algebra, and statistics abacus - an early counting tool used for basic arithmetic absolute value - always a positive number, refers to the distance of a number from 0, the distances are positive acute angle - the measure of an . (mathematics) a mathematical statement that two expressions are equal: it is either an identity in which the variables can assume any value, or a conditional equation in which the variables have only certain values (roots).
kwizNET Subscribers, please login to turn off the Ads! Email us to get an instant on highly effective K-12 Math & English Online Quiz ( Questions Per Quiz = Grade 6 - Mathematics 9.11 Classifying Triangles by Sides Classification based on sides Triangles can be divided into three kinds according to the measures of their sides. A triangle whose sides are equal is called an All the angles of an equilateral triangle are equal. A triangle in which two sides are equal is called an In an isosceles triangle the unequal side is called the base of the triangle. The base angles of an isosceles triangle are congruent. If no two sides of a triangle are equal, it is called a Read the above properties of triangles and answer the following questions: Illustrate each of the above properties by drawing a triangle. Write in your own words, the different classification of triangles based on sides. : In a (an) _________ triangle the unequal side is called the base of the triangle : The sides of a triangle are given by 26/2 cm, 39/3 cm, 52/4 cm. The triangle is a (an) _________ triangle. : Name the triangle whose sides are given by 10'', 10'' and 10''. : If the sides of a triangle are of lengths 45/3 cm, 24/2 cm and 30/2 cm, then the triangle is a (an) _________ triangle. : "In an equilateral triangle all the sides are _________". : If the angles of a triangle in degree measure are 60, 120/2 and 180/3, then it is a (an) _________ triangle. : "The base angles of an isosceles triangle are congruent". : If the sides of a triangle are given by 6 cm, 5 cm and 7 cm, then the triangle is a _________ triangle. Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only! Subscription to kwizNET Learning System offers the following benefits: Unrestricted access to grade appropriate lessons, quizzes, & printable worksheets Instant scoring of online quizzes Progress tracking and award certificates to keep your student motivated Unlimited practice with auto-generated 'WIZ MATH' quizzes Child-friendly website with no advertisements Choice of Math, English, Science, & Social Studies Curriculums Excellent value for K-12 and ACT, SAT, & TOEFL Test Preparation Get discount offers by sending an email to Terms of Service
Nuclear magnetic resonance spectroscopy This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. (November 2016) (Learn how and when to remove this template message) Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy or magnetic resonance spectroscopy (MRS), is a spectroscopic technique to observe local magnetic fields around atomic nuclei. The sample is placed in a magnetic field and the NMR signal is produced by excitation of the nuclei sample with radio waves into nuclear magnetic resonance, which is detected with sensitive radio receivers. The intramolecular magnetic field around an atom in a molecule changes the resonance frequency, thus giving access to details of the electronic structure of a molecule and its individual functional groups. As the fields are unique or highly characteristic to individual compounds, in modern organic chemistry practice, NMR spectroscopy is the definitive method to identify monomolecular organic compounds. Similarly, biochemists use NMR to identify proteins and other complex molecules. Besides identification, NMR spectroscopy provides detailed information about the structure, dynamics, reaction state, and chemical environment of molecules. The most common types of NMR are proton and carbon-13 NMR spectroscopy, but it is applicable to any kind of sample that contains nuclei possessing spin. NMR spectra are unique, well-resolved, analytically tractable and often highly predictable for small molecules. Different functional groups are obviously distinguishable, and identical functional groups with differing neighboring substituents still give distinguishable signals. NMR has largely replaced traditional wet chemistry tests such as color reagents or typical chromatography for identification. A disadvantage is that a relatively large amount, 2–50 mg, of a purified substance is required, although it may be recovered through a workup. Preferably, the sample should be dissolved in a solvent, because NMR analysis of solids requires a dedicated magic angle spinning machine and may not give equally well-resolved spectra. The timescale of NMR is relatively long, and thus it is not suitable for observing fast phenomena, producing only an averaged spectrum. Although large amounts of impurities do show on an NMR spectrum, better methods exist for detecting impurities, as NMR is inherently not very sensitive - though at higher frequencies, sensitivity is higher. Correlation spectroscopy is a development of ordinary NMR. In two-dimensional NMR, the emission is centered around a single frequency, and correlated resonances are observed. This allows identifying the neighboring substituents of the observed functional group, allowing unambiguous identification of the resonances. There are also more complex 3D and 4D methods and a variety of methods designed to suppress or amplify particular types of resonances. In nuclear Overhauser effect (NOE) spectroscopy, the relaxation of the resonances is observed. As NOE depends on the proximity of the nuclei, quantifying the NOE for each nucleus allows for construction of a three-dimensional model of the molecule. NMR spectrometers are relatively expensive; universities usually have them, but they are less common in private companies. Between 2000 and 2015, an NMR spectrometer cost around 500,000 - 5 million USD. Modern NMR spectrometers have a very strong, large and expensive liquid helium-cooled superconducting magnet, because resolution directly depends on magnetic field strength. Less expensive machines using permanent magnets and lower resolution are also available, which still give sufficient performance for certain applications such as reaction monitoring and quick checking of samples. There are even benchtop nuclear magnetic resonance spectrometers. NMR can be observed in magnetic fields less than a millitesla. Low-resolution NMR produces broader peaks which can easily overlap one another causing issues in resolving complex structures. The use of higher strength magnetic fields result in clear resolution of the peaks and is the standard in industry. - 1 Inventors - 2 History - 3 Basic NMR techniques - 4 Correlation spectroscopy - 5 Solid-state nuclear magnetic resonance - 6 Biomolecular NMR spectroscopy - 7 See also - 8 References - 9 Further reading - 10 External links Credit for the discovery of NMR goes to Isidor Isaac Rabi, who received the Nobel Prize in Physics in 1944. The Purcell group at Harvard University and the Bloch group at Stanford University independently developed NMR spectroscopy in the late 1940s and early 1950s. Edward Mills Purcell and Felix Bloch shared the 1952 Nobel Prize in Physics for their discoveries The Purcell group at Harvard University and the Bloch group at Stanford University independently developed NMR spectroscopy in the late 1940s and early 1950s. Edward Mills Purcell and Felix Bloch shared the 1952 Nobel Prize in Physics for their discoveries. Basic NMR techniquesEdit When placed in a magnetic field, NMR active nuclei (such as 1H or 13C) absorb electromagnetic radiation at a frequency characteristic of the isotope. The resonant frequency, energy of the radiation absorbed, and the intensity of the signal are proportional to the strength of the magnetic field. For example, in a 21 Tesla magnetic field, hydrogen atoms (commonly referred to as protons) resonate at 900 MHz. It is common to refer to a 21 T magnet as a 900 MHz magnet since hydrogen is the most common nucleus detected, however different nuclei will resonate at different frequencies at this field strength in proportion to their nuclear magnetic moments. An NMR spectrometer typically consists of a spinning sample-holder inside a very strong magnet, a radio-frequency emitter and a receiver with a probe (an antenna assembly) that goes inside the magnet to surround the sample, optionally gradient coils for diffusion measurements, and electronics to control the system. Spinning the sample is usually necessary to average out diffusional motion, however some experiments call for a stationary sample when solution movement is an important variable. For instance, measurements of diffusion constants (diffusion ordered spectroscopy or DOSY) are done using a stationary sample with spinning off, and flow cells can be used for online analysis of process flows. The vast majority of molecules in a solution are solvent molecules, and most regular solvents are hydrocarbons and so contain NMR-active protons. In order to avoid detecting only signals from solvent hydrogen atoms, deuterated solvents are used where 99+% of the protons are replaced with deuterium (hydrogen-2). The most widely used deuterated solvent is deuterochloroform (CDCl3), although other solvents may be used for various reasons, such as solubility of a sample, desire to control hydrogen bonding, or melting or boiling points. The chemical shifts of a molecule will change slightly between solvents, and the solvent used will almost always be reported with chemical shifts. NMR spectra are often calibrated against the known solvent residual proton peak instead of added tetramethylsilane. Shim and lockEdit To detect the very small frequency shifts due to nuclear magnetic resonance, the applied magnetic field must be constant throughout the sample volume. High resolution NMR spectrometers use shims to adjust the homogeneity of the magnetic field to parts per billion (ppb) in a volume of a few cubic centimeters. In order to detect and compensate for inhomogeneity and drift in the magnetic field, the spectrometer maintains a "lock" on the solvent deuterium frequency with a separate lock unit. In modern NMR spectrometers shimming is adjusted automatically, though in some cases the operator has to optimize the shim parameters manually to obtain the best possible resolution. Acquisition of spectraEdit Upon excitation of the sample with a radio frequency (60–1000 MHz) pulse, a nuclear magnetic resonance response - a free induction decay (FID) - is obtained. It is a very weak signal, and requires sensitive radio receivers to pick up. A Fourier transform is carried out to extract the frequency-domain spectrum from the raw time-domain FID. A spectrum from a single FID has a low signal-to-noise ratio, but it improves readily with averaging of repeated acquisitions. Good 1H NMR spectra can be acquired with 16 repeats, which takes only minutes. However, for elements heavier than hydrogen, the relaxation time is rather long, e.g. around 8 seconds for 13C. Thus, acquisition of quantitative heavy-element spectra can be time-consuming, taking tens of minutes to hours. Following the pulse, the nuclei are, on average, excited to a certain angle vs. the spectrometer magnetic field. The extent of excitation can be controlled with the pulse width, typically ca. 3-8 µs for the optimal 90° pulse. The pulse width can be determined by plotting the (signed) intensity as a function of pulse width. It follows a sine curve, and accordingly, changes sign at pulse widths corresponding to 180° and 360° pulses. Decay times of the excitation, typically measured in seconds, depend on the effectiveness of relaxation, which is faster for lighter nuclei and in solids, and slower for heavier nuclei and in solutions, and they can be very long in gases. If the second excitation pulse is sent prematurely before the relaxation is complete, the average magnetization vector has not decayed to ground state, which affects the strength of the signal in an unpredictable manner. In practice, the peak areas are then not proportional to the stoichiometry; only the presence, but not the amount of functional groups is possible to discern. An inversion recovery experiment can be done to determine the relaxation time and thus the required delay between pulses. A 180° pulse, an adjustable delay, and a 90° pulse is transmitted. When the 90° pulse exactly cancels out the signal, the delay corresponds to the time needed for 90° of relaxation. Inversion recovery is worthwhile for quantitive 13C, 2D and other time-consuming experiments. A spinning charge generates a magnetic field that results in a magnetic moment proportional to the spin. In the presence of an external magnetic field, two spin states exist (for a spin 1/2 nucleus): one spin up and one spin down, where one aligns with the magnetic field and the other opposes it. The difference in energy (ΔE) between the two spin states increases as the strength of the field increases, but this difference is usually very small, leading to the requirement for strong NMR magnets (1-20 T for modern NMR instruments). Irradiation of the sample with energy corresponding to the exact spin state separation of a specific set of nuclei will cause excitation of those set of nuclei in the lower energy state to the higher energy state. For spin 1/2 nuclei, the energy difference between the two spin states at a given magnetic field strength is proportional to their magnetic moment. However, even if all protons have the same magnetic moments, they do not give resonant signals at the same frequency values. This difference arises from the differing electronic environments of the nucleus of interest. Upon application of an external magnetic field, these electrons move in response to the field and generate local magnetic fields that oppose the much stronger applied field. This local field thus "shields" the proton from the applied magnetic field, which must therefore be increased in order to achieve resonance (absorption of rf energy). Such increments are very small, usually in parts per million (ppm). For instance, the proton peak from an aldehyde is shifted ca. 10 ppm compared to a hydrocarbon peak, since as an electron-withdrawing group, the carbonyl deshields the proton by reducing the local electron density. The difference between 2.3487 T and 2.3488 T is therefore about 42 ppm. However a frequency scale is commonly used to designate the NMR signals, even though the spectrometer may operate by sweeping the magnetic field, and thus the 42 ppm is 4200 Hz for a 100 MHz reference frequency (rf). However, given that the location of different NMR signals is dependent on the external magnetic field strength and the reference frequency, the signals are usually reported relative to a reference signal, usually that of TMS (tetramethylsilane). Additionally, since the distribution of NMR signals is field dependent, these frequencies are divided by the spectrometer frequency. However, since we are dividing Hz by MHz, the resulting number would be too small, and thus it is multiplied by a million. This operation therefore gives a locator number called the "chemical shift" with units of parts per million. In general, chemical shifts for protons are highly predictable since the shifts are primarily determined by simpler shielding effects (electron density), but the chemical shifts for many heavier nuclei are more strongly influenced by other factors including excited states ("paramagnetic" contribution to shielding tensor). The chemical shift provides information about the structure of the molecule. The conversion of the raw data to this information is called assigning the spectrum. For example, for the 1H-NMR spectrum for ethanol (CH3CH2OH), one would expect signals at each of three specific chemical shifts: one for the CH3 group, one for the CH2 group and one for the OH group. A typical CH3 group has a shift around 1 ppm, a CH2 attached to an OH has a shift of around 4 ppm and an OH has a shift anywhere from 2–6 ppm depending on the solvent used and the amount of hydrogen bonding. While the O atom does draw electron density away from the attached H through their mutual sigma bond, the electron lone pairs on the O bathe the H in their shielding effect. In paramagnetic NMR spectroscopy, measurements are conducted on paramagnetic samples. The paramagnetism gives rise to very diverse chemical shifts. In 1H NMR spectroscopy, the chemical shift range can span 500 ppm. Because of molecular motion at room temperature, the three methyl protons average out during the NMR experiment (which typically requires a few ms). These protons become degenerate and form a peak at the same chemical shift. The shape and area of peaks are indicators of chemical structure too. In the example above—the proton spectrum of ethanol—the CH3 peak has three times the area of the OH peak. Similarly the CH2 peak would be twice the area of the OH peak but only 2/3 the area of the CH3 peak. Software allows analysis of signal intensity of peaks, which under conditions of optimal relaxation, correlate with the number of protons of that type. Analysis of signal intensity is done by integration—the mathematical process that calculates the area under a curve. The analyst must integrate the peak and not measure its height because the peaks also have width—and thus its size is dependent on its area not its height. However, it should be mentioned that the number of protons, or any other observed nucleus, is only proportional to the intensity, or the integral, of the NMR signal in the very simplest one-dimensional NMR experiments. In more elaborate experiments, for instance, experiments typically used to obtain carbon-13 NMR spectra, the integral of the signals depends on the relaxation rate of the nucleus, and its scalar and dipolar coupling constants. Very often these factors are poorly known - therefore, the integral of the NMR signal is very difficult to interpret in more complicated NMR experiments. Some of the most useful information for structure determination in a one-dimensional NMR spectrum comes from J-coupling or scalar coupling (a special case of spin-spin coupling) between NMR active nuclei. This coupling arises from the interaction of different spin states through the chemical bonds of a molecule and results in the splitting of NMR signals. For a proton, the local magnetic field is slightly different depending on whether an adjacent nucleus points towards or against the spectrometer magnetic field, which gives rise to two signals per proton instead of one. These splitting patterns can be complex or simple and, likewise, can be straightforwardly interpretable or deceptive. This coupling provides detailed insight into the connectivity of atoms in a molecule. Coupling to n equivalent (spin ½) nuclei splits the signal into a n+1 multiplet with intensity ratios following Pascal's triangle as described on the right. Coupling to additional spins will lead to further splittings of each component of the multiplet e.g. coupling to two different spin ½ nuclei with significantly different coupling constants will lead to a doublet of doublets (abbreviation: dd). Note that coupling between nuclei that are chemically equivalent (that is, have the same chemical shift) has no effect on the NMR spectra and couplings between nuclei that are distant (usually more than 3 bonds apart for protons in flexible molecules) are usually too small to cause observable splittings. Long-range couplings over more than three bonds can often be observed in cyclic and aromatic compounds, leading to more complex splitting patterns. For example, in the proton spectrum for ethanol described above, the CH3 group is split into a triplet with an intensity ratio of 1:2:1 by the two neighboring CH2 protons. Similarly, the CH2 is split into a quartet with an intensity ratio of 1:3:3:1 by the three neighboring CH3 protons. In principle, the two CH2 protons would also be split again into a doublet to form a doublet of quartets by the hydroxyl proton, but intermolecular exchange of the acidic hydroxyl proton often results in a loss of coupling information. Coupling to any spin ½ nuclei such as phosphorus-31 or fluorine-19 works in this fashion (although the magnitudes of the coupling constants may be very different). But the splitting patterns differ from those described above for nuclei with spin greater than ½ because the spin quantum number has more than two possible values. For instance, coupling to deuterium (a spin 1 nucleus) splits the signal into a 1:1:1 triplet because the spin 1 has three spin states. Similarly, a spin 3/2 nucleus splits a signal into a 1:1:1:1 quartet and so on. Coupling combined with the chemical shift (and the integration for protons) tells us not only about the chemical environment of the nuclei, but also the number of neighboring NMR active nuclei within the molecule. In more complex spectra with multiple peaks at similar chemical shifts or in spectra of nuclei other than hydrogen, coupling is often the only way to distinguish different nuclei. Second-order (or strong) couplingEdit The above description assumes that the coupling constant is small in comparison with the difference in NMR frequencies between the inequivalent spins. If the shift separation decreases (or the coupling strength increases), the multiplet intensity patterns are first distorted, and then become more complex and less easily analyzed (especially if more than two spins are involved). Intensification of some peaks in a multiplet is achieved at the expense of the remainder, which sometimes almost disappear in the background noise, although the integrated area under the peaks remains constant. In most high-field NMR, however, the distortions are usually modest and the characteristic distortions (roofing) can in fact help to identify related peaks. Second-order effects decrease as the frequency difference between multiplets increases, so that high-field (i.e. high-frequency) NMR spectra display less distortion than lower frequency spectra. Early spectra at 60 MHz were more prone to distortion than spectra from later machines typically operating at frequencies at 200 MHz or above. More subtle effects can occur if chemically equivalent spins (i.e., nuclei related by symmetry and so having the same NMR frequency) have different coupling relationships to external spins. Spins that are chemically equivalent but are not indistinguishable (based on their coupling relationships) are termed magnetically inequivalent. For example, the 4 H sites of 1,2-dichlorobenzene divide into two chemically equivalent pairs by symmetry, but an individual member of one of the pairs has different couplings to the spins making up the other pair. Magnetic inequivalence can lead to highly complex spectra which can only be analyzed by computational modeling. Such effects are more common in NMR spectra of aromatic and other non-flexible systems, while conformational averaging about C-C bonds in flexible molecules tends to equalize the couplings between protons on adjacent carbons, reducing problems with magnetic inequivalence. Correlation spectroscopy is one of several types of two-dimensional nuclear magnetic resonance (NMR) spectroscopy or 2D-NMR. This type of NMR experiment is best known by its acronym, COSY. Other types of two-dimensional NMR include J-spectroscopy, exchange spectroscopy (EXSY), Nuclear Overhauser effect spectroscopy (NOESY), total correlation spectroscopy (TOCSY) and heteronuclear correlation experiments, such as HSQC, HMQC, and HMBC. In correlation spectroscopy, emission is centered on the peak of an individual nucleus; if its magnetic field is correlated with another nucleus by through-bond (COSY, HSQC, etc.) or through-space (NOE) coupling, a response can also be detected on the frequency of the correlated nucleus. Two-dimensional NMR spectra provide more information about a molecule than one-dimensional NMR spectra and are especially useful in determining the structure of a molecule, particularly for molecules that are too complicated to work with using one-dimensional NMR. The first two-dimensional experiment, COSY, was proposed by Jean Jeener, a professor at Université Libre de Bruxelles, in 1971. This experiment was later implemented by Walter P. Aue, Enrico Bartholdi and Richard R. Ernst, who published their work in 1976. Solid-state nuclear magnetic resonanceEdit A variety of physical circumstances do not allow molecules to be studied in solution, and at the same time not by other spectroscopic techniques to an atomic level, either. In solid-phase media, such as crystals, microcrystalline powders, gels, anisotropic solutions, etc., it is in particular the dipolar coupling and chemical shift anisotropy that become dominant to the behaviour of the nuclear spin systems. In conventional solution-state NMR spectroscopy, these additional interactions would lead to a significant broadening of spectral lines. A variety of techniques allows establishing high-resolution conditions, that can, at least for 13C spectra, be comparable to solution-state NMR spectra. Two important concepts for high-resolution solid-state NMR spectroscopy are the limitation of possible molecular orientation by sample orientation, and the reduction of anisotropic nuclear magnetic interactions by sample spinning. Of the latter approach, fast spinning around the magic angle is a very prominent method, when the system comprises spin 1/2 nuclei. Spinning rates of ca. 20 kHz are used, which demands special equipment. A number of intermediate techniques, with samples of partial alignment or reduced mobility, is currently being used in NMR spectroscopy. Applications in which solid-state NMR effects occur are often related to structure investigations on membrane proteins, protein fibrils or all kinds of polymers, and chemical analysis in inorganic chemistry, but also include "exotic" applications like the plant leaves and fuel cells. For example, Rahmani et al. studied the effect of pressure and temperature on the bicellar structures' self-assembly using deuterium NMR spectroscopy. Biomolecular NMR spectroscopyEdit Much of the innovation within NMR spectroscopy has been within the field of protein NMR spectroscopy, an important technique in structural biology. A common goal of these investigations is to obtain high resolution 3-dimensional structures of the protein, similar to what can be achieved by X-ray crystallography. In contrast to X-ray crystallography, NMR spectroscopy is usually limited to proteins smaller than 35 kDa, although larger structures have been solved. NMR spectroscopy is often the only way to obtain high resolution information on partially or wholly intrinsically unstructured proteins. It is now a common tool for the determination of Conformation Activity Relationships where the structure before and after interaction with, for example, a drug candidate is compared to its known biochemical activity. Proteins are orders of magnitude larger than the small organic molecules discussed earlier in this article, but the basic NMR techniques and some NMR theory also applies. Because of the much higher number of atoms present in a protein molecule in comparison with a small organic compound, the basic 1D spectra become crowded with overlapping signals to an extent where direct spectral analysis becomes untenable. Therefore, multidimensional (2, 3 or 4D) experiments have been devised to deal with this problem. To facilitate these experiments, it is desirable to isotopically label the protein with 13C and 15N because the predominant naturally occurring isotope 12C is not NMR-active and the nuclear quadrupole moment of the predominant naturally occurring 14N isotope prevents high resolution information from being obtained from this nitrogen isotope. The most important method used for structure determination of proteins utilizes NOE experiments to measure distances between atoms within the molecule. Subsequently, the distances obtained are used to generate a 3D structure of the molecule by solving a distance geometry problem. NMR can also be used to obtain information on the dynamics and conformational flexibility of different regions of a protein. "Nucleic acid NMR" is the use of NMR spectroscopy to obtain information about the structure and dynamics of polynucleic acids, such as DNA or RNA. As of 2003[update], nearly half of all known RNA structures had been determined by NMR spectroscopy. Nucleic acid and protein NMR spectroscopy are similar but differences exist. Nucleic acids have a smaller percentage of hydrogen atoms, which are the atoms usually observed in NMR spectroscopy, and because nucleic acid double helices are stiff and roughly linear, they do not fold back on themselves to give "long-range" correlations. The types of NMR usually done with nucleic acids are 1H or proton NMR, 13C NMR, 15N NMR, and 31P NMR. Two-dimensional NMR methods are almost always used, such as correlation spectroscopy (COSY) and total coherence transfer spectroscopy (TOCSY) to detect through-bond nuclear couplings, and nuclear Overhauser effect spectroscopy (NOESY) to detect couplings between nuclei that are close to each other in space. Parameters taken from the spectrum, mainly NOESY cross-peaks and coupling constants, can be used to determine local structural features such as glycosidic bond angles, dihedral angles (using the Karplus equation), and sugar pucker conformations. For large-scale structure, these local parameters must be supplemented with other structural assumptions or models, because errors add up as the double helix is traversed, and unlike with proteins, the double helix does not have a compact interior and does not fold back upon itself. NMR is also useful for investigating nonstandard geometries such as bent helices, non-Watson–Crick basepairing, and coaxial stacking. It has been especially useful in probing the structure of natural RNA oligonucleotides, which tend to adopt complex conformations such as stem-loops and pseudoknots. NMR is also useful for probing the binding of nucleic acid molecules to other molecules, such as proteins or drugs, by seeing which resonances are shifted upon binding of the other molecule. Carbohydrate NMR spectroscopy addresses questions on the structure and conformation of carbohydrates. The analysis of carbohydrates by 1H NMR is challenging due to the limited variation in functional groups, which leads to 1H resonances concentrated in narrow bands of the NMR spectrum. In other words, there is poor spectral dispersion. The anomeric proton resonances are segregated from the others due to fact that the anomeric carbons bear two oxygen atoms. For smaller carbohydrates, the dispersion of the anomeric proton resonances facilitates the use of 1D TOCSY experiments to investigate the entire spin systems of individual carbohydrate residues. - Distance geometry - Earth's field NMR - In vivo magnetic resonance spectroscopy - Functional magnetic resonance spectroscopy of the brain - Low field NMR - Magnetic Resonance Imaging - NMR crystallography - NMR spectra database - NMR tube - includes a section on sample preparation - NMR spectroscopy of stereoisomers - Nuclear magnetic resonance spectroscopy of proteins - Nuclear quadrupole resonance - Pulsed field magnet - Proton-enhanced nuclear induction spectroscopy - Relaxation (NMR) - Triple-resonance nuclear magnetic resonance spectroscopy - Zero field NMR - Structural biology : practical NMR applications (PDF) (2nd ed.). Springer. p. 67. ISBN 978-1-4614-3964-6. Retrieved 7 December 2018. - Marc S. Reisch (June 29, 2015). "NMR Instrument Price Hikes Spook Users". 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"Accurate Molecular Weight Determination of Small Molecules via DOSY-NMR by Using External Calibration Curves with Normalized Diffusion Coefficients". Chem. Sci. 6 (6): 3354–3364. doi:10.1039/C5SC00670H. PMC 5656982. PMID 29142693. - "Center for NMR Spectroscopy: The Lock". nmr.chem.wsu.edu. - "NMR Artifacts". www2.chemistry.msu.edu. - Parella, Teodor. "INVERSION-RECOVERY EXPERIMENT". triton.iqfr.csic.es. - James Keeler. "Chapter 2: NMR and energy levels" (reprinted at University of Cambridge). Understanding NMR Spectroscopy. University of California, Irvine. Retrieved 2007-05-11. - Pople, J.A.; Bernstein, H. J.; Schneider, W. G. (1957). "The Analysis of Nuclear Magnetic Resonanace Spectra". Can. J. Chem. 35: 65–81. - Aue, W. P. (1976). "Two-dimensional spectroscopy. Application to nuclear magnetic resonance". The Journal of Chemical Physics. 64 (5): 2229. Bibcode:1976JChPh..64.2229A. doi:10.1063/1.432450. - Jeener, Jean (2007). Jeener, Jean: Reminiscences about the Early Days of 2D NMR. Encyclopedia of Magnetic Resonance. doi:10.1002/9780470034590.emrhp0087. ISBN 978-0470034590. - Martin, G.E; Zekter, A.S., Two-Dimensional NMR Methods for Establishing Molecular Connectivity; VCH Publishers, Inc: New York, 1988 (p.59) - "National Ultrahigh-Field NMR Facility for Solids". Retrieved 2014-09-22. - A. Rahmani, C. Knight, and M. R. Morrow. Response to hydrostatic pressure of bicellar dispersions containing anionic lipid: Pressure-induced interdigitation. 2013, 29 (44), pp 13481–13490, doi:10.1021/la4035694 - Fürtig, Boris; Richter, Christian; Wöhnert, Jens; Schwalbe, Harald (2003). "NMR Spectroscopy of RNA". ChemBioChem. 4 (10): 936–62. doi:10.1002/cbic.200300700. PMID 14523911. - Addess, Kenneth J.; Feigon, Juli (1996). "Introduction to 1H NMR Spectroscopy of DNA". In Hecht, Sidney M. (ed.). Bioorganic Chemistry: Nucleic Acids. New York: Oxford University Press. ISBN 978-0-19-508467-2. - Wemmer, David (2000). "Chapter 5: Structure and Dynamics by NMR". In Bloomfield, Victor A.; Crothers, Donald M.; Tinoco, Ignacio (eds.). Nucleic acids: Structures, Properties, and Functions. Sausalito, California: University Science Books. ISBN 978-0-935702-49-1. - John D. Roberts (1959). Nuclear Magnetic Resonance : applications to organic chemistry. McGraw-Hill Book Company. ISBN 9781258811662. - J.A.Pople; W.G.Schneider; H.J.Bernstein (1959). High-resolution Nuclear Magnetic Resonance. McGraw-Hill Book Company. - A. Abragam (1961). The Principles of Nuclear Magnetism. Clarendon Press. ISBN 9780198520146. - Charles P. Slichter (1963). Principles of magnetic resonance: with examples from solid state physics. Harper & Row. ISBN 9783540084761. - John Emsley; James Feeney; Leslie Howard Sutcliffe (1965). High Resolution Nuclear Magnetic Resonance Spectroscopy. Pergamon. ISBN 9781483184081. \|Wikimedia Commons has media related to Nuclear magnetic resonance spectroscopy.\| - James Keeler. "Understanding NMR Spectroscopy" (reprinted at University of Cambridge). University of California, Irvine. Retrieved 2007-05-11. - The Basics of NMR - A non-technical overview of NMR theory, equipment, and techniques by Dr. Joseph Hornak, Professor of Chemistry at RIT - GAMMA and PyGAMMA Libraries - GAMMA is an open source C++ library written for the simulation of Nuclear Magnetic Resonance Spectroscopy experiments. PyGAMMA is a Python wrapper around GAMMA. - relax Software for the analysis of NMR dynamics - Vespa - VeSPA (Versatile Simulation, Pulses and Analysis) is a free software suite composed of three Python applications. These GUI based tools are for magnetic resonance (MR) spectral simulation, RF pulse design, and spectral processing and analysis of MR data.
A chord, in music, is any harmonic set of pitches consisting of multiple notes (also called "pitches") that are heard as if sounding simultaneously. For many practical and theoretical purposes, arpeggios and broken chords (in which the notes of the chord are sounded one after the other, rather than simultaneously), or sequences of chord tones, may also be considered as chords. Chords and sequences of chords are frequently used in modern West African and Oceanic music, Western classical music, and Western popular music; yet, they are absent from the music of many other parts of the world. In tonal Western classical music (music with a tonic key or "home key"), the most frequently encountered chords are triads, so called because they consist of three distinct notes: the root note, and intervals of a third and a fifth above the root note. Chords with more than three notes include added tone chords, extended chords and tone clusters, which are used in contemporary classical music, jazz and other genres. A series of chords is called a chord progression. One example of a widely used chord progression in Western traditional music and blues is the 12 bar blues progression. Although any chord may in principle be followed by any other chord, certain patterns of chords are more common in Western music, and some patterns have been accepted as establishing the key (tonic note) in common-practice harmony—notably the resolution of a dominant chord to a tonic chord. To describe this, Western music theory has developed the practice of numbering chords using Roman numerals to represent the number of diatonic steps up from the tonic note of the scale. Common ways of notating or representing chords in Western music (other than conventional staff notation) include Roman numerals, the Nashville Number System, figured bass, macro symbols (sometimes used in modern musicology), and chord charts. - 1 Definition - 2 History - 3 Notation - 4 Characteristics - 5 Common types of chords - 6 References - 7 Sources - 8 Further reading - 9 External links The English word chord derives from Middle English cord, a shortening of accord in the original sense of agreement and later, harmonious sound. A sequence of chords is known as a chord progression or harmonic progression; these are frequently used in Western music. A chord progression "aims for a definite goal" of establishing (or contradicting) a tonality founded on a key, root or tonic chord; the study of harmony involves chords and chord progressions and the principles of connection that govern them. Ottó Károlyi writes that, "Two or more notes sounded simultaneously are known as a chord," though, since instances of any given note in different octaves may be taken as the same note, it is more precise for the purposes of analysis to speak of distinct pitch classes. Furthermore, as three notes are needed to define any common chord, three is often taken as the minimum number of notes that form a definite chord. Hence, Andrew Surmani, for example, (2004, p. 72) states, "When three or more notes are sounded together, the combination is called a chord." George T. Jones (1994, p. 43) agrees: "Two tones sounding together are usually termed an interval, while three or more tones are called a chord." According to Monath (1984, p. 37); "A chord is a combination of three or more tones sounded simultaneously," and the distances between the tones are called intervals. However, sonorities of two pitches, or even single-note melodies, are commonly heard as implying chords. A simple example of two notes being interpreted as a chord is when the root and third are played but the fifth is omitted. In the key of C major, if the music comes to rest on the two notes G and B, most listeners will hear this as a G major chord. Since a chord may be understood as such even when all its notes are not simultaneously audible, there has been some academic discussion regarding the point at which a group of notes may be called a chord. Jean-Jacques Nattiez (1990, p. 218) explains that, "We can encounter 'pure chords' in a musical work," such as in the Promenade of Modest Mussorgsky's Pictures at an Exhibition but, "Often, we must go from a textual given to a more abstract representation of the chords being used," as in Claude Debussy's Première arabesque. In the medieval era, early Christian hymns featured organum (which used the simultaneous perfect intervals of a fourth, a fifth, and an octave), with chord progressions and harmony an incidental result of the emphasis on melodic lines during the medieval and then Renaissance (15th to 17th centuries). The Baroque period, the 17th and 18th centuries, began to feature the major and minor scale based tonal system and harmony, including chord progressions and circle progressions, it was in the Baroque period that the accompaniment of melodies with chords was developed, as in figured bass, and the familiar cadences (perfect authentic, etc.). In the Renaissance, certain dissonant sonorities that suggest the dominant seventh occurred with frequency. In the Baroque period, the dominant seventh proper was introduced and was in constant use in the Classical and Romantic periods; the leading-tone seventh appeared in the Baroque period and remains in use. Composers began to use nondominant seventh chords in the Baroque period, they became frequent in the Classical period, gave way to altered dominants in the Romantic period, and underwent a resurgence in the Post-Romantic and Impressionistic period. The Romantic period, the 19th century, featured increased chromaticism. Composers began to use secondary dominants in the Baroque, and they became common in the Romantic period. Many contemporary popular Western genres continue to rely on simple diatonic harmony, though far from universally: notable exceptions include the music of film scores, which often use chromatic, atonal or post-tonal harmony, and modern jazz (especially circa 1960), in which chords may include up to seven notes (and occasionally more); when referring to chords that do not function as harmony, such as in atonal music, the term "sonority" is often used specifically to avoid any tonal implications of the word "chord". Chords can be represented in various ways; the most common notation systems are: - Plain staff notation, used in classical music - Roman numerals, commonly used in harmonic analysis to denote the scale step on which the chord is built. - Figured bass, much used in the Baroque era, uses numbers added to a bass line written on a staff, to enable keyboard players to improvise chords with the right hand while playing the bass with their left. - Macro symbols, sometimes used in modern musicology, to denote chord root and quality. - Various chord names and symbols used in popular music lead sheets, fake books, and chord charts, to quickly lay out the harmonic ground plan of a piece so that the musician may improvise, jam, or vamp on it. While scale degrees are typically represented in musical analysis or musicology articles with Arabic numerals (e.g., 1, 2, 3, ..., sometimes with a circumflex above the numeral: , , , ...), the triads (three-note chords) that have these degrees as their roots are often identified by Roman numerals (e.g., I, IV, V, which in the key of C major would be the triads C major, F major, G major). In some conventions (as in this and related articles) upper-case Roman numerals indicate major triads (e.g., I, IV, V) while lower-case Roman numerals indicate minor triads (e.g., I for a major chord and i for a minor chord, or using the major key, ii, iii and vi representing typical diatonic minor triads); other writers (e.g. Schoenberg) use upper case Roman numerals for both major and minor triads; some writers use upper-case Roman numerals to indicate the chord is diatonic in the major scale, and lower-case Roman numerals to indicate that the chord is diatonic in the minor scale. Diminished triads may be represented by lower-case Roman numerals with a degree symbol (e.g., viio7 indicates a diminished seventh chord built on the seventh scale degree; in the key of C major, this chord would be B diminished seventh, which consists of the notes B, D, F and A♭). Roman numerals can also be used in stringed instrument notation to indicate the position or string to play. In some string music, the string on which it is suggested that the performer play the note is indicated with a Roman numeral (e.g., on a four-string orchestral string instrument, I indicates the highest-pitched, thinnest string and IV indicates the lowest-pitched, thickest bass string). In some orchestral parts, chamber music and solo works for string instruments, the composer specifies to the performer which string should be used with the Roman numeral. Alternately, the note name of the string that the composer wishes the performer to use are stated using letters (e.g., "sul G" means "play on the G string"). Figured bass notation 2 or 2 Figured bass or thoroughbass is a kind of musical notation used in almost all Baroque music (c. 1600–1750), though rarely in music from later than 1750, to indicate harmonies in relation to a conventionally written bass line. Figured bass is closely associated with chord-playing basso continuo accompaniment instruments, which include harpsichord, pipe organ and lute. Added numbers, symbols, and accidentals beneath the staff indicate the intervals above the bass note to play; that is, the numbers stand for the number of scale steps above the written note to play the figured notes. For example, in the figured bass below, the bass note is a C, and the numbers 4 and 6 indicate that notes a fourth and a sixth above (F and A) should be played, giving the second inversion of the F major triad. - can be realized as If no numbers are written beneath a bass note, the figure is assumed to be 5 3, which calls for a third and a fifth above the bass note (i.e., a root position triad). In the 2010s, some classical musicians who specialize in music from the Baroque era can still perform chords using figured bass notation; in many cases, however, the chord-playing performers read a fully notated accompaniment that has been prepared for the piece by the music publisher; such a part, with fully written-out chords, is called a "realization" of the figured bass part. Macro analysis is used by musicologists, music theorists and advanced university music students to analyze songs and pieces. Macro analysis uses upper-case and lower-case letters to indicate the roots of chords, followed by symbols that specify the chord quality. Notation in popular music In most genres of popular music, including jazz, pop, and rock, a chord name and the corresponding symbol are typically composed of one or more parts. In these genres, chord-playing musicians in the rhythm section (e.g., electric guitar, acoustic guitar, piano, Hammond organ, etc.) typically improvise the specific "voicing" of each chord from a song's chord progression by interpreting the written chord symbols appearing in the lead sheet or fake book. Normally, these chord symbols include: - A (big) letter indicating the root note (e.g. C). - A symbol or abbreviation indicating the chord quality (e.g. minor, aug or o ). If no chord quality is specified, the chord is assumed to be a major triad by default. - Number(s) indicating the stacked intervals above the root note (e.g. 7 or 13). - Additional musical symbols or abbreviations for special alterations (e.g. ♭5, ♯5 or add13). - An added slash "/" and an upper case letter indicates that a bass note other than the root should be played. These are called slash chords. For instance, C/F indicates that an C major triad should be played with an added F in the bass. In some genres of modern jazz, two chords with a slash between them may indicate an advanced chord type called a polychord, which is the playing of two chords simultaneously; the correct notation of this should be F/, which sometimes get mixed up with slash chords. Chord qualities are related with the qualities of the component intervals that define the chord; the main chord qualities are: - Major and minor (a chord is "Major" by default and altered with added info: "C" = C major, "Cm" = c minor). - augmented, diminished, and half-diminished, - dominant seventh. The symbols used for notating chords are: - m, min, or − indicates a minor chord. The "m" must be lowercase to distinguish it from the "M" for major. - M, Ma, Maj, Δ, or (no symbol) indicates a major chord. In a jazz context, this typically indicates that the player should use any suitable chord of a major quality, for example a a major seventh chord or a 6/9 chord. In a lot of jazz styles, an unembellished major triad is rarely if ever played, but in a lead sheet the choice of which major quality chord to use is left to the performer. - + or aug indicates an augmented chord (A or a is not used). - o or dim indicates a diminished chord, either a diminished triad or a diminished seventh chord (d is not used). - ø indicates a half-diminished seventh chord. In some fake books, the abbreviation m7(♭5) is used as an equivalent symbol. - 2 is mostly used as an extra note in a chord (e.g. add2, sus2). - 3 is the minor or major quality of the chord and is rarely written as a number. - 4 is mostly used as an extra note in a chord (e.g. add4, sus4). - 5 is the (perfect) fifth of the chord and is only written as a number when altered (e.g. F7(♭5)). In guitar music, like rock, a "5" indicates that a power chord, which consists of only the root and fifth, possibly with the root doubled an octave higher. - 6 indicates a sixth chord. There are no rules if the 6 replaces the 5th or not. - 7 indicates a dominant seventh chord. However, if Maj7, M7 or Δ7 is indicated, this is a major 7th chord (e.g. GM7 or FΔ7). Very rarely, also dom is used for dominant 7th. - 9 indicates a ninth chord, which in jazz usually includes the dominant seventh as well, if it is a dominant chord. - 11 indicates a eleventh chord, which in jazz usually includes the dominant seventh and ninth as well, if it is a dominant chord. - 13 indicates a thirteenth chord, which in jazz usually includes the dominant seventh, ninth and eleventh as well. - 6/9 indicates a triad with the addition of the sixth and ninth. - sus4 (or simply 4) indicates a sus chord with the third omitted and the fourth used instead. Other notes may be added to a sus4 chord, indicated with the word "add" and the scale degree (e.g., Asus4(add9) or Asus4(add7)). - sus2 (or simply 2) indicates a sus chord with the third omitted and the second (which may also be called the ninth) used instead. As with "sus4", a "sus2" chord can have other scale degrees added (e.g., Asus2(add♭7) or Asus2(add4)). - (♭9) (parenthesis) is used to indicate explicit chord alterations (e.g., A7(♭9)). The parenthesis is probably left from older days when jazz musicians weren't used to "altered chords". Albeit important, the parenthesis can be left unplayed (with no "musical harm"). - add indicates that an additional interval number should be added to the chord. (e.g. C7add13 is a C 7th chord plus an added 13th). - alt or alt dom indicates an altered dominant seventh chord (e.g. G7♯11). - omit5 (or simply no5) indicates that the (indicated) note should be omitted. The table below lists common chord types, their symbols, and their components. Chord Components Name Symbol (on C) Interval P1 m2 M2 m3 M3 P4 d5 P5 A5 M6/d7 m7 M7 Short Long Semitones 0 1 2 3 4 5 6 7 8 9 10 11 Major triad C P1 M3 P5 Major sixth chord C6 Cmaj6 P1 M3 P5 M6 Dominant seventh chord C7 Cdom7 P1 M3 P5 m7 Major seventh chord CM7 Cmaj7 P1 M3 P5 M7 Augmented triad C+ Caug P1 M3 A5 Augmented seventh chord C+7 Caug7 P1 M3 A5 m7 Minor triad Cm Cmin P1 m3 P5 Minor sixth chord Cm6 Cmin6 P1 m3 P5 M6 Minor seventh chord Cm7 Cmin7 P1 m3 P5 m7 Minor-major seventh chord CmM7 P1 m3 P5 M7 Diminished triad Co Cdim P1 m3 d5 Diminished seventh chord Co7 Cdim7 P1 m3 d5 d7 Half-diminished seventh chord Cø P1 m3 d5 m7 The basic function of chord symbols is to eliminate the need to write out sheet music; the modern jazz player has extensive knowledge of the chordal functions and can mostly play music by reading the chord symbols only. Advanced chords are common especially in modern jazz. Altered 9ths, 11ths and 5ths are not common in pop music. In jazz, a chord chart is used by comping musicians (jazz guitar, jazz piano, Hammond organ) to improvise a chordal accompaniment and to play improvised solos. Jazz bass players improvise a bassline from a chord chart. Chord charts are used by horn players and other solo instruments to guide their solo improvisations. Interpretation of chord symbols depends on the genre of music being played. In jazz from the bebop era or later, major and minor chords are typically realized as seventh chords even if only "C" or "Cm" appear in the chart. In jazz charts, seventh chords are often realized with upper extensions, such as the ninth, sharp eleventh, and thirteenth, even if the chart only indicates "A7". In jazz, the root and fifth are often omitted from chord voicings, except when there is a diminished fifth or an augmented fifth. In a pop or rock context, however, "C" and "Cm" would almost always be played as triads, with no sevenths. In pop and rock, in the relatively less common cases where songwriters wish a dominant seventh, major seventh, or minor seventh chord, they will indicate this explicitly with the indications "C7", "Cmaj7" or "Cm7". Within the diatonic scale, every chord has certain characteristics, which include: - the number of pitch classes (distinct notes without respect to octave) in the chord, - the scale degree of the root note, - the position or inversion of the chord, - the general type of intervals it is constructed from—for example, seconds, thirds, or fourths, and - counts of each pitch class as occur between all combinations of notes the chord contains. Number of notes Two-note combinations, whether referred to as chords or intervals, are called dyads. In the context of a specific section in a piece of music, dyads can be heard as chords if they have the most important notes that identify a certain chord. For example, in a piece in C Major, after a section of tonic C Major chords, if a dyad containing the notes B and D is played, listeners will likely hear this as a first inversion G Major chord. Other dyads are more ambiguous, an aspect that composers can use creatively. For example, a dyad with a perfect fifth has no third, so it does not sound major or minor; a composer who ends a section on a perfect fifth could subsequently add the missing third. Another example is a dyad outlining the tritone, such as the notes C and F# in C Major; this dyad could be heard as implying a D7 chord (resolving to G Major) or as implying a C diminished chord (resolving to Db Major). In unaccompanied duos for two instruments, such as flute duos, the only combinations of notes that are possible are dyads, which means that all of the chord progressions must be implied through dyads, as well as with arpeggios. Chords constructed of three notes of some underlying scale are described as triads. Chords of four notes are known as tetrads, those containing five are called pentads and those using six are hexads. Sometimes the terms trichord, tetrachord, pentachord, and hexachord are used—though these more usually refer to the pitch classes of any scale, not generally played simultaneously. Chords that may contain more than three notes include pedal point chords, dominant seventh chords, extended chords, added tone chords, clusters, and polychords. Polychords are formed by two or more chords superimposed. Often these may be analysed as extended chords; examples include tertian, altered chord, secundal chord, quartal and quintal harmony and Tristan chord. Another example is when G7(♯11♭9) (G–B–D–F–A♭–C♯) is formed from G major (G–B–D) and D♭ major (D♭–F–A♭). A nonchord tone is a dissonant or unstable tone that lies outside the chord currently heard, though often resolving to a chord tone. \|viio / ♭VII\|\|leading tone / subtonic\| In the key of C major, the first degree of the scale, called the tonic, is the note C itself. A C major chord, the major triad built on the note C (C–E–G), is referred to as the one chord of that key and notated in Roman numerals as I; the same C major chord can be found in other scales: it forms chord III in the key of A minor (A→B→C) and chord IV in the key of G major (G→A→B→C). This numbering indicates the chords's function. Many analysts use lower-case Roman numerals to indicate minor triads and upper-case numerals for major triads, and degree and plus signs ( o and + ) to indicate diminished and augmented triads respectively. Otherwise, all the numerals may be upper-case and the qualities of the chords inferred from the scale degree. Chords outside the scale can be indicated by placing a flat/sharp sign before the chord—for example, the chord E♭ major in the key of C major is represented by ♭III. The tonic of the scale may be indicated to the left (e.g. "F♯:") or may be understood from a key signature or other contextual clues. Indications of inversions or added tones may be omitted if they are not relevant to the analysis. Roman numeral analysis indicates the root of the chord as a scale degree within a particular major key as follows. In the harmony of Western art music, a chord is in root position when the tonic note is the lowest in the chord (the bass note), and the other notes are above it; when the lowest note is not the tonic, the chord is inverted. Chords that have many constituent notes can have many different inverted positions as shown below for the C major chord: Bass note Position Order of notes (starting from the bass) Notation C root position C–E–G or C–G–E 5 3 as G is a fifth above C and E is a third above C E first inversion E–G–C or E–C–G 6 3 as C is a sixth above E and G is a third above E G second inversion G–C–E or G–E–C 6 4 as E is a sixth above G and C is a fourth above G Further, a four-note chord can be inverted to four different positions by the same method as triadic inversion. For example, a G7 chord can be in root position (G as bass note); first inversion (B as bass note); second inversion (D as bass note); or third inversion (F as bass note). Secundal, tertian, and quartal chords \|Secundal\|\|Seconds: major second, minor second\| \|Tertian\|\|Thirds: major third, minor third\| \|Quartal\|\|Fourth: perfect fourth, augmented fourth\| \|Quintal\|\|Fifths: diminished fifth, perfect fifth\| Many chords are a sequence of notes separated by intervals of roughly the same size. Chords can be classified into different categories by this size: - Tertian chords can be decomposed into a series of (major or minor) thirds. For example, the C major triad (C–E–G) is defined by a sequence of two intervals, the first (C–E) being a major third and the second (E–G) being a minor third. Most common chords are tertian. - Secundal chords can be decomposed into a series of (major or minor) seconds. For example, the chord C–D–E♭ is a series of seconds, containing a major second (C–D) and a minor second (D–E♭). - Quartal chords can be decomposed into a series of (perfect or augmented) fourths. Quartal harmony normally works with a combination of perfect and augmented fourths. Diminished fourths are enharmonically equivalent to major thirds, so they are uncommon. For example, the chord C–F–B is a series of fourths, containing a perfect fourth (C–F) and an augmented fourth/tritone (F–B). These terms can become ambiguous when dealing with non-diatonic scales, such as the pentatonic or chromatic scales; the use of accidentals can also complicate the terminology. For example, the chord B♯–E–A♭ appears to be quartal, as a series of diminished fourths (B♯–E and E–A♭), but it is enharmonically equivalent to (and sonically indistinguishable from) the tertian chord C–E–G♯, which is a series of major thirds (C–E and E–G♯). The notes of a chord form intervals with each of the other notes of the chord in combination. A 3-note chord has 3 of these harmonic intervals, a 4-note chord has 6, a 5-note chord has 10, a 6-note chord has 15; the absence, presence, and placement of certain key intervals plays a large part in the sound of the chord, and sometimes of the selection of the chord that follows. A chord containing tritones is called tritonic; one without tritones is atritonic. Harmonic tritones are an important part of dominant seventh chords, giving their sound a characteristic tension, and making the tritone interval likely to move in certain stereotypical ways to the following chord. Tritones are also present in diminished seventh and half-diminished chords. A chord containing semitones, whether appearing as minor seconds or major sevenths, is called hemitonic; one without semitones is anhemitonic. Harmonic semitones are an important part of major seventh chords, giving their sound a characteristic high tension, and making the harmonic semitone likely to move in certain stereotypical ways to the following chord. A chord containing major sevenths but no minor seconds is much less harsh in sound than one containing minor seconds as well. Other chords of interest might include the - Diminished triad, which has many minor thirds and no major thirds, many tritones but no perfect fifths - Augmented triad, which has many major thirds and no minor thirds or perfect fifths - Dominant seventh flat five chord, which has many major thirds and tritones and no minor thirds or perfect fifths Common types of chords This article needs additional citations for verification. (April 2019) (Learn how and when to remove this template message) Triads, also called triadic chords, are tertian chords with three notes; the four basic triads are described below. Type Component intervals Chord symbol Notes Audio Third Fifth Major triad major perfect C, CM, Cmaj, CΔ, Cma C E G play (help·info) Minor triad minor perfect Cm, Cmin, C−, Cmi C E♭ G play (help·info) Augmented triad major augmented Caug, C+, C+ C E G♯ play (help·info) Diminished triad minor diminished Cdim, Co, Cm(♭5) C E♭ G♭ play (help·info) Seventh chords are tertian chords, constructed by adding a fourth note to a triad, at the interval of a third above the fifth of the chord; this creates the interval of a seventh above the root of the chord, the next natural step in composing tertian chords. The seventh chord built on the fifth step of the scale (the dominant seventh) is the only dominant seventh chord available in the major scale: it contains all three notes of the diminished triad of the seventh and is frequently used as a stronger substitute for it. There are various types of seventh chords depending on the quality of both the chord and the seventh added. In chord notation the chord type is sometimes superscripted and sometimes not (e.g. Dm7, Dm7, and Dm7 are all identical). Type Component intervals Chord symbol Notes Audio Third Fifth Seventh Diminished seventh minor diminished diminished Co7, Cdim7 C E♭ G♭ B Play (help·info) Half-diminished seventh minor diminished minor Cø7, Cm7♭5, C−(♭5) C E♭ G♭ B♭ Play (help·info) Minor seventh minor perfect minor Cm7, Cmin7, C−7, C E♭ G B♭ Play (help·info) Minor major seventh minor perfect major CmM7, Cmmaj7, C−(j7), C−Δ7, C−M7 C E♭ G B Play (help·info) Dominant seventh major perfect minor C7, Cdom7 C E G B♭ Play (help·info) Major seventh major perfect major CM7, CM7, Cmaj7, CΔ7, Cj7 C E G B Play (help·info) Augmented seventh major augmented minor C+7, Caug7, C7+, C7+5, C7♯5 C E G♯ B♭ Play (help·info) Augmented major seventh major augmented major C+M7, CM7+5, CM7♯5, C+j7, C+Δ7 C E G♯ B Play (help·info) Extended chords are triads with further tertian notes added beyond the seventh: the ninth, eleventh, and thirteenth chords. For example, a dominant thirteenth chord consists of the notes C–E–G–B♭–D–F–A: The upper structure or extensions, i.e. the notes beyond the seventh, are shown in red. This chord is just a theoretical illustration of this chord. In practice, a jazz pianist or jazz guitarist would not normally play the chord all in thirds as illustrated. Jazz voicings typically use the third, seventh, and then the extensions such as the ninth and thirteenth, and in some cases the eleventh; the root is often omitted from chord voicings, as the bass player will play the root. The fifth is often omitted if it is a perfect fifth. Augmented and diminished fifths are normally included in voicings. After the thirteenth, any notes added in thirds duplicate notes elsewhere in the chord; all seven notes of the scale are present in the chord, so adding more notes does not add new pitch classes; such chords may be constructed only by using notes that lie outside the diatonic seven-note scale. Type Components Chord Notes Audio Chord Extensions Dominant ninth dominant seventh major ninth — — C9 C E G B♭ D Play (help·info) Dominant eleventh dominant seventh (the third is usually omitted) major ninth perfect eleventh — C11 C E G B♭ D F Play (help·info) Dominant thirteenth dominant seventh major ninth perfect eleventh major thirteenth C13 C E G B♭ D F A Play (help·info) Other extended chords follow similar rules, so that for example maj9, maj11, and maj13 contain major seventh chords rather than dominant seventh chords, while m9, m11, and m13 contain minor seventh chords. The third and seventh of the chord are always determined by the symbols shown above; the root cannot be so altered without changing the name of the chord, while the third cannot be altered without altering the chord's quality. Nevertheless, the fifth, ninth, eleventh and thirteenth may all be chromatically altered by accidentals. These are noted alongside the altered element. Accidentals are most often used with dominant seventh chords. Altered dominant seventh chords (C7alt) may have a minor ninth, a sharp ninth, a diminished fifth, or an augmented fifth; some write this as C7+9, which assumes also the minor ninth, diminished fifth and augmented fifth. The augmented ninth is often referred to in blues and jazz as a blue note, being enharmonically equivalent to the minor third or tenth; when superscripted numerals are used the different numbers may be listed horizontally or vertically. Type Components Chord symbol Notes Audio Chord Alteration Seventh augmented fifth dominant seventh augmented fifth C7+5, C7♯5 C E G♯ B♭ Play (help·info) Seventh minor ninth dominant seventh minor ninth C7−9, C7♭9 C E G B♭ D♭ Play (help·info) Seventh sharp ninth dominant seventh augmented ninth C7+9, C7♯9 C E G B♭ D♯ Play (help·info) Seventh augmented eleventh dominant seventh augmented eleventh C7+11, C7♯11 C E G B♭ D F♯ Play (help·info) Seventh diminished thirteenth dominant seventh minor thirteenth C7−13, C7♭13 C E G B♭ D F A♭ Play (help·info) Half-diminished seventh minor seventh diminished fifth Cø, Cø7, Cm7♭5 C E♭ G♭ B♭ Play (help·info) Added tone chords An added tone chord is a triad with an added, non-tertian note, such as an added sixth or a chord with an added second (ninth) or fourth (eleventh) or a combination of the three; these chords do not include "intervening" thirds as in an extended chord. Added chords can also have variations. Thus, madd9, m4 and m6 are minor triads with extended notes. Sixth chords can belong to either of two groups. One is first inversion chords and added sixth chords that contain a sixth from the root; the other group is inverted chords in which the interval of a sixth appears above a bass note that is not the root. The major sixth chord (also called, sixth or added sixth with the chord notation 6, e.g., C6) is by far the most common type of sixth chord of the first group. It comprises a major triad with the added major sixth above the root, common in popular music. For example, the chord C6 contains the notes C–E–G–A; the minor sixth chord (min6 or m6, e.g., Cm6) is a minor triad, still with a major 6. For example, the chord Cm6 contains the notes C–E♭–G–A. The augmented sixth chord usually appears in chord notation as its enharmonic equivalent, the seventh chord; this chord contains two notes separated by the interval of an augmented sixth (or, by inversion, a diminished third, though this inversion is rare). The augmented sixth is generally used as a dissonant interval most commonly used in motion towards a dominant chord in root position (with the root doubled to create the octave the augmented sixth chord resolves to) or to a tonic chord in second inversion (a tonic triad with the fifth doubled for the same purpose). In this case, the tonic note of the key is included in the chord, sometimes along with an optional fourth note, to create one of the following (illustrated here in the key of C major): The augmented sixth family of chords exhibits certain peculiarities. Since they are not based on triads, as are seventh chords and other sixth chords, they are not generally regarded as having roots (nor, therefore, inversions), although one re-voicing of the notes is common (with the namesake interval inverted to create a diminished third). The second group of sixth chords includes inverted major and minor chords, which may be called sixth chords in that the six-three (6 3) and six-four (6 4) chords contain intervals of a sixth with the bass note, though this is not the root. Nowadays, this is mostly for academic study or analysis (see figured bass) but the Neapolitan sixth chord is an important example; a major triad with a flat supertonic scale degree as its root that is called a "sixth" because it is almost always found in first inversion. Though a technically accurate Roman numeral analysis would be ♭II, it is generally labelled N6. In C major, the chord is notated (from root position) D♭, F, A♭. Because it uses chromatically altered tones, this chord is often grouped with the borrowed chords but the chord is not borrowed from the relative major or minor and it may appear in both major and minor keys. Type Components Chord Notes Audio Chord Interval(s) Add nine major triad major ninth — C2, Cadd9 C E G D Play (help·info) Add fourth major triad perfect fourth — C4, Cadd11 C E G F Play (help·info) Add sixth major triad major sixth — C6 C E G A Play (help·info) Six-nine major triad major sixth major ninth C6/9 C E G A D — Seven-six major triad major sixth minor seventh C7/6 C E G A B♭ — Mixed-third major triad minor third — — C E♭ E G Play (help·info) A suspended chord, or "sus chord", is a chord in which the third is replaced by either the second or the fourth; this produces two main chord types: the suspended second (sus2) and the suspended fourth (sus4). The chords, Csus2 and Csus4, for example, consist of the notes C–D–G and C–F–G, respectively. There is also a third type of suspended chord, in which both the second and fourth are present, for example the chord with the notes C–D–F–G. The name suspended derives from an early polyphonic technique developed during the common practice period, in which a stepwise melodic progress to a harmonically stable note in any particular part was often momentarily delayed, or suspended, by extending the duration of the previous note; the resulting unexpected dissonance could then be all the more satisfyingly resolved by the eventual appearance of the displaced note. In traditional music theory, the inclusion of the third in either chord would negate the suspension, so such chords would be called added ninth and added eleventh chords instead. In modern layman usage, the term is restricted to the displacement of the third only and the dissonant second or fourth no longer needs to be held over (prepared) from the previous chord. Neither is it now obligatory for the displaced note to make an appearance at although in the majority of cases the conventional stepwise resolution to the third is still observed. In post-bop and modal jazz compositions and improvisations, suspended seventh chords are often used in nontraditional ways: these often do not function as V chords and do not resolve from the fourth to the third; the lack of resolution gives the chord an ambiguous, static quality. Indeed, the third is often played on top of a sus4 chord. A good example is the jazz standard, "Maiden Voyage". Extended versions are also possible, such as the seventh suspended fourth, which, with root C, contains the notes C–F–G–B♭ and is notated as C7sus4. Csus4 is sometimes written Csus since the sus4 is more common than the sus2. Type Components Chord Notes Audio Chord Interval(s) Suspended second open fifth major second — — Csus2 C D G Play (help·info) Suspended fourth open fifth perfect fourth — — Csus4 C F G Play (help·info) Jazz sus open fifth perfect fourth minor seventh major ninth C9sus4 C F G B♭ D Play (help·info) A borrowed chord is one from a different key than the home key, the key of the piece it is used in; the most common occurrence of this is where a chord from the parallel major or minor key is used. Particularly good examples can be found throughout the works of composers such as Schubert. For instance, for a composer working in the C major key, a major ♭III chord (e.g., an E♭ major chord) would be borrowed, as this chord appears only in the key of C minor. Although borrowed chords could theoretically include chords taken from any key other than the home key, this is not how the term is used when a chord is described in formal musical analysis. When a chord is analysed as "borrowed" from another key it may be shown by the Roman numeral corresponding with that key after a slash. For example, V/V (pronounced "five of five") indicates the dominant chord of the dominant key of the present home-key; the dominant key of C major is G major so this secondary dominant is the chord of the fifth degree of the G major scale, which is D major (which can also be described as II relative to the key of C major, not to be confused with the supertonic ii namely D minor.). If used for a significant duration, the use of the D major chord may cause a modulation to a new key (in this case to G major). Borrowed chords are widely used in Western popular music and rock music. For example, there are a number of songs in E major which use the ♭III chord (e.g., a G major chord used in an E major song), the ♭VII chord (e.g., a D major chord used in an E major song) and the ♭VI chord (e.g., a C major chord used in an E major song). All of these chords are "borrowed" from the key of E minor. - Benward & Saker (2003). Music: In Theory and Practice, Vol. I, pp. 67, 359. Seventh Edition. ISBN 978-0-07-294262-0."A chord is a harmonic unit with at least three different tones sounding simultaneously." "A combination of three or more pitches sounding at the same time." - Károlyi, Otto (1965). Introducing Music. Penguin Books. p. 63. Two or more notes sounding simultaneously are known as a chord. - Mitchell, Barry (January 16, 2008). "An explanation for the emergence of Jazz (1956)", Theory of Music. - Linkels, Ad, The Real Music of Paradise", In Broughton, Simon and Ellingham, Mark with McConnachie, James and Duane, Orla (Ed.), World Music, Vol. 2: Latin & North America, Caribbean, India, Asia and Pacific, pp. 218–29. Rough Guides Ltd, Penguin Books. ISBN 1-85828-636-0 - Malm, William P. (1996). Music Cultures of the Pacific, the Near East, and Asia. p.15. ISBN 0-13-182387-6. Third edition: "Indeed, this harmonic orientation is one of the major differences between Western and much non-Western music." - Moylan, William (2014-06-20). Understanding and Crafting the Mix: The Art of Recording. CRC Press. ISBN 9781136117589. - Arnold Schoenberg, Structural Functions of Harmony, Faber and Faber, 1983, pp. 1–2. - Benward & Saker (2003), p. 77. - Merriam-Webster, Inc. (1995). "Chord", Merriam-Webster's dictionary of English usage, p.243. ISBN 978-0-87779-132-4. - "Chord", Oxford Dictionaries. - Dahlhaus, Car. "Harmony". In Deane L. Root (ed.). Grove Music Online. Oxford Music Online. Oxford University Press. (subscription required) - Károlyi, Ottó, Introducing Music, p. 63. England: Penguin Books. - Arnold Schoenberg, Theory of Harmony, p.26: "It is required of a chord that it consist of three different tones." - Schellenberg, E. Glenn; Bigand, Emmanuel; Poulin-Charronnat, Benedicte; Garnier, Cecilia; Stevens, Catherine (Nov 2005). "Children's implicit knowledge of harmony in Western music". Developmental Science. 8 (8): 551–566. doi:10.1111/j.1467-7687.2005.00447.x. PMID 16246247. - Duarter, John (2008). Melody & Harmony for Guitarists, p.49. ISBN 978-0-7866-7688-0. - Benward & Saker (2003), p.185. - Benward & Saker (2003), p.70. - Benward & Saker (2003), p. 77. - Benward & Saker (2003), p.100. - Benward & Saker (2003), p.201. - Benward & Saker (2003), p.220. - Benward & Saker (2003), p.231. - Benward & Saker (2003), p.274. - Winston Harrison, The Rockmaster System: Relating Ongoing Chords to the Keyboard – Rock, Book 1, Dellwin Publishing Co. 2005, p. 33 - Pachet, François, Surprising Harmonies, International Journal on ComputingAnticipatory Systems, 1999. Archived March 30, 2011, at the Wayback Machine - William G Andrews and Molly Sclater (2000). Materials of Western Music Part 1, p. 227. ISBN 1-55122-034-2. - Benward & Saker (2003). Music: In Theory and Practice, Vol. I, pp. 74–75. Seventh Edition. ISBN 978-0-07-294262-0. - The assumption that a chord can be indicated "the German way"; using only capital or small letters ("C" for Major, or "c" for minor) is a fatal misunderstanding. The German tradition only uses this when describing the tonality of the key (g-minor, or F#-Major). To try to use this for chords is woefully inaccurate and shouldn't be used. - Haerle, Dan (1982). The Jazz Language: A Theory Text for Jazz Composition and Improvisation, p. 30. ISBN 978-0-7604-0014-2. - Policastro, Michael A. (1999). Understanding How to Build Guitar Chords and Arpeggios, p. 168. ISBN 978-0-7866-4443-8. - Benward & Saker (2003), p. 92. - Bert Weedon, Play in a Day, Faber Music Ltd, ISBN 0-571-52965-8, passim – among a wide range of other guitar tutors - Connie E. Mayfield (2012) "Theory Essentials", p. 523. ISBN 1-133-30818-X. - Hanson, Howard. (1960) Harmonic Materials of Modern Music, pp. 7ff. New York: Appleton-Century-Crofts. LOC 58-8138. - Benjamin, Horvit, and Nelson (2008). Techniques and Materials of Music, pp. 46–47. ISBN 0-495-50054-2. - Benjamin, Horvit, and Nelson (2008). Techniques and Materials of Music, pp. 48–49. ISBN 0-495-50054-2. - Hawkins, Stan. "Prince- Harmonic Analysis of 'Anna Stesia'", pp. 329, 334n7, Popular Music, Vol. 11, No. 3 (Oct., 1992), pp. 325–35. - Miller, Michael (2005). The Complete Idiot's Guide to Music Theory, p. 119. ISBN 978-1-59257-437-7. - Piston, Walter (1987). Harmony (5th ed.), p. 66. New York: W.W. Norton & Company. ISBN 0-393-95480-3. - Bartlette, Christopher, and Steven G. Laitz (2010). Graduate Review of Tonal Theory. New York: Oxford University Press. ISBN 978-0-19-537698-2 - Grout, Donald Jay (1960). A History Of Western Music. Norton Publishing. - Dahlhaus, Carl. Gjerdingen, Robert O. trans. (1990). Studies in the Origin of Harmonic Tonality, p. 67. Princeton University Press. ISBN 0-691-09135-8. - Goldman (1965). Cited in Nattiez (1990). - Jones, George T. (1994). HarperCollins College Outline Music Theory. ISBN 0-06-467168-2. - Nattiez, Jean-Jacques (1990). Music and Discourse: Toward a Semiology of Music (Musicologie générale et sémiologue, 1987). Translated by Carolyn Abbate (1990). ISBN 0-691-02714-5. - Norman Monath, Norman (1984). How To Play Popular Piano In 10 Easy Lessons. Fireside Books. ISBN 0-671-53067-4. - Stanley Sadie and John Tyrrell, eds. (2001). The New Grove Dictionary of Music and Musicians. ISBN 1-56159-239-0. - Surmani, Andrew (2004). Essentials of Music Theory: A Complete Self-Study Course for All Musicians. ISBN 0-7390-3635-1. - Benward, Bruce & Saker, Marilyn (2002). Music in Theory and Practice, Volumes I & II (7th ed.). New York: McGraw Hill. ISBN 0-07-294262-2. - Persichetti, Vincent (1961). Twentieth-century Harmony: Creative Aspects and Practice. New York: W. W. Norton. ISBN 0-393-09539-8. OCLC 398434. - Schejtman, Rod (2008). Music Fundamentals; the Piano Encyclopedia. ISBN 978-987-25216-2-2.
LESSON PLAN in Intermolecular Forces, Polarity, Naming Compounds, Molecular Formula, Covalent Bonding, Ionic Bonding, Molecular Structure, VSEPR Theory, Molecular Geometry, Resonance, Electronegativity, Metallic Bonding. Last updated October 2, 2020. The AACT high school classroom resource library has everything you need to put together a unit plan for your classroom: lessons, activities, labs, projects, videos, simulations, and animations. We constructed a unit plan using AACT resources that is designed to teach Chemical Bonding to your students. By the end of this unit, students should be able to - Distinguish between the locations of metal atoms versus non-metal atoms on the periodic table. - Use electronegativity values to predict whether an ionic or covalent bond is most likely to form. - Identify compounds as ionic, covalent, or metallic based on their chemical formula. - Predict the number of atoms needed in a molecular formula. - Examine ratios of atoms in compounds. - List some properties of ionic, covalent, and metallic bonds. - Compare and contrast the basic structure of ionic and molecular compounds. - Determine the number of valence electrons for an atom. - Create a Lewis dot structure for an atom, covalent compound, and ionic compound. - Predict the charge of an ion. - Predict the molecular shape of a covalent molecule based upon its Lewis dot structure. - Explain why stable, neutral ionic compounds are formed from cations and anions. - Explain why different quantities of ions combine to make different compounds. - Explain the purposes of superscripts and subscripts in chemical formulas. - Name and write the formulas for binary and ternary ionic compounds. - Visualize “free-moving electrons” in metallic bonding. - Identify that different metals have different properties. - Conceptualize the impact of one electron pair domain acting upon another, and understand how those interactions result in the molecular geometries predicted by VSEPR theory. - Describe the implications of electron pair repulsions on molecular shape. - Understand that the molecular shape names are descriptions of the actual shape. - Make the correlation between geometry, nonbonding pairs and molecular shape. - Relate the shape of a molecule and the relative electronegativity values of its constituent atoms to the polarity of the molecule. - Explain the meaning of the following: cohesion, adhesion, surface tension, and capillary action. - Describe the unique behaviors of water molecules, and why they are important. - Determine the polarity of molecules. - Rank molecules in order of increasing strength of van der Waals forces, given a set of structural formulas for several compounds. - Manipulate models to demonstrate molecular orientations giving rise to London dispersion forces, dipole-dipole forces and hydrogen bonds. - Identify the intermolecular forces present in chemical substances. - Recognize that physical properties are related to intermolecular forces. This unit supports students’ understanding of - Ionic Bonding - Covalent Bonding - Naming Compounds - Molecular Formulas - Molecular Structure - Lewis Dot Structures - Molecular Shapes - VSEPR Theory - Molecular Geometry - Physical Properties - Metallic Bonds - Electric current - Lenz’s Law - Properties of Water - Intermolecular Forces - London Dispersion Forces - Dipole-dipole Forces - Hydrogen Bonding Teacher Preparation: See individual resources. Lesson: 8-12 class periods, depending on class level. - Refer to the materials list given with each individual activity. - Refer to the safety instructions given with each individual activity. - The activities shown below are listed in the order that they should be completed. - The number of activities you use will depend upon the level of students you are teaching. - The teacher notes, student handouts, and additional materials can be accessed on the page for each individual activity. - Please note that most of these resources are AACT member benefits. - Help students visualize how different chemical bonds form by using the Bonding Animation to introduce the concept of bonding. Examples of ionic, covalent, and polar covalent bonds are animated, and students are given a set of compounds to predict the bonding types. - Use the from the to allow students to investigate ionic and covalent bonding. Students interact with different combinations of atoms and are tasked with determining the type of bond and the number of atoms needed to form each. The simulation visually differentiates between the transferring of electrons when forming an ionic compound and the sharing of electrons when forming a covalent compound. Students also become familiar with the molecular formula and geometric shape, as well as the naming system for each type of bond. This simulation is unlocked and can be used by your students. It also includes a . Covalent, Ionic & Metallic Bonding and Properties - In the lab You Light Up My Life, students participate in a guided inquiry investigation which allows them to test different physical properties of given samples. This lab can be used to introduce ionic, covalent and metallic bonds and their properties. It will also help students make connections and differentiate between the types of bonds and helps them to better understand the nomenclature of ionic and covalent compounds. - Students construct ionic compounds by balancing the charges on cations and ions in the activity, Constructing Ionic Compounds. This activity shows students how to form stable ionic compounds, explain why different number of cations and ions are needed to form those compounds, and use superscripts and subscripts in chemical formulas. Another option is the Ionic Bonding Puzzle which provides puzzle pieces that students use to create neutral ionic compounds. Once they have made a neutral ionic compound they can use electron dot diagrams to show the formation of the compounds. Finally they will name the ionic compounds. - Students build models of ionic and covalent compounds with the Lego Modeling of Compounds lab. By the end of this lab, they will be able to build molecular models, examine the ratio of atoms in compounds, and compare the basic structure of ionic and covalent substances. - Use one of our ionic bonding “bracket” activities to help students demonstrate their understanding of ionic bonding and ionic properties. - The activity, My Name is Bond, Ionic Bond begins with pairs of students playing a game of “Ionic Compound War” to build eight compounds. Then then transfer the compounds to a “bracket” and use their knowledge of ionic bonding, along with a solubility chart, to predict the strongest and weakest bond between four pairs of ionic substances. - With a similar “brackets” resource, Ionic Bonding Brackets, students apply their knowledge of ionic bond strength and its relationship to melting point and solubility. After analyzing the ionic charge and radius to predict the strongest and weakest bond between four pairs of ionic substances, they will then determine which will be the least soluble. - The demonstration, Metallic Bonding & Magnetics can be used to show your students how electrons flow through a metal using tubes made of different metals. This demo will allow your students to visualize the “free-moving electrons” in metallic bonding, understand magnetic fields, and identify that different metals have different properties because of their electron structure. - The activity, Isn’t it Ionic uses clues and questions to help students learn how to form ionic and covalent compounds. By the end of this activity, students should be able to predict ionic charges, ionic bonds, and covalent bonds. This activity can also be used to help students solve stoichiometric problems for limiting and excess reactant calculations. - Use the lab, Ionic vs. Covalent Compounds to allow your students to compare two visually similar substances, salt and sugar. After melting a sample of each substance and analyzing their chemical composition, students draw conclusions regarding the properties of ionic and covalent compounds. Lewis Structures, Molecular Geometry (VSEPR) and Polarity - The Molecular Compound lesson teaches students how to name molecular compounds and create Lewis Dot Structures using a single dice and element cards. This resource includes a set of element cards for your students to use as they work through the activity. - Introduce molecular geometry with the VSEPR Modeling activity, which has students construct physical models of molecules and then derive the arrangement of the atoms. This guided inquiry activity allows them to conceptualize the impact of one electron pair domain acting upon another. They will also understand how those interactions result in the molecular geometries predicted by VSEPR theory. Find out more about this VSEPR Modeling Activity in a related article from the September 2017 issue of Chemistry Solutions. - An alternate option is the activity, VSEPR with Balloons, which allows students to explore Valence Shell Electron Pair Repulsion Theory using balloon models. Since balloons tend to take up as much space as they can when tied together, they can look like models of central atoms in VSEPR theory, making a great metaphor for the model. This activity is an extension of Shapes of Molecules found on the AACT website. - Students can investigate the VSEPR geometry of covalent compounds in the lab, Shapes of Molecules. They draw Lewis structures, use molecular models, and determine the geometry of covalent compounds. The following molecular shapes are covered in this lab: tetrahedral, trigonal pyramidal, trigonal planar, bent, and linear. Note this activity includes a lot of repetition so that students gain as much practice as needed to master this concept. - Students can further explore Valence Shell Electron Pair Repulsion Theory using the activity, VSEPR with Balloons. Balloons tend to take up as much space as they can when tied together, so they look like models of central atoms in VSEPR theory, making a great metaphor for the model. This resource is an extension of the Shapes of Molecules activity. - In the activity, Making Connections Between Electronegativity, Molecular Shape, and Polarity students find the electronegativity values of a variety of elements, draw the Lewis structures of molecules made with those elements, and identify the molecular shape of each molecule. Students then determine if the molecules are polar or nonpolar based on the electronegativity values of the atoms and the shape. Finally, students use Ptable.com to find information about atoms and molecules and connect what they find to observable properties. - Students can become familiar with the special properties of water by investigating cohesion, adhesion, surface tension, and capillary action with the activity, What Makes Water So Special? Their observations will help them define the physical properties investigate, describe the unique behaviors of water, and explain why they are important. - The Polarity lesson plan helps students learn some valuable tips for determining if a molecule is polar or nonpolar based on its Lewis Structure, VSEPR structure, and polarity. The student activity includes a “Decision Tree” to help students work through the steps of determining if a substance is polar. Intermolecular Forces (IMFs) - Introduce the relationship between molecular structure and properties with the lesson, The Chemistry of Water Video. Students watch a video that is part of the American Chemical Society video series Chemistry Basics and answer questions as it plays. This activity will help them learn about how the shape of a molecule will determine properties such as melting and boiling point. - Students investigate intermolecular attractive forces in a lesson plan, The Great Race: A Study of van der Waals Forces by constructing molecules and determining the forces of attraction between them: London dispersion, dipole-dipole, and hydrogen bonding. Given a set of structural formulas, they then rank the molecules in order of increasing strength of van der Waals forces. - The Intermolecular Forces & Physical Properties demonstration allows students to observe and compare the properties of surface tension, beading, evaporation, and miscibility for water and acetone. This resource includes alignment with both the AP Chemistry Curriculum Framework and NGSS. - If you’d prefer a lab activity, use the Physical Properties lab to lead them through an investigation of how intermolecular forces affect physical properties. This lab will help them understand what happens in the freezing and melting process and how solubility works. - If your students are tactile learners, use one or both of these resources to help them model covalent bonding and polarity with the use of string and Styrofoam balls. - In the activity, Modeling Bond Polarity, students model the pull of electrons in a bond between two elements, demonstrating covalent bonding. In particular differentiating between polar and nonpolar bonds. - In a similar activity, Modeling Molecular Polarity, students use electronegativity values and their knowledge of covalent bonding to model the bonds in a molecule. They then use that information to help them determine the overall polarity of a molecule. - Students can investigate London dispersion and dipole-dipole intermolecular forces with the Comparing Attractive Forces simulation. In the analysis that follows the investigation, they relate IMFs (including hydrogen bonding) to physical properties, such as boiling point and solubility. The simulation was created by the Concord Consortium for AACT using Next-Generation Molecular Workbench software. - Another option is the Intermolecular Forces simulation, which allows students to review the three major types of intermolecular forces – London dispersion forces, dipole-dipole interactions, and hydrogen bonding – through short video clips and accompanying text. They then answer quiz questions using the relative strengths of these forces to compare different substances given their name, formula, and Lewis structure, and put them in order based on the strength of their intermolecular forces, their boiling point, or their vapor pressure. The simulation is designed as a five question quiz for students to use multiple times. - Wrap up your study of IMFs with the Intermolecular Forces Review lesson that helps your students review the five types of interactions (London dispersion, dipole-induced dipoles, dipole forces, hydrogen bonding, and ionic bonding). The lesson includes a PowerPoint presentation and a student note sheet to use during the review. Connect chemistry with current events with one or both of the following activities: - The Chemistry of Hand Sanitizer and Soap lab also shows students connections between chemistry and current events. They model the interaction between hand sanitizer particles and virus particles, as well as between soap particles and virus particles. They then apply their understanding of molecular structure and intermolecular forces to analyze their observations and behavior of the particles. - In addition to connecting chemistry with current events, give your students extra unit conversion practice with the activity, Designing an Effective Respiratory Cloth Mask. Students use unit conversion to help compare sizes of molecules, viruses, and droplets and then use them to interpret graphical data. They then use their findings to design a cloth mask that helps protect its wearer against infection by SARS-CoV-2, the coronavirus that causes COVID-19. Do you like to end your unit with a culminating activity? We have two projects in our Molecules & Bonding resource library. - Using Molecular Modeling, students research a molecule selected from a teacher approved list, construct a three-dimensional model of the molecule, and present their research to the class in a 7-10 minute oral presentation. - If you do not have the time for students to complete a long-term project, use Properties of Common Molecular Substance instead of the Molecular Modelingproject. This resource allows students to apply their knowledge of molecular polarity, shape, and intermolecular forces to explain the differences in properties between different covalent substances. - The Evolution of Materials Science in Everyday Products project connects everyday products to chemistry and helps students understand the progression of development of common items and display their knowledge through a creative video.
In Chapter 1 we looked at the Standard Atmosphere, the environment in which aircrafts operate, at Bernoulli’s equation and its relationship to airplane (or more specifically, wing) aerodynamics, and at some basic parameters that influence the aerodynamic performance of an airplane. In this chapter we will look at the way that we account for airplane propulsion; i.e., jet or propeller engines. This means we will be looking at the factors that affect things like airplane thrust and power. We will also find that the same factors that explain thrust can also be used to account for some of the drag on an airplane. In looking at thrust, power, and drag we are interested in how these may vary with airplane speed and with altitude. We must have a basic understanding of these dependencies if we are to eventually use these in determining the performance of an airplane. Airplane engines are, of course, the subject of entire engineering courses dealing with things such as internal combustion engines and air-breathing jet engines. We want to confine ourselves to a very simple approach to understanding how propulsion works without going into any more of the details than are absolutely necessary. Fortunately, we will be able to do this. 2.1 Jet Engines Jet engines come in a wide range of designs. Most are considered “turbine” engines because turbines are used to extract energy from the high speed exhaust flow to drive a “compressor” to compress the flow into the engine prior to fuel addition and combustion, but at very high speeds (hypersonic flow) it is possible to get compression through shock waves and a non-turbine jet engine called a “ramjet” is the result. However, we are going to restrict ourselves to subsonic, incompressible flight where turbines and compressors are always needed. The most basic type of jet engine is called a “turbojet” and it consists basically of an inlet, followed by a compressor that increases the pressure (and lowers the speed) of the air before it enters the combustion chamber where fuel is added and ignited. After combustion a turbine extracts enough energy from the high energy (high speed) exhaust products to drive the compressor, and the flow then exits through the engine exhaust at high speed to provide thrust. It turns out that a pure turbojet isn’t a very efficient way to make thrust. It creates thrust through a very high speed exhaust and this is both very noisy and very loss prone. The high speed exhaust jet essentially rips its way through the surrounding air and this violent interaction between exhaust and atmosphere results in a lot of friction-like losses and makes a lot of noise. We will look at jet propulsion in terms of momentum changes (energy per unit time) with the difference between the momentum in the exhaust and the engine inlet accounting for the thrust and, at first glance, it will seem that any way we can get a change in momentum is just as good as any other way, but that is not the case. Momentum is essentially the mass multiplied by speed (velocity). This means that there are two ways to get a momentum change. One is to take a small amount of mass and accelerate it to a very high speed as is done in a turbojet engine. Another is to take a large amount of mass and accelerate it by a lesser amount. As it turns out, the latter way is the most efficient way to get thrust. It is sort of like comparing the effects of a large ceiling fan rotating slowly with those of a little “personal” fan. If you made two propeller driven air boats of the type used in swamps, one boat with a small propeller and the other with a large one, you would find that the boat with the larger prop would need less power to move at a given speed than the one with the small prop. Fan-jets rely on this principle to provide more efficient thrust to an airplane than turbo-jets. In a fan-jet, the engine turbine or turbines drive both the compressor that works on the air going into the combustion chamber and a large fan that adds momentum to a large mass of air going around the engine core without being used to burn fuel. This fan or “bypass” air then mixes with the higher speed core, combustion products to give a high momentum total engine exhaust that derives its momentum from the large mass of the bypass flow and the high speed of the core flow. So, for a given amount of thrust we will need a given amount of momentum change of the air going through the engine between its entrance and exit. We will look at how this momentum change mathematically accounts for the thrust a little later. The point here is that the most efficient way to get this momentum change with minimal losses is to accelerate a large mass of air by a small amount (small change in speed). This means that the bigger the bypass ratio (the ratio of the bypass air mass to the mass of air going through the engine core) the more efficient the engine is. But there is a limit to this. As the fan jet engine gets larger due to higher bypass ratio design, the engine enclosure (nacelle) also gets larger and it produces more drag. So at some point it makes more sense to replace the bypass “fan” with a large propeller. The result is the “turboprop” engine. In the turboprop engine the flow through the engine core is really not used to produce any significant thrust. The exhaust turbine is designed to take all of the energy it can from the exhaust to drive the propeller and all of the engine’s thrust comes from the flow through the propeller. In a turboprop engine the amount of thrust that comes from the core flow is so negligible that, in some engine designs, the core flow actually goes “backwards”. We might wonder, if the turboprop engine is more efficient than the fan-jet, which is in turn more efficient than the turbojet, why fan-jets are the engine of choice for most airplanes today? The answer is in the desired speed of flight. Just as there is a big drag rise on a wing as it approaches the speed of sound, there are drag type losses on a propeller blade when its speed approaches Mach one. In fact, for a given propeller rotation speed, the limit on practical diameter for the prop is determined by the radius at which the propeller blade section reaches its critical Mach number. And, since the airspeed seen by the propeller blades is a function of both their rotational speed and the speed of the airplane, this limits the speed of the aircraft. Propeller design can extend this speed range somewhat with things like swept blade tips but the turboprop will always impose limits on aircraft cruise speeds. Also, it turns out that the rotational speeds needed for a turboprop propeller are an order of magnitude below those of those in an efficient turbine core and this necessitates speed reduction gears between the turbine and the prop and this introduces both noise and vibrations that are not found in the fan-jet. 2.2 Propeller Engines So what is the difference between a turboprop and a propeller driven by an internal combustion engine? From the point of view of the thrust provided by the propeller, there isn’t much difference. The difference is in the engine and the gearing that drives the propeller. The turboprop is driven by a small turbine (jet) engine that sends as much of its energy as possible to the propeller through a driveshaft and reduction gear system. The IC engine propeller is attached to the driveshaft of an internal combustion engine that, like most automobile engines, uses the burning of gasoline or diesel fuel in a piston/cylinder type motor to turn the shaft. Today most internal combustion driven propeller engines are found on smaller general aviation aircraft. This type of engine has provided reliable, affordable power for airplanes since the first flight of the Wright brothers in 1903. Over the years there have been many fascinating variations of IC engine used in airplanes, from the “rotary” engines of World War I in which the driveshaft was attached to the airplane and the propeller and engine actually rotated together around the shaft, to the massive piston engines of the 1940s and 1950s with dozens of cylinders arranged around the driveshaft like kernels on an ear of corn, to the four and six cylinder, car type but air cooled, engines usually found on today’s GA airplanes. These many varieties of IC engines would make an interesting and exhausting study in themselves, but that is beyond the scope of this text. As far as we will be concerned, a propeller engine is a propeller engine, whether driven by a turbine or an IC engine or a rubber band. We will merely be concerned with the “power” output by the engine and we will call this the “shaft power” regardless of the type of engine that drives the shaft. 2.3 Thrust and Power This brings us to the main difference in the way we will talk about propulsion for jet and prop engines. For jet powered aircraft, whether turbojets or fanjets, we will characterize the propulsion properties of the airplane in terms of thrust. For propeller powered airplanes, whether the propeller is attached to an IC engine or a turbine, we will talk about performance in terms of power. Power and thrust are merely two different ways of looking at aircraft propulsion and performance. They are directly related to each other through speed. Power = (Thrust)(Velocity) While we normally talk about jet propulsion in terms of thrust and propeller propulsion in terms of power, there is little reason beyond convention that we must do so. We could talk about the power of a jet engine and the thrust of a propeller and we sometimes do so. Perhaps one reason for this distinction is that we will later find it convenient to look at the variation of both power and thrust with velocity and we will find that it is common to assume that thrust is fairly constant with speed for a jet and power is fairly constant with speed for a propeller driven plane. The units normally associated with power and thrust, respectively, are pounds and horsepower. Yes, these are “politically incorrect” units; nonetheless, they are far more widely used than Newtons and Watts, their SI equivalents. [Have you ever heard anyone talk about the power of their car engine in watts?] This, of course, means we need to learn how the unit of horsepower relates to basic units in the “English” system. 1 horsepower = 550 foot-pounds / second. [ A bit of engineering trivia: this conversion was used so often in the days of slide rule calculations that most slide rules had a special mark on them at the 550 location on the slide.] 2.4 Thrust and Conservation Laws To find out how things like altitude and airspeed affect thrust and power we need to take a look at how the air goes through the propeller or the jet engine when an airplane is in flight and how the momentum of the air changes as it follows that path. To do this we will need to look at two “conservation laws”, conservation of mass and conservation of momentum. 2.4.1 Mass Conservation In its simplest concept mass conservation is often stated something like “mass cannot be either created or destroyed; i.e., it is constant or conserved”. This is often accompanied by a qualifier noting that, in an atomic reaction, mass can actually be created (fusion reaction) or destroyed (fission reaction). This is an interesting way to look at mass if one is looking at the mass in the universe or in a closed container but it doesn’t help us when talking about engines. We need to look at the conservation of mass in a flow; that is, in the air going through a room or a pipe or a propeller or a jet engine. If we had a sealed room filled with air it would be simple to state that the amount of air in the room is a constant. We could have people and plants in the room with the chemical reactions that are part of human breathing and plant chemistry continually altering the chemical constituencies in the “air”; nonetheless, the total mass of the “air” would remain constant. The picture changes when we add ventilation to the room, either by using a forced ventilation system such as an air conditioning or heating system or by simply opening windows and doors. With either system there would be new air coming into the windows, doors, or intake vents and old air going out of other windows, doors, or exhaust vents. If we had a room with only a forced air inlet and no exhaust, the mass of air in the room would increase as air came in through the inlet. To accommodate this increasing mass the room would either have to expand like a balloon or the pressure and density of the air in the room would have to increase. Note that, if we assumed that the air was “incompressible” it would be impossible to pump new air into the room without providing an exhaust for an equal amount of air to escape. This would require conservation in the mass of the air in the room. So in the example of room ventilation, conservation of mass for the air in the room would simply mean that, as a mass of new air enters the room, the same amount of mass of air must leave the room. Room or window air conditioners work this way, taking a given mass flow rate from the room, sending it through cooling coils, and returning that same mass flow rate to the room after some heat was removed from the air. This brings us to the subject of mass flow rate, often called “m-dot” and given the symbol of a lower case “m” with a dot on top of the letter to represent a time derivative of the mass; i.e., mass per unit time, dm/dt. When we speak of a room with vents or doors and windows we must talk about mass flow rates, and we say that in order to have mass conservation we must have no change in the mass within the room per unit time, simply another way of saying that the amount of mass that goes in during a given time period must equal the amount of mass that goes out in that same time. This is stated as: dm/dt = 0 . In other words, the amount of mass in the room does not change with time. We often put this in equation form, saying that dm/dt = Σ ρVA = 0. Here, we are saying that the mass flow rate is equal to the density of the air, multiplied by its speed, as it passes through an area of size “A”. In other words, if air at sea level density is blowing through a window at a speed of 20 feet-per-second and if that window has an opening of 2 feet by 4 feet, we can calculate the mass of air per unit time that is passing through the window. dm/dt = ρVA = (0.002378 sl/ft3)(20 ft/sec.)(2 ft x 4 ft) = 0.3805 sl/sec. [Note here that the units of mass rate of flow have been found to be slugs per second. In the SI system they would be found in kilograms per second and in a version of the “English” system often used in fields such as Mechanical Engineering the units of mass flow rate would be pounds-mass per second.] Now, if conservation of mass is met for the air in the room, the same mass of air per unit time must be going out of another opening or openings. (dm/dt)in + (dm/dt)out = 0 (ρVA)in + (ρVA)out = 0 So, if there is a single window letting in the air flow found above and the exit is through a door, we can use conservation of mass to determine the speed of the air going out the door. (ρVA)out = – (ρVA)in . Just as three factors, the size (area) of the window, the speed of the air flow through the window, and the density of the air, determined the “mass flow rate” of the air coming into the room, the same three things determine the exit mass flow rate. In reality, all three of these things could be different at the exit (door, in this case), so, if we want to find the speed of the exiting air we must know both the area of the door and the density of the air at the door. However, there is no reason why the air flowing through the room would have changed density so we are safe in assuming “incompressible” flow, that is, density is constant. This gives us a simple equation: (VA)out = – (VA)in . So, if the door is 3 feet wide by 7 feet high, giving an area of 21 ft2, while the window had an area of 8 ft2, the speed of the air going out the door is: Vout/Vin = – Ain/Aout Vout = – Vin(Ain/Aout) or in this case, Vout = – 20 ft/sec. (8 ft2 / 21 ft2) = – 7.62 ft/sec. Now, why is there a minus sign with the exit velocity? This is because we, for no real reason, chose to give a positive sense to the velocity going in the window and since velocity is a vector; i.e., it has a direction, we have designated the flow of air into the room as positive. This means that the negative sign on the exit air velocity tells us it is going out of the room. While this may seem like an un-needed complication here, there are cases where it can help us figure out what is happening. For example, suppose there are five windows and two doors in our room and we are told that air is coming into all five windows at a certain speed and is going out one door at a given speed, what is happening at the other door? Is the flow through that second door going into or out of the room? We would have to write the complete equation for mass flow conservation to find both the amount and direction of the flow through the second door. (ρVA)w1 + (ρVA)w2 + (ρVA)w3 + (ρVA)w4 + (ρVA)w5 – (ρVA)D1 + (ρVA)D2 = 0 . Note that we have assigned positive values to the flow through all the windows since we were told that the flow was coming into all of them. We have also assigned a negative value to the flow out the first door since the flow was said to be out of that door. Also note that we did not assign a sign (direction) to the flow through the second door because we have no idea which way it is going. Now, if we put all the needed information for the five windows and first door into the terms in the equation and if we know the area of the second door and assume that density is the same everywhere (incompressible flow), we can solve for the speed (velocity) of the flow using the mass conservation relationship above and find both the magnitude of the speed and its direction (sign). Try doing the above problem assuming that all five windows are 2 ft X 4 ft in size and that air is blowing in at 20 ft/sec. Assume that the two doors are both 3 ft X 7 ft in size and that the flow out of the first door is measured at 50 ft/sec. Find the speed and direction of the flow through the second door. NOTE: Here we considered all flow INTO our “system” or “control volume” as POSITIVE, and all flow OUT of the system as NEGATIVE. If we do not know its direction, we assume it is positive in value and the solution of the equation will give us a negative answer if we assumed the wrong direction. Later, when we look at the Momentum Equation we will use a unit vector, n, to assign a positive direction within our chosen axis system for flow through an opening, and that unit vector will always point OUT of the system. OK, that was simple enough, but how do we deal with mass conservation when we are looking at flow through a jet engine or a propeller? Mass conservation through a propeller or a jet engine works just like mass conservation in a flow going through a room. In fact, for the jet engine it is even simpler than the average room because there is only one well defined entrance and exit, or is that really the case? Technically, there is a second source of incoming mass in any jet engine and that is the mass flow of fuel coming into the engine. There is air coming into the engine inlet of a known area at (supposedly) a known speed and density, but the flow going out of the engine isn’t really just air, it is the gas that comes from combustion of the incoming air and the incoming fuel. The mass rate of flow coming out of the exit must account for both the mass of the entering air and the entering fuel, so our mass conservation relationship must recognize this. (dm/dt)inlet + (dm/dt)fuel + (dm/dt)exhaust = 0 We would normally write this as: (ρAV)inlet + (dm/dt)fuel = – (ρAV)exhaust . So we must know the mass flow rate of the fuel. Usually the mass flow rate of the fuel is very small compared to that of the inlet air so perhaps that term can be neglected. So what’s the big deal? If we can neglect the fuel flow rate we are back to the one window, one door example and life is easy. Unfortunately there is another factor that we must not forget and that is density. Usually the flow through the exhaust of a jet engine is going pretty fast, near or greater than the speed of sound; i.e., we can no longer assume that density is constant as we did in the room ventilation example. To solve this problem we have to know either the exit flow density or its speed in order to solve the equation for the “other” parameter (exit speed of density), and since the fuel mass flow contributes to this exit density we probably should not assume it to be negligible even if its velocity is almost negligible. Making mass conservation for a jet even more complex is the fact that most of today’s jets are “fan jets” where there are essentially two entrance flows, one that goes through the engine core, mixing with the fuel to form a high speed exhaust, and another, larger, flow that is accelerated through the fan. We might analyze this problem by accounting for two separate entrance flows and two separate exit flows, or by assuming (correctly in most cases) that the two exit flows mix before leaving the engine covering or “nacelle” to form a single, mixed exhaust. In any case, the jet engine flow problem is a little simpler for many people to understand than the propeller flow problem because the entrance and exit areas are normally pretty well defined. How do we define entrance and exit flows when we draw the flow through a propeller? When a flow is going through a propeller, just what are the entrance and exit areas? There really is no physical entrance or exit. Of course, we know the flow goes through the propeller itself, so, is the propeller area used for both the flow “entrance” and its “exit”? This hardly makes sense. How can we talk about the changes in the flow between the entrance and exit when there is no physical distance between the entrance and exit? Let’s look at what we know intuitively about the flow through a propeller (or a fan). We know that the flow behind the propeller or fan is moving faster than the flow in front of it. We know that in some way, a way that can be analyzed in detail by looking at each propeller or fan blade as a little rotating wing that does work on the air, the propeller essentially adds energy to the flow. We also know, if we think about it a bit, that we cannot use Bernoulli’s equation to compare the flow upstream and downstream of the prop or fan because energy is added at the prop or fan and Bernoulli’s equation assumes that energy is constant through the flow. We also know that there are limits to what a fan or propeller can do to accelerate a flow due to tip speed limits on the blades themselves and these limits essentially mean that we can pretty safely assume incompressible flow through the system. Putting all these facts together, we can draw a picture that looks something like the flow should appear through a propeller or fan. We know that somewhere upstream of the propeller the flow is undisturbed; i.e., it is at “free-stream” or atmospheric conditions. We know that somewhere downstream of the prop the static pressure in the mass of air that went through the propeller must return to its free-stream value. We will imagine a “stream-tube”, or three-dimensional path of constant mass flow, that starts out in the undisturbed flow upstream of the prop, goes through the prop (becoming the same diameter as the prop at that location, and then continues downstream until the point we mentioned above where the static pressure has returned to the atmospheric value. What must that “stream-tube” look like? A stream-tube is defined as a three-dimensional flow path in which the mass flow rate is the same at every point along its journey. Essentially, as shown in the following figure, the upstream cross sectional area of the stream-tube (its “capture” area) must have the same amount of mass flow rate through it as goes through the prop itself. Likewise, the “exit” area for our stream-tube must also allow passage of the same mass flow as went through the capture area and the prop “disk” area. So why is the “stream-tube” in the figure above getting progressively smaller as the flow goes from the atmospheric pressure, free-stream capture area to the atmospheric pressure exit area somewhere downstream? First, we know the velocity in the exit area must be larger than in the capture (inlet) area; hence, if mass flow rate is the same and the flow is incompressible, the area must decrease in inverse proportion to the speed increases. But why do we assume that this area decrease (and speed increase) is smooth and continuous? Isn’t there simply a big jump in speed across the propeller disk? Well, we probably could analyze everything in terms of some kind of instantaneous jump in flow speed at the propeller disk based on an energy balance, assuming that the energy added by the prop produces a sudden increase in flow kinetic energy and speed. However, we know from real world measurements that this speed increase is not instantaneous and that part of the increase is seen in front of the propeller as the flow speeds up from its “free-stream” velocity to the velocity right at the front of the prop disk. We also know that it takes a couple of propeller diameters downstream before the flow in the “propwash” reaches top speed. Based on this combination of reality and convenience, we choose to model the speed increase as a continuous one within a “stream-tube” shaped like a converging nozzle of circular cross section, as shown in the figure above. This ideal picture, of course, ignores a lot of things such as the losses due to turbulence and rotational flow effects; nonetheless, it is one that works fairly well. So, what do we propose to do with this model and with the model of the flow through a jet engine? What we want to do is use these to determine how thrust is produced and find the properties that determine how thrust varies with speed and altitude. Our goal is to take a look at propulsion. How do we account for thrust or power in aircraft performance evaluations? There are two ways to do this. One would look at energy additions to the flow and a conservation of energy. But, as noted in the propeller discussion above, this would be very tedious, requiring us to do aerodynamic analyses of each propeller blade, accounting for losses due to compressibility effects near the blade tips and for the interference between the flow over one blade and the following blade. There are books on how to do this, the oldest of which went under titles such as “Airscrew Theory”, and this is the type of analysis that companies making propellers must use. The problem would be even more interesting in a jet engine with us having to account for energy gains and losses due to flow around compressor blades and turbine blades, combustion of fuel, and flow though internal nozzles. It turns out that the simplest way to look at thrust is to look at momentum conservation. 2.4.3 Momentum conservation Momentum conservation, like mass conservation and energy conservation, is one of the “big three” conservation “laws” that we all saw somewhere back in some Physics course. On the face of it, conservation of momentum is a simple concept. Just as in mass conservation of a flow we must account for all mass flows that enter or leave the flow-field under consideration, in looking at momentum conservation we must consider all things that could possibly account for momentum changes and, ultimately, in forces. Essentially, the concept we are looking at is one that says that the change of momentum in a body or “system” with time must equal the forces on that body or system. The idea is that either forces on a body or system will cause its momentum to change or a momentum change within the system or body will result in a force. (d/dt)(momentum) = (d/dt)(mv) = Force This is a simple idea that is often made to look very complicated when derived in most textbooks on fluid mechanics. If, for example, you kick a soccer ball, the force you impart to the ball will result in a change in momentum in the ball. If the ball was standing still before it was kicked, the force will change its momentum from zero to a value related to the force of the impact and the mass of the ball. If the ball was already moving, the kick may send moving in another direction, so this concept is directional; i.e., it is a vector concept, as would be expected when a force is involved. In looking at aircraft propulsion we are interested in the reverse action; that is, creating a momentum change in order to get a force, changing the momentum of the flow through the engine or propeller to create thrust. Just as in working with Bernoulli’s equation we had a choice of modeling the flow as a moving fluid going past a wing or body, or as a body moving through still air, we have to make a similar choice here. We will, for example, choose to look at the flow through a jet engine or a propeller as if the engine (prop) is standing still and the flow is moving past it. This is really a choice between having to consider the momentum of the moving engine or the momentum of the moving air. Either view will give the same answer for the thrust, but the moving air model is usually a little easier to work with. Either way, we must be very careful to account for all possible momentum changes in both the engine and the flow. We first need to look at what kinds of momentum changes might be present as well as what kinds of forces might be involved. To do this, let’s look at one of the simplest of “jet” engines, but one of the hardest to analyze, a rubber balloon that is inflated and released. Let’s look at the illustration above and list all of the ways that momentum might play a role as well as all the forces involved. There will be at least two sources of change of momentum for the balloon and at least three forces that might be involved. Momentum change sources: - The change in momentum of the balloon (the “system”) with time because of the change in mass of air inside the balloon with time and due to any changes in velocity of that mass. [As the balloon expels air through its inlet/outlet, the mass of the “system” itself is changing and, even if its speed was constant, the momentum of the system would change.] - The momentum of the flow exiting the “system” (balloon); i.e., the mass flow of air through the inlet/outlet (jet) multiplied by its velocity. Both of these terms above are directional because of the velocities associated with them. The momentum of the balloon itself is related to the balloon’s velocity and the momentum of the flow through the exit is obviously related to the direction of the flow through the exit. Forces on the balloon: - The major force on the balloon will be the one we choose to call thrust. This is essentially what we are trying to find. - nother force on the balloon that we might not think of at first is that due to gravity; i.e., its weight. - Finally, there would be any pressure forces caused by pressures acting on areas. These might include pressure drag on the balloon itself or differences in pressure across system boundaries. Often we find that pressure forces tend to balance out or sum to zero but there are some cases where these must be considered. - We could also consider friction forces or even electromagnetic or other forces if we wished but we will limit ourselves to the first three forces mentioned above. How do we describe each of these sources of momentum change or forces in a very general way? Let’s look at each of these listed above. 1. The change in momentum of the “system” with time involves the changes in both mass and velocity of the system: d/dt [(mass)(velocity)] , and, since the system mass can be written as its density times its volume, we might look at this as 2. The change in momentum due to the flow out of (and in general) into the system with time is essentially the mass rate of flow (dm/dt) across any entrances or exits multiplied by the speed at which that mass is passing through the entrance or exit areas. We know that the mass rate of flow is the density multiplied by both the velocity and the flow cross sectional area, so this term is expressed as: (dm/dt)(velocity) = (density)(velocity)(area)x(velocity) . 3. The weight is just the mass (density x volume) multiplied by the acceleration of gravity. 4. The pressure forces are just pressures acting on an area: Now, to work with all these we need to put them together in the form of some kind of equation. The equation must essentially say that the momentum changes must be balanced by the forces involved. This can be thought of as forces causing momentum change (the soccer player’s foot kicks the ball) or momentum changes causing forces (the thrust from a released balloon). The equation that usually results from a much more formal derivation is a complicated looking, vector relationship called the momentum equation. 2.4.4 The Momentum Equation Before you panic at the vector notation and the double and triple integrals, take a deep breath and see how these terms relate to the ones presented above. A triple integral over “R” (the mathematical “region” or the “system”) is nothing but the volume. If the density and velocity of everything contained in the region or system is the same; i.e., if it is a homogeneous system, then this term is nothing but the time derivative of the density times the volume times the velocity; i.e., of the system mass times its speed as it was stated in the section above. So why do we make it so complicated looking? One reason might be just to impress our friends in liberal arts or to show our parents how hard our courses are. A better reason is to allow the momentum equation to account for non-homogenous system effects. Suppose, for example, that our “system” was not a balloon filled with nice homogenous air, but a baseball or golf ball with a solid filling made of several layers, each with different densities, and further, that someone had made the ball with its heavier core somewhat “off center”. You can buy such “trick” golf balls at novelty shops and when you hit them with a golf club (impart a force to the system!), instead of traveling in a straight line they wobble around as if they were drunk. Because the momentum equation can account for this “non-homogeneity” it can account for the wobbly motion of the trick golf ball. In a similar way the last term on the right, the gravity or weight term, can account for gravitational effects on a non-homogeneous mass. Two of the terms in the equation have double integrals. You might have guessed by now that the double integral over a distance “S” must relate to some kind of area, and looking at the terms would confirm that. The double integral term on the left relates to the momentum carried with a flow into or out of the system over an entrance or exit area. This term is written in this complex way to be able to account for non-uniform velocities over the entrance or exit and even for non-uniform densities over these areas. If we assume that all of the entrance or exit flow is the same fluid moving at the same speed then the density and velocity terms can come outside the integral and the integral itself becomes nothing but the entrance or exit area. So, again, why make it look this complicated? Well, in many cases the flow out of an opening is not uniform because friction forces cause it to move more slowly near the edges of the opening than at the center, and this comprehensive form of the momentum equation can account for that if we want it to do so. Similarly, the pressure term on the right hand side of the equation can account for pressure variation over a surface. What about the vector notation, the V•n term, in the double integral term on the left? First, the momentum equation is a vector equation, meaning that each of the terms has a direction and the solution of the equation for a force such as thrust or drag will give both a magnitude and a direction for that force. Second, for one of the terms on each side of the equation, it is only the parameter “normal” to a defined surface or boundary that will cause a force and the “unit vector” n is used to designate that normal direction. We will always define the direction for this unit vector as pointing out of the system, even where the flow is coming into the system. What then do these vector quantities mean? Each of the velocities can have up to three terms in them, one associated with each direction in a selected axis system. In the case of velocity in a conventional x, y, z axis system, we normally use the terms u, v, and w to designate the x, y, and z components of velocity, respectively. So we would write a velocity vector as: V = ui + vj + wk , where i, j, and k are the unit vectors in the positive x, y, and z directions. In a similar manner, the gravity vector could have up to three components; however, we sometimes try to define our coordinate system so one axis is in the direction of gravitational acceleration to eliminate two of these components. The V•n term is then the “dot product” of two vectors where both the V and the n vectors may have x, y, and z components, but only the like directed components multiply with each other, then sum to give a “scalar” quantity with a magnitude but no direction. So, if the velocity is in the same direction as the normal vector (as is often the case for flows into or out of a system) the result is simply the magnitude of the velocity. At the other extreme, if the velocity is at a 90 degree angle to the normal vector the dot product gives zero. Again one might ask, why make things so complicated with all these integrals and vectors and dot products and the like? It is done this way because it is a very versatile equation that can account for fully three dimensional motion. For example, should that soccer player kick the ball at a 90 degree angle to its existing direction of motion, this relationship would, provided we knew the force of the kick and the mass and velocity of the ball, tell us the ball’s new direction and speed even though the direction would be in neither the original direction of motion or in the direction of the kick. Similarly, if there is a bend in a pipe we can use the equation to find the magnitude and direction of the force that will occur when water flows through that bend in the pipe. The trick to using the momentum equation is to follow the rule of thumb that often distinguishes an engineer from a pure scientist or mathematician; that is to use proper alignment of axis systems and to set system boundaries and to make good assumptions that will eliminate as much of the complexity as possible. Fortunately we can do a lot of this as we use the momentum equation to look at thrust. 2.4.5 Thrust (again) Let’s look at the flow through a jet engine in terms of the momentum equation. In the illustration above we have aligned the engine with the “x” axis and we have flow coming into the engine inlet in the x direction and another flow coming out of the engine, also in the x direction. We want to know the thrust as a function of this information. Let’s look at what we can say about the various terms in the momentum equation. The first term on the left hand side of the equation is a “time dependent” term to account for changes in momentum of the “system” itself with time. Here our system is the entire jet engine, and, if we assume that the engine (airplane) is in “steady” or constant speed flight, there is nothing in the term (density, velocity, or volume) that is changing with time. So, this term is zero. The second term on the left accounts for the momentum carried into or out of the system as flow enters or leaves. Obviously, this term will not go away since we have air coming into the engine and combustion products going out the other end. First we need to ask if these two flows are “uniform” across their respective entrance or exit areas. If we can assume that they are uniform and can assume that all of the flow has the same density, then this term (actually two terms, one for the entrance and one for the exit) becomes: ρ1V1(V1•n1)A1 + ρ2V2(V2•n2)A2 . Now, what do we do with the vector business? The flows are both in the positive x direction. The first normal unit vector is in the negative x direction while the second is in the positive x direction. The result is: – ρ1V12A1 + ρ2V22A2 , (all in the x direction) Ok, that takes care of the left hand side of the momentum equation. What happens to the terms on the right? The first term on the right is the “external” force which, in this case, is the thrust we want to find. The second term on the right is perhaps the hardest to understand physically so we will come back to this. The third term on the right is the gravity term, really the weight. If we assume that this is acting at a 90 degree angle to the x axis or the direction of flight and thus is perpendicular to all the other forces and momentum changes in which we have an interest we might simply neglect this term. Actually it would be more proper to say that its component in the x direction is zero. In reality, this term would tell us that there must be a force to oppose the weight and this would be the aerodynamic lift which, in turn, would be related in the momentum equation to a vertical change in momentum of the flow as it moved around the wing and the corresponding pressure distribution around the wing. In essence we are choosing to ignore the vertical components of the forces and momentum changes. Now let’s go back to the second term on the right, the only term with pressures in it. This term looks at forces caused by pressures acting on areas. If we were looking at the lift force we would use this term to integrate the pressure distribution around a wing. On the engine we will assume that the flows over the outside of the engine casing or nacelle are symmetrical, that is that the same pressure distribution exists on the top as on the bottom of the nacelle, and that the net effect of these pressures (at least in the x direction) is zero. But what about pressures across the entrance and exit? Pressures across the entrance and exit?!! How can this mean anything when there are no real surfaces here, just flows going in or out? This is where the concept of a “system” boundary gets interesting. When there is a real boundary such as the engine nacelle the bounds of the system are easy to understand. But these “open” ends of the “system” are also boundaries over which we must account for all the terms in the equation. In other words, just as we had to account for the flow through these somewhat imaginary boundaries, we must also account for pressure changes across them. But how can these pressures cause real forces when there are no “real” surfaces for them to act on? This becomes one of those “leaps of faith” that we often must take in applying equations to physical situations. No, there are no surfaces at the entrance and exit where the pressure differences across the surface cause a force; however, we must account for them anyway if there is a pressure differential between the surrounding atmosphere and the flow into the entrance and out of the exit. This is probably the easiest to understand when we look at the exhaust flow. Coming out of the exhaust is a flow of the combustion products of air and fuel that has been heated and pressurized in the engine combustor. After combustion we want to turn that added energy into as high a momentum (the second term on the left hand side of the momentum equation) as possible. This means that we want to “expand” the gas in a exit nozzle, lowering its pressure with a corresponding increase in speed (ala Bernoulli’s equation) as much as possible to get a high momentum. The ideal situation is to expand it to the point where the exiting gas has the same pressure as the atmosphere into which it will exit. If it expands too much or too little there will be losses as the flow pressure comes to equilibrium with the atmosphere. It turns out (and the momentum equation essentially tells us this) that the losses from over or under-expansion are equivalent to the pressure force that would be on a surface with the same area as the exit with a pressure difference equal to that under or over-expansion delta-P. This is why some high performance jets have variable area exit nozzles on their engines. The same problem can occur to a lesser degree at the engine inlet but a properly designed engine inlet and compressor section can eliminate most of the loss. So, how do we deal with this pressure term? We either must know the differences between the atmospheric pressure and those of the entrance and exit flows and compute values for these terms, being careful to account properly for the unit vector signs, or we must assume that these losses are negligible. Let us take the easy way out and assume that these terms are of little consequence because we have a properly designed engine. OK, where does this leave us? We have ended up with a relatively simple equation: – ρ1V12A1 + ρ2V22A2 = – Fe rearranging this gives: Thrust = Fe = ρ1V12A1 – ρ2V22A2 . Looking at this we see that the second term on the right will be much greater than the first term, so, the thrust will have a negative sign. Is this ok? Sure it is. It just says the thrust force is in the negative x direction, toward the left, just as we want it to be. Wow! That sure was a lot of work to get a fairly obvious answer; the thrust is equal to the momentum change from engine inlet to exit! Isn’t this somewhat intuitive? Yes, it sortof is intuitive to many of us. On the other handit does keep the mathematicians and theoreticians in our midst happy, and more importantly, it tells us that in arriving at this “intuitive” answer we have made some important assumptionsabout pressure behavior and axis system selection, etc. Ok, now that we have all that under our belts what important facts about propulsion can be drawn from this solution? To see this, let’s play around with the equation above a little by accounting for conservation of mass. Now, recognizing that V1 is our “free stream” speed, V∞, and that the entering air density is also that of the atmosphere, ρ∞, we can write this as Thrust = ρ∞V∞2A1 – ρ2V22A2 And looking only at the magnitude of the thrust (as said above, the relationship above gives a negative thrust, signifying simply that it is to the left in our original illustration of the engine moving from right to left) Thrust = ρ2V22A2 – ρ∞V∞2A1 We now define the “static thrust” as T0, the thrust when the engine is standing still (V∞ = 0). This is the amount of thrust that would be measured on an engine test stand and is a standard piece of information that would exist for any engine. T0 = ρ2V22A2 This allows us to rewrite the general thrust relationship as: Thrust = T0 – ρ∞V∞2A1 , or simply as: T = T0 – a V∞2 , a = ρ∞A1 What does all this tell us? First, all the thrust equations tell us that thrust is a function of the atmospheric density. Unlike velocity, which we earlier found to vary with the square root of density, thrust decreases in direct proportion to the decrease of density in the atmosphere. Thus, we write: Talt = Tsl(ρalt/ρSL) This is an important relationship between thrust and altitude that we will use in all performance calculations. Second, we learn that, in general, the thrust of an engine varies with speed according to the relationship: T = T0 – a V∞2 It should be noted, as always, that these equations involve important assumptions, such as the assumption that engine exit pressure and entrance pressure are both equal to the pressure in the free stream atmosphere. Pilots of jet aircraft will tell you that the thrust to static thrust relationship shown above doesn’t, for example, account for an engine surge on initial acceleration down the runway as a “ram effect” into the engine inlet occurs. This “ram effect” is essentially one of these pressure effects that we chose to ignore. 2.4.6 Propeller Thrust It should be noted that we would get essentially the exact same thrust equation looking at the flow through a propeller as we do with a jet engine. Keeping in mind an earlier discussion, we would draw our “system” as shown below using boundaries that represent a “stream tube” of constant mass flow. In this case we have no easy way of knowing the exact values for the entering flow area or the exit area but we would get exactly the same equation as we found for the jet and we would still find T = T0 – aV∞2. In this chapter we have looked at the relatively simple models of aircraft propulsion that we will use in examining aircraft performance. In doing this we have used some basic physical concepts of conservation (mass and momentum), both of which can provide very powerful tools for evaluating forces and motions in fluid flows and other areas. We made a lot of simplifying assumptions along the way in order to understand some very basic concepts related to jet and propeller propulsion; in particular, to give a basis for modeling the way both thrust and power vary with speed and altitude. We will find these concepts very useful in later chapters. 1. In a wind tunnel the speed changes as the cross sectional area of the tunnel changes. If the speed in a 6′ x 6′ square test section in 100 mph, what was the speed upstream of the test section where the tunnel measures 20′ x 20′? Use conservation of mass and assume incompressible flow. Conservation of mass requires that as the flow moves through a path or a duct the product of the density, velocity and cross sectional area must remain constant; i.e. that ρVA = constant. 2. A model is being tested in a wind tunnel at a speed of 100 mph. (a) If the flow in the test section is at sea level standard conditions, what is the pressure at the model’s stagnation point? (b) The tunnel speed is being measured by a pitot-static tube connected to a U-tube manometer. What is the reading on that manometer in inches of water. (c) At one point on the model a pressure of 2058 psf is measured. What is the local airspeed at that point? Figure 2.1: Claire Colvin (2021). “TurboJet Engine Illustration.” CC BY 4.0. Figure 2.2: Claire Colvin (2021). “Illustration of a Turbo-Fan or Fan-Jet Engine.” CC BY 4.0. Figure 2.3: Claire Colvin (2021). “Turboprop Engine Illustration.” CC BY 4.0. Figure 2.4: Claire Colvin (2021). “Mass Flows for a Turb-Jet Engine.” CC BY 4.0. Figure 2.5: Claire Colvin (2021). “Flows Through a Fan-Jet Engine.” CC BY 4.0. Figure 2.6: James F. Marchman (2004). “The Stream-tube Concept for a Propeller Flow.” CC BY 4.0. Figure 2.8: Claire Colvin (2021). “Momentum Equation Terms for Turbo-Jet.” CC BY 4.0. <!– pb_fixme –><!– pb_fixme –>
It turns out the galaxy's twin black holes are actually triplets. Almost every known galaxy — including our own Milky Way — has a single supermassive black hole swirling at its center. Occasionally, astronomers will spot a pair of black holes together, a sign that two galaxies are merging into one. But now, an international research team has discovered the first known galaxy containing three black holes — and it could explain how some galaxies get so big, so fast. Two Become Three But in a new study, published in the journal Astronomy & Astrophysics, researchers observed the galaxy using the Multi Unit Spectroscopic Explorer instrument on the European Southern Observatory’s Very Large Telescope. The surprise result: the galaxy appears to be home to not two but three black holes — each with a mass greater than 90 million Suns. This discovery affects far more than our understanding of just NGC 6240. Astronomers have long wondered how the most massive galaxies in our universe managed to form in just the 14 billion years since the Big Bang. Now, it seems the answer might be that their evolution involved multiple galaxies merging simultaneously. "Up until now, such a concentration of three supermassive black holes had never been discovered in the universe," researcher Peter Weilbacher said in a press release. "The present case provides evidence of a simultaneous merging process of three galaxies along with their central black holes." READ MORE: Astronomers find cosmic anomaly: Three supermassive black holes in one galaxy [Digital Trends] More on black holes: Two Supermassive Black Holes Are on a Devastating Crash Course
Addition, subtraction, multiplication and division are foundational skills that are applied to many mathematical concepts. Often, when we are hoping for student automaticity and fluency in numbers, number operations are what we are talking about. Models are the way we are representing numbers so that we can do number operations. There are a number of different models that are helpful to students understanding number operations. Models that Emphasize 10 Models that Emphasize Place Value Models that Emphasize Patterns Models that Emphasize Partitioning Number The Importance of Partitioning Numbers Regardless of what number operation we are talking about, it is important that children are able to break numbers into parts. Friendly Numbers – children are often able to understand number operations with ‘friendly’ numbers like 2, 5, and 10. Breaking a 7 into a and a 2 allows us to use number facts that are more familiar. Place Value Partitioning – when we are working with multi-digit numbers, it is helpful for us to break numbers up into the values of their digits – for example, 327 is 300 + 20 + 7. Number Operation Strategies There are many different strategies that children use to perform number operations. A misconception is that all children need to know and use all strategies. It is important for us to expose children to different strategies through classroom discussion and routines such as number talks and number strings. When combined with Margaret Smith’s ideas around Orchestrating Classroom Discussion, we can set a task for students and - Predict what strategies they might use. Order these from least to most complex. - Observe students doing mathematical tasks – using white boards allows us to see their thinking. We can then identify different strategies being used. - Have students share their thinking in an order from least to most complex. This should not include every child sharing for every task. A small handful of children sharing in a logical order can help students understand the next more complex solution. In this way, children are being exposed to other strategies, will be able to understand those that are close to their own, and increase the sophistication of their thinking. \|Strategies\|\|Connection to Addition\|\|Connection to Multiplication\| \|Counting: This is a common strategy when one of the numbers is small.\|\|Addition by counting or counting on from one number. Ex: 25 + 7 = 25, 26, 27, 28, 29, 30, 31, 32.\|\|Skip counting by one of the numbers being multiplied. 9 x 5 = 9, 18, 27, 36, 45\| \|Decomposing Numbers: breaking numbers apart.\|\|Adding friendly numbers. Ex: when you need to add 12, breaking it into +10 and then +2 more. \| Making 10. Ex: when adding 5 + 7, recognizing that 5 + 5 = 10, and so it is 10 + 2 more = 12. Breaking one or both numbers into place value. Ex: 23 + 47 is 20 + 40; 3 + 7 \|Multiplying friendly numbers. Ex: when you need to multiply by 6, break it into x 5 and 1 more. \| Partial Products: Breaking one or both numbers into place value. Ex: 23 x 47 is (20 + 3) x (40 + 7) \|Compensation: this is very common when a number is close to 10.\|\|Rounding one of the numbers to a friendly number, then compensating the answer at the end for the difference. Ex: 36 + 9 is close to 36 + 10, subtract 1. Ex: 36 + 11 is close to 36 + 10, add 1.\|\|Rounding one of the numbers to a friendly number, then compensating the answer at the end for the difference. Ex: 99 x 5 is close to 100 x 5, subtract 5 Ex: 101 x 5 is close to 100 x , add 5\| \|Double/Half\|\|Recognizing that 4 + 4 is double 4, or 8. Recognizing that 4 + 3 is almost double 4, subtract 1.\|\|Recognizing that 5 x a number is the same as ½ of 10 x a number. Ex: 9 x 5 is half of 9 x 10 = 45\| \|Standard Algorithm\|\|Traditional algorithm, symbolic regrouping.\|\|Traditional algorithm, symbolic regrouping.\| A Bridge between Addition and Multiplication: Doubles - Doubles are one way to think about adding a number to itself, as well as the start to multiplicative thinking. - Doubles are an important bridge between adding and multiplication. - You can read more about teaching doubles here. Addition is the bringing together of two or more numbers, or quantities to make a new total. Sometimes, when we add numbers, the total in a given place value is more than 10. This means that we need to regroup, or carry, a digit to the next place. There is a great explanation of regrouping for addition and subtraction on Study.com. Subtraction is the opposite operation to addition. For each set of three numbers, there are two subtraction and one addition number facts. These are called fact families. For example: For the numbers 7, 3, 10: 7 + 3 = 10 10 – 3 = 7 10 – 7 = 3 As we move from single digit to multi-digit addition and subtraction, it is important that we maintain place value, and continue to move through the concrete to abstract continuum. A helpful progression for teaching addition and subtraction can be found on the Math Smarts site. Multiplication and Division - This is the first structure that we introduce children to. - It builds on the understanding of addition but in the context of equal sized groups. Rectangular Array/Area Model - This is often the second representation of multiplication introduced It is useful to show the commutative property that 3 x 4 = 4 x 3 = 12 - A number line can represent skip counting visually. - Scaling is the most abstract structure, as it cannot be understood through counting. - Scaling is frequently used in everyday life when comparing quantities or measuring. Single Digit Multiplication Facts Multiplication facts should be introduced and mastered by relating to existing knowledge. If students are stuck in a ‘counting’ stage – either by ones or skip-counting to know their single-digit multiplication facts, it is important that they understand strategies beyond counting before they practice. Counting is a dangerous stage for students, as they can get stuck in this inefficient and often inaccurate stage. Students should not move to multi-digit multiplication before they understand multiplication strategies for single-digit multiplication. - It is important that students understand the commutative property 2 x 4 = 8 and 4 x 2 = 8. - 2 x 4 should be related to the addition fact 4 + 4 = 8, or double 4. - Using a multiplication table as a visual structure is helpful to see patterns in multiplication facts. - Same as (1 facts) - Doubles. (2 facts) - Doubles and 1 more (3 facts) - Double Doubles (4 facts) - Tens and fives (10, 5 facts) - Relating to tens (9 facts) - Remaining facts (6, 7, 8 facts) Conceptual Structures for Division In an equal grouping (quotition) question, the total number are known, and the size of each group is known. - The unknown is how many groups there are. In an equal sharing (partition) question, the total number are known, and the number of groups is known. - The unknown is how many are in each group. This is a comparison of the scale of two quantities and is often referred to as scale factor. This is a difficult concept as you can’t subtract to find the ratio. Relate division facts back to multiplication facts families: Ex) 6 x 8 = 48 8 x 6 = 48 48 ÷ 6 = 8 48 ÷ 8 = 6 Once students have understanding and fluency with single digit multiplication and division fact families they are ready to move on to multi-digit fact families. So What do Students DO with Number Operations? Simple computation is not enough for children to experience. They need to have opportunities to explore and wonder about numbers and how they work together. Regardless of the routine or task, children should be encouraged to use different concrete and pictorial models to show their thinking. Some examples of rich interactions include: - Number talks promote classroom discussion. Combining number talks with visual or concrete models can help us see what students are thinking. - Number strings can help children see the pattern in number operations. They are helpful for children to see the pattern in number operations, which is the foundation for algebraic thinking. - You can see the structure for building number strings here. - SPLAT encourages both additive thinking and subitizing. More complex SPLAT lessons are also great for encouraging algebraic thinking with unknowns. - Building problem stories are powerful for children to understand contexts of mathematics in their every day life. - Using real objects or pictures encourages children to see math in their environments. - Invitations that are created to inspire mathematical thinking encourage exploration, vocabulary building and wonder. - There are so many games and puzzles that can have children play with number operations. - Open middle problems allow for flexible thinking and exploration. You can see a sample here.
This Module 6: Quadratic Functions unit also includes: Linear, exponential, now it's time for quadratic patterns! Learners build on their skills of modeling patterns by analyzing situations with quadratic functions. The sixth module in the Algebra I series has pupils analyze multiple representations of quadratic functions and compare the behavior of quadratic functions with both linear and exponential functions. - Create a graphic organizer outlining the key features of linear, quadratic, and quadratic functions - Use the Set problems as whiteboard practice to check for understanding - Requires a solid understanding of both linear and exponential functions - Includes answer keys with explanations - Uses inquiry-based openers to help build understanding
EvolutionWikipedia open wikipedia design. \|Part of a series on\| Evolution is change in the heritable characteristics of biological populations over successive generations. These characteristics are the expressions of genes that are passed on from parent to offspring during reproduction. Different characteristics tend to exist within any given population as a result of mutation, genetic recombination and other sources of genetic variation. Evolution occurs when evolutionary processes such as natural selection (including sexual selection) and genetic drift act on this variation, resulting in certain characteristics becoming more common or rare within a population. It is this process of evolution that has given rise to biodiversity at every level of biological organisation, including the levels of species, individual organisms and molecules. The scientific theory of evolution by natural selection was proposed by Charles Darwin and Alfred Russel Wallace in the mid-19th century and was set out in detail in Darwin's book On the Origin of Species (1859). Evolution by natural selection was first demonstrated by the observation that more offspring are often produced than can possibly survive. This is followed by three observable facts about living organisms: 1) traits vary among individuals with respect to their morphology, physiology and behaviour (phenotypic variation), 2) different traits confer different rates of survival and reproduction (differential fitness) and 3) traits can be passed from generation to generation (heritability of fitness). Thus, in successive generations members of a population are more likely to be replaced by the progenies of parents with favourable characteristics that have enabled them to survive and reproduce in their respective environments. In the early 20th century, other competing ideas of evolution such as mutationism and orthogenesis were refuted as the modern synthesis reconciled Darwinian evolution with classical genetics, which established adaptive evolution as being caused by natural selection acting on Mendelian genetic variation. All life on Earth shares a last universal common ancestor (LUCA) that lived approximately 3.5–3.8 billion years ago. The fossil record includes a progression from early biogenic graphite, to microbial mat fossils, to fossilised multicellular organisms. Existing patterns of biodiversity have been shaped by repeated formations of new species (speciation), changes within species (anagenesis) and loss of species (extinction) throughout the evolutionary history of life on Earth. Morphological and biochemical traits are more similar among species that share a more recent common ancestor, and can be used to reconstruct phylogenetic trees. Evolutionary biologists have continued to study various aspects of evolution by forming and testing hypotheses as well as constructing theories based on evidence from the field or laboratory and on data generated by the methods of mathematical and theoretical biology. Their discoveries have influenced not just the development of biology but numerous other scientific and industrial fields, including agriculture, medicine and computer science. - 1 History of evolutionary thought - 2 Heredity - 3 Variation - 4 Mechanisms - 5 Outcomes - 6 Evolutionary history of life - 7 Applications - 8 Social and cultural responses - 9 See also - 10 References - 11 Bibliography - 12 Further reading - 13 External links History of evolutionary thought The proposal that one type of organism could descend from another type goes back to some of the first pre-Socratic Greek philosophers, such as Anaximander and Empedocles. Such proposals survived into Roman times. The poet and philosopher Lucretius followed Empedocles in his masterwork De rerum natura (On the Nature of Things). In contrast to these materialistic views, Aristotelianism considered all natural things as actualisations of fixed natural possibilities, known as forms. This was part of a medieval teleological understanding of nature in which all things have an intended role to play in a divine cosmic order. Variations of this idea became the standard understanding of the Middle Ages and were integrated into Christian learning, but Aristotle did not demand that real types of organisms always correspond one-for-one with exact metaphysical forms and specifically gave examples of how new types of living things could come to be. In the 17th century, the new method of modern science rejected the Aristotelian approach. It sought explanations of natural phenomena in terms of physical laws that were the same for all visible things and that did not require the existence of any fixed natural categories or divine cosmic order. However, this new approach was slow to take root in the biological sciences, the last bastion of the concept of fixed natural types. John Ray applied one of the previously more general terms for fixed natural types, "species," to plant and animal types, but he strictly identified each type of living thing as a species and proposed that each species could be defined by the features that perpetuated themselves generation after generation. The biological classification introduced by Carl Linnaeus in 1735 explicitly recognised the hierarchical nature of species relationships, but still viewed species as fixed according to a divine plan. Other naturalists of this time speculated on the evolutionary change of species over time according to natural laws. In 1751, Pierre Louis Maupertuis wrote of natural modifications occurring during reproduction and accumulating over many generations to produce new species. Georges-Louis Leclerc, Comte de Buffon suggested that species could degenerate into different organisms, and Erasmus Darwin proposed that all warm-blooded animals could have descended from a single microorganism (or "filament"). The first full-fledged evolutionary scheme was Jean-Baptiste Lamarck's "transmutation" theory of 1809, which envisaged spontaneous generation continually producing simple forms of life that developed greater complexity in parallel lineages with an inherent progressive tendency, and postulated that on a local level, these lineages adapted to the environment by inheriting changes caused by their use or disuse in parents. (The latter process was later called Lamarckism.) These ideas were condemned by established naturalists as speculation lacking empirical support. In particular, Georges Cuvier insisted that species were unrelated and fixed, their similarities reflecting divine design for functional needs. In the meantime, Ray's ideas of benevolent design had been developed by William Paley into the Natural Theology or Evidences of the Existence and Attributes of the Deity (1802), which proposed complex adaptations as evidence of divine design and which was admired by Charles Darwin. The crucial break from the concept of constant typological classes or types in biology came with the theory of evolution through natural selection, which was formulated by Charles Darwin in terms of variable populations. Partly influenced by An Essay on the Principle of Population (1798) by Thomas Robert Malthus, Darwin noted that population growth would lead to a "struggle for existence" in which favourable variations prevailed as others perished. In each generation, many offspring fail to survive to an age of reproduction because of limited resources. This could explain the diversity of plants and animals from a common ancestry through the working of natural laws in the same way for all types of organism. Darwin developed his theory of "natural selection" from 1838 onwards and was writing up his "big book" on the subject when Alfred Russel Wallace sent him a version of virtually the same theory in 1858. Their separate papers were presented together at an 1858 meeting of the Linnean Society of London. At the end of 1859, Darwin's publication of his "abstract" as On the Origin of Species explained natural selection in detail and in a way that led to an increasingly wide acceptance of Darwin's concepts of evolution at the expense of alternative theories. Thomas Henry Huxley applied Darwin's ideas to humans, using paleontology and comparative anatomy to provide strong evidence that humans and apes shared a common ancestry. Some were disturbed by this since it implied that humans did not have a special place in the universe. Pangenesis and heredity The mechanisms of reproductive heritability and the origin of new traits remained a mystery. Towards this end, Darwin developed his provisional theory of pangenesis. In 1865, Gregor Mendel reported that traits were inherited in a predictable manner through the independent assortment and segregation of elements (later known as genes). Mendel's laws of inheritance eventually supplanted most of Darwin's pangenesis theory. August Weismann made the important distinction between germ cells that give rise to gametes (such as sperm and egg cells) and the somatic cells of the body, demonstrating that heredity passes through the germ line only. Hugo de Vries connected Darwin's pangenesis theory to Weismann's germ/soma cell distinction and proposed that Darwin's pangenes were concentrated in the cell nucleus and when expressed they could move into the cytoplasm to change the cell's structure. De Vries was also one of the researchers who made Mendel's work well known, believing that Mendelian traits corresponded to the transfer of heritable variations along the germline. To explain how new variants originate, de Vries developed a mutation theory that led to a temporary rift between those who accepted Darwinian evolution and biometricians who allied with de Vries. In the 1930s, pioneers in the field of population genetics, such as Ronald Fisher, Sewall Wright and J. B. S. Haldane set the foundations of evolution onto a robust statistical philosophy. The false contradiction between Darwin's theory, genetic mutations, and Mendelian inheritance was thus reconciled. The 'modern synthesis' In the 1920s and 1930s the so-called modern synthesis connected natural selection and population genetics, based on Mendelian inheritance, into a unified theory that applied generally to any branch of biology. The modern synthesis explained patterns observed across species in populations, through fossil transitions in palaeontology, and complex cellular mechanisms in developmental biology. The publication of the structure of DNA by James Watson and Francis Crick with contribution of Rosalind Franklin in 1953 demonstrated a physical mechanism for inheritance. Molecular biology improved understanding of the relationship between genotype and phenotype. Advancements were also made in phylogenetic systematics, mapping the transition of traits into a comparative and testable framework through the publication and use of evolutionary trees. In 1973, evolutionary biologist Theodosius Dobzhansky penned that "nothing in biology makes sense except in the light of evolution," because it has brought to light the relations of what first seemed disjointed facts in natural history into a coherent explanatory body of knowledge that describes and predicts many observable facts about life on this planet. Since then, the modern synthesis has been further extended to explain biological phenomena across the full and integrative scale of the biological hierarchy, from genes to species. One extension, known as evolutionary developmental biology and informally called "evo-devo," emphasises how changes between generations (evolution) acts on patterns of change within individual organisms (development). Since the beginning of the 21st century and in light of discoveries made in recent decades, some biologists have argued for an extended evolutionary synthesis, which would account for the effects of non-genetic inheritance modes, such as epigenetics, parental effects, ecological inheritance and cultural inheritance, and evolvability. Evolution in organisms occurs through changes in heritable traits—the inherited characteristics of an organism. In humans, for example, eye colour is an inherited characteristic and an individual might inherit the "brown-eye trait" from one of their parents. Inherited traits are controlled by genes and the complete set of genes within an organism's genome (genetic material) is called its genotype. The complete set of observable traits that make up the structure and behaviour of an organism is called its phenotype. These traits come from the interaction of its genotype with the environment. As a result, many aspects of an organism's phenotype are not inherited. For example, suntanned skin comes from the interaction between a person's genotype and sunlight; thus, suntans are not passed on to people's children. However, some people tan more easily than others, due to differences in genotypic variation; a striking example are people with the inherited trait of albinism, who do not tan at all and are very sensitive to sunburn. Heritable traits are passed from one generation to the next via DNA, a molecule that encodes genetic information. DNA is a long biopolymer composed of four types of bases. The sequence of bases along a particular DNA molecule specify the genetic information, in a manner similar to a sequence of letters spelling out a sentence. Before a cell divides, the DNA is copied, so that each of the resulting two cells will inherit the DNA sequence. Portions of a DNA molecule that specify a single functional unit are called genes; different genes have different sequences of bases. Within cells, the long strands of DNA form condensed structures called chromosomes. The specific location of a DNA sequence within a chromosome is known as a locus. If the DNA sequence at a locus varies between individuals, the different forms of this sequence are called alleles. DNA sequences can change through mutations, producing new alleles. If a mutation occurs within a gene, the new allele may affect the trait that the gene controls, altering the phenotype of the organism. However, while this simple correspondence between an allele and a trait works in some cases, most traits are more complex and are controlled by quantitative trait loci (multiple interacting genes). Recent findings have confirmed important examples of heritable changes that cannot be explained by changes to the sequence of nucleotides in the DNA. These phenomena are classed as epigenetic inheritance systems. DNA methylation marking chromatin, self-sustaining metabolic loops, gene silencing by RNA interference and the three-dimensional conformation of proteins (such as prions) are areas where epigenetic inheritance systems have been discovered at the organismic level. Developmental biologists suggest that complex interactions in genetic networks and communication among cells can lead to heritable variations that may underlay some of the mechanics in developmental plasticity and canalisation. Heritability may also occur at even larger scales. For example, ecological inheritance through the process of niche construction is defined by the regular and repeated activities of organisms in their environment. This generates a legacy of effects that modify and feed back into the selection regime of subsequent generations. Descendants inherit genes plus environmental characteristics generated by the ecological actions of ancestors. Other examples of heritability in evolution that are not under the direct control of genes include the inheritance of cultural traits and symbiogenesis. An individual organism's phenotype results from both its genotype and the influence from the environment it has lived in. A substantial part of the phenotypic variation in a population is caused by genotypic variation. The modern evolutionary synthesis defines evolution as the change over time in this genetic variation. The frequency of one particular allele will become more or less prevalent relative to other forms of that gene. Variation disappears when a new allele reaches the point of fixation—when it either disappears from the population or replaces the ancestral allele entirely. Natural selection will only cause evolution if there is enough genetic variation in a population. Before the discovery of Mendelian genetics, one common hypothesis was blending inheritance. But with blending inheritance, genetic variance would be rapidly lost, making evolution by natural selection implausible. The Hardy–Weinberg principle provides the solution to how variation is maintained in a population with Mendelian inheritance. The frequencies of alleles (variations in a gene) will remain constant in the absence of selection, mutation, migration and genetic drift. Variation comes from mutations in the genome, reshuffling of genes through sexual reproduction and migration between populations (gene flow). Despite the constant introduction of new variation through mutation and gene flow, most of the genome of a species is identical in all individuals of that species. However, even relatively small differences in genotype can lead to dramatic differences in phenotype: for example, chimpanzees and humans differ in only about 5% of their genomes. Mutations are changes in the DNA sequence of a cell's genome. When mutations occur, they may alter the product of a gene, or prevent the gene from functioning, or have no effect. Based on studies in the fly Drosophila melanogaster, it has been suggested that if a mutation changes a protein produced by a gene, this will probably be harmful, with about 70% of these mutations having damaging effects, and the remainder being either neutral or weakly beneficial. Mutations can involve large sections of a chromosome becoming duplicated (usually by genetic recombination), which can introduce extra copies of a gene into a genome. Extra copies of genes are a major source of the raw material needed for new genes to evolve. This is important because most new genes evolve within gene families from pre-existing genes that share common ancestors. For example, the human eye uses four genes to make structures that sense light: three for colour vision and one for night vision; all four are descended from a single ancestral gene. New genes can be generated from an ancestral gene when a duplicate copy mutates and acquires a new function. This process is easier once a gene has been duplicated because it increases the redundancy of the system; one gene in the pair can acquire a new function while the other copy continues to perform its original function. Other types of mutations can even generate entirely new genes from previously noncoding DNA. The generation of new genes can also involve small parts of several genes being duplicated, with these fragments then recombining to form new combinations with new functions. When new genes are assembled from shuffling pre-existing parts, domains act as modules with simple independent functions, which can be mixed together to produce new combinations with new and complex functions. For example, polyketide synthases are large enzymes that make antibiotics; they contain up to one hundred independent domains that each catalyse one step in the overall process, like a step in an assembly line. Sex and recombination In asexual organisms, genes are inherited together, or linked, as they cannot mix with genes of other organisms during reproduction. In contrast, the offspring of sexual organisms contain random mixtures of their parents' chromosomes that are produced through independent assortment. In a related process called homologous recombination, sexual organisms exchange DNA between two matching chromosomes. Recombination and reassortment do not alter allele frequencies, but instead change which alleles are associated with each other, producing offspring with new combinations of alleles. Sex usually increases genetic variation and may increase the rate of evolution. The two-fold cost of sex was first described by John Maynard Smith. The first cost is that in sexually dimorphic species only one of the two sexes can bear young. (This cost does not apply to hermaphroditic species, like most plants and many invertebrates.) The second cost is that any individual who reproduces sexually can only pass on 50% of its genes to any individual offspring, with even less passed on as each new generation passes. Yet sexual reproduction is the more common means of reproduction among eukaryotes and multicellular organisms. The Red Queen hypothesis has been used to explain the significance of sexual reproduction as a means to enable continual evolution and adaptation in response to coevolution with other species in an ever-changing environment. Gene flow is the exchange of genes between populations and between species. It can therefore be a source of variation that is new to a population or to a species. Gene flow can be caused by the movement of individuals between separate populations of organisms, as might be caused by the movement of mice between inland and coastal populations, or the movement of pollen between heavy-metal-tolerant and heavy-metal-sensitive populations of grasses. Gene transfer between species includes the formation of hybrid organisms and horizontal gene transfer. Horizontal gene transfer is the transfer of genetic material from one organism to another organism that is not its offspring; this is most common among bacteria. In medicine, this contributes to the spread of antibiotic resistance, as when one bacteria acquires resistance genes it can rapidly transfer them to other species. Horizontal transfer of genes from bacteria to eukaryotes such as the yeast Saccharomyces cerevisiae and the adzuki bean weevil Callosobruchus chinensis has occurred. An example of larger-scale transfers are the eukaryotic bdelloid rotifers, which have received a range of genes from bacteria, fungi and plants. Viruses can also carry DNA between organisms, allowing transfer of genes even across biological domains. Large-scale gene transfer has also occurred between the ancestors of eukaryotic cells and bacteria, during the acquisition of chloroplasts and mitochondria. It is possible that eukaryotes themselves originated from horizontal gene transfers between bacteria and archaea. From a neo-Darwinian perspective, evolution occurs when there are changes in the frequencies of alleles within a population of interbreeding organisms, for example, the allele for black colour in a population of moths becoming more common. Mechanisms that can lead to changes in allele frequencies include natural selection, genetic drift, genetic hitchhiking, mutation and gene flow. Evolution by means of natural selection is the process by which traits that enhance survival and reproduction become more common in successive generations of a population. It has often been called a "self-evident" mechanism because it necessarily follows from three simple facts: - Variation exists within populations of organisms with respect to morphology, physiology, and behaviour (phenotypic variation). - Different traits confer different rates of survival and reproduction (differential fitness). - These traits can be passed from generation to generation (heritability of fitness). More offspring are produced than can possibly survive, and these conditions produce competition between organisms for survival and reproduction. Consequently, organisms with traits that give them an advantage over their competitors are more likely to pass on their traits to the next generation than those with traits that do not confer an advantage. This teleonomy is the quality whereby the process of natural selection creates and preserves traits that are seemingly fitted for the functional roles they perform. Consequences of selection include nonrandom mating and genetic hitchhiking. The central concept of natural selection is the evolutionary fitness of an organism. Fitness is measured by an organism's ability to survive and reproduce, which determines the size of its genetic contribution to the next generation. However, fitness is not the same as the total number of offspring: instead fitness is indicated by the proportion of subsequent generations that carry an organism's genes. For example, if an organism could survive well and reproduce rapidly, but its offspring were all too small and weak to survive, this organism would make little genetic contribution to future generations and would thus have low fitness. If an allele increases fitness more than the other alleles of that gene, then with each generation this allele will become more common within the population. These traits are said to be "selected for." Examples of traits that can increase fitness are enhanced survival and increased fecundity. Conversely, the lower fitness caused by having a less beneficial or deleterious allele results in this allele becoming rarer—they are "selected against." Importantly, the fitness of an allele is not a fixed characteristic; if the environment changes, previously neutral or harmful traits may become beneficial and previously beneficial traits become harmful. However, even if the direction of selection does reverse in this way, traits that were lost in the past may not re-evolve in an identical form (see Dollo's law). However, a re-activation of dormant genes, as long as they have not been eliminated from the genome and were only suppressed perhaps for hundreds of generations, can lead to the re-occurrence of traits thought to be lost like hindlegs in dolphins, teeth in chickens, wings in wingless stick insects, tails and additional nipples in humans etc. "Throwbacks" such as these are known as atavisms. Natural selection within a population for a trait that can vary across a range of values, such as height, can be categorised into three different types. The first is directional selection, which is a shift in the average value of a trait over time—for example, organisms slowly getting taller. Secondly, disruptive selection is selection for extreme trait values and often results in two different values becoming most common, with selection against the average value. This would be when either short or tall organisms had an advantage, but not those of medium height. Finally, in stabilising selection there is selection against extreme trait values on both ends, which causes a decrease in variance around the average value and less diversity. This would, for example, cause organisms to eventually have a similar height. A special case of natural selection is sexual selection, which is selection for any trait that increases mating success by increasing the attractiveness of an organism to potential mates. Traits that evolved through sexual selection are particularly prominent among males of several animal species. Although sexually favoured, traits such as cumbersome antlers, mating calls, large body size and bright colours often attract predation, which compromises the survival of individual males. This survival disadvantage is balanced by higher reproductive success in males that show these hard-to-fake, sexually selected traits. Natural selection most generally makes nature the measure against which individuals and individual traits, are more or less likely to survive. "Nature" in this sense refers to an ecosystem, that is, a system in which organisms interact with every other element, physical as well as biological, in their local environment. Eugene Odum, a founder of ecology, defined an ecosystem as: "Any unit that includes all of the organisms...in a given area interacting with the physical environment so that a flow of energy leads to clearly defined trophic structure, biotic diversity, and material cycles (i.e., exchange of materials between living and nonliving parts) within the system...." Each population within an ecosystem occupies a distinct niche, or position, with distinct relationships to other parts of the system. These relationships involve the life history of the organism, its position in the food chain and its geographic range. This broad understanding of nature enables scientists to delineate specific forces which, together, comprise natural selection. Natural selection can act at different levels of organisation, such as genes, cells, individual organisms, groups of organisms and species. Selection can act at multiple levels simultaneously. An example of selection occurring below the level of the individual organism are genes called transposons, which can replicate and spread throughout a genome. Selection at a level above the individual, such as group selection, may allow the evolution of cooperation, as discussed below. In addition to being a major source of variation, mutation may also function as a mechanism of evolution when there are different probabilities at the molecular level for different mutations to occur, a process known as mutation bias. If two genotypes, for example one with the nucleotide G and another with the nucleotide A in the same position, have the same fitness, but mutation from G to A happens more often than mutation from A to G, then genotypes with A will tend to evolve. Different insertion vs. deletion mutation biases in different taxa can lead to the evolution of different genome sizes. Developmental or mutational biases have also been observed in morphological evolution. For example, according to the phenotype-first theory of evolution, mutations can eventually cause the genetic assimilation of traits that were previously induced by the environment. Mutation bias effects are superimposed on other processes. If selection would favour either one out of two mutations, but there is no extra advantage to having both, then the mutation that occurs the most frequently is the one that is most likely to become fixed in a population. Mutations leading to the loss of function of a gene are much more common than mutations that produce a new, fully functional gene. Most loss of function mutations are selected against. But when selection is weak, mutation bias towards loss of function can affect evolution. For example, pigments are no longer useful when animals live in the darkness of caves, and tend to be lost. This kind of loss of function can occur because of mutation bias, and/or because the function had a cost, and once the benefit of the function disappeared, natural selection leads to the loss. Loss of sporulation ability in Bacillus subtilis during laboratory evolution appears to have been caused by mutation bias, rather than natural selection against the cost of maintaining sporulation ability. When there is no selection for loss of function, the speed at which loss evolves depends more on the mutation rate than it does on the effective population size, indicating that it is driven more by mutation bias than by genetic drift. In parasitic organisms, mutation bias leads to selection pressures as seen in Ehrlichia. Mutations are biased towards antigenic variants in outer-membrane proteins. Genetic drift is the random fluctuations of allele frequencies within a population from one generation to the next. When selective forces are absent or relatively weak, allele frequencies are equally likely to drift upward or downward at each successive generation because the alleles are subject to sampling error. This drift halts when an allele eventually becomes fixed, either by disappearing from the population or replacing the other alleles entirely. Genetic drift may therefore eliminate some alleles from a population due to chance alone. Even in the absence of selective forces, genetic drift can cause two separate populations that began with the same genetic structure to drift apart into two divergent populations with different sets of alleles. The neutral theory of molecular evolution proposed that most evolutionary changes are the result of the fixation of neutral mutations by genetic drift. Hence, in this model, most genetic changes in a population are the result of constant mutation pressure and genetic drift. This form of the neutral theory is now largely abandoned, since it does not seem to fit the genetic variation seen in nature. However, a more recent and better-supported version of this model is the nearly neutral theory, where a mutation that would be effectively neutral in a small population is not necessarily neutral in a large population. Other alternative theories propose that genetic drift is dwarfed by other stochastic forces in evolution, such as genetic hitchhiking, also known as genetic draft. The time for a neutral allele to become fixed by genetic drift depends on population size, with fixation occurring more rapidly in smaller populations. The number of individuals in a population is not critical, but instead a measure known as the effective population size. The effective population is usually smaller than the total population since it takes into account factors such as the level of inbreeding and the stage of the lifecycle in which the population is the smallest. The effective population size may not be the same for every gene in the same population. It is usually difficult to measure the relative importance of selection and neutral processes, including drift. The comparative importance of adaptive and non-adaptive forces in driving evolutionary change is an area of current research. Recombination allows alleles on the same strand of DNA to become separated. However, the rate of recombination is low (approximately two events per chromosome per generation). As a result, genes close together on a chromosome may not always be shuffled away from each other and genes that are close together tend to be inherited together, a phenomenon known as linkage. This tendency is measured by finding how often two alleles occur together on a single chromosome compared to expectations, which is called their linkage disequilibrium. A set of alleles that is usually inherited in a group is called a haplotype. This can be important when one allele in a particular haplotype is strongly beneficial: natural selection can drive a selective sweep that will also cause the other alleles in the haplotype to become more common in the population; this effect is called genetic hitchhiking or genetic draft. Genetic draft caused by the fact that some neutral genes are genetically linked to others that are under selection can be partially captured by an appropriate effective population size. Gene flow involves the exchange of genes between populations and between species. The presence or absence of gene flow fundamentally changes the course of evolution. Due to the complexity of organisms, any two completely isolated populations will eventually evolve genetic incompatibilities through neutral processes, as in the Bateson-Dobzhansky-Muller model, even if both populations remain essentially identical in terms of their adaptation to the environment. If genetic differentiation between populations develops, gene flow between populations can introduce traits or alleles which are disadvantageous in the local population and this may lead to organisms within these populations evolving mechanisms that prevent mating with genetically distant populations, eventually resulting in the appearance of new species. Thus, exchange of genetic information between individuals is fundamentally important for the development of the Biological Species Concept (BSC). During the development of the modern synthesis, Sewall Wright developed his shifting balance theory, which regarded gene flow between partially isolated populations as an important aspect of adaptive evolution. However, recently there has been substantial criticism of the importance of the shifting balance theory. Evolution influences every aspect of the form and behaviour of organisms. Most prominent are the specific behavioural and physical adaptations that are the outcome of natural selection. These adaptations increase fitness by aiding activities such as finding food, avoiding predators or attracting mates. Organisms can also respond to selection by cooperating with each other, usually by aiding their relatives or engaging in mutually beneficial symbiosis. In the longer term, evolution produces new species through splitting ancestral populations of organisms into new groups that cannot or will not interbreed. These outcomes of evolution are distinguished based on time scale as macroevolution versus microevolution. Macroevolution refers to evolution that occurs at or above the level of species, in particular speciation and extinction; whereas microevolution refers to smaller evolutionary changes within a species or population, in particular shifts in allele frequency and adaptation. In general, macroevolution is regarded as the outcome of long periods of microevolution. Thus, the distinction between micro- and macroevolution is not a fundamental one—the difference is simply the time involved. However, in macroevolution, the traits of the entire species may be important. For instance, a large amount of variation among individuals allows a species to rapidly adapt to new habitats, lessening the chance of it going extinct, while a wide geographic range increases the chance of speciation, by making it more likely that part of the population will become isolated. In this sense, microevolution and macroevolution might involve selection at different levels—with microevolution acting on genes and organisms, versus macroevolutionary processes such as species selection acting on entire species and affecting their rates of speciation and extinction. A common misconception is that evolution has goals, long-term plans, or an innate tendency for "progress", as expressed in beliefs such as orthogenesis and evolutionism; realistically however, evolution has no long-term goal and does not necessarily produce greater complexity. Although complex species have evolved, they occur as a side effect of the overall number of organisms increasing and simple forms of life still remain more common in the biosphere. For example, the overwhelming majority of species are microscopic prokaryotes, which form about half the world's biomass despite their small size, and constitute the vast majority of Earth's biodiversity. Simple organisms have therefore been the dominant form of life on Earth throughout its history and continue to be the main form of life up to the present day, with complex life only appearing more diverse because it is more noticeable. Indeed, the evolution of microorganisms is particularly important to modern evolutionary research, since their rapid reproduction allows the study of experimental evolution and the observation of evolution and adaptation in real time. Adaptation is the process that makes organisms better suited to their habitat. Also, the term adaptation may refer to a trait that is important for an organism's survival. For example, the adaptation of horses' teeth to the grinding of grass. By using the term adaptation for the evolutionary process and adaptive trait for the product (the bodily part or function), the two senses of the word may be distinguished. Adaptations are produced by natural selection. The following definitions are due to Theodosius Dobzhansky: - Adaptation is the evolutionary process whereby an organism becomes better able to live in its habitat or habitats. - Adaptedness is the state of being adapted: the degree to which an organism is able to live and reproduce in a given set of habitats. - An adaptive trait is an aspect of the developmental pattern of the organism which enables or enhances the probability of that organism surviving and reproducing. Adaptation may cause either the gain of a new feature, or the loss of an ancestral feature. An example that shows both types of change is bacterial adaptation to antibiotic selection, with genetic changes causing antibiotic resistance by both modifying the target of the drug, or increasing the activity of transporters that pump the drug out of the cell. Other striking examples are the bacteria Escherichia coli evolving the ability to use citric acid as a nutrient in a long-term laboratory experiment, Flavobacterium evolving a novel enzyme that allows these bacteria to grow on the by-products of nylon manufacturing, and the soil bacterium Sphingobium evolving an entirely new metabolic pathway that degrades the synthetic pesticide pentachlorophenol. An interesting but still controversial idea is that some adaptations might increase the ability of organisms to generate genetic diversity and adapt by natural selection (increasing organisms' evolvability). Adaptation occurs through the gradual modification of existing structures. Consequently, structures with similar internal organisation may have different functions in related organisms. This is the result of a single ancestral structure being adapted to function in different ways. The bones within bat wings, for example, are very similar to those in mice feet and primate hands, due to the descent of all these structures from a common mammalian ancestor. However, since all living organisms are related to some extent, even organs that appear to have little or no structural similarity, such as arthropod, squid and vertebrate eyes, or the limbs and wings of arthropods and vertebrates, can depend on a common set of homologous genes that control their assembly and function; this is called deep homology. During evolution, some structures may lose their original function and become vestigial structures. Such structures may have little or no function in a current species, yet have a clear function in ancestral species, or other closely related species. Examples include pseudogenes, the non-functional remains of eyes in blind cave-dwelling fish, wings in flightless birds, the presence of hip bones in whales and snakes, and sexual traits in organisms that reproduce via asexual reproduction. Examples of vestigial structures in humans include wisdom teeth, the coccyx, the vermiform appendix, and other behavioural vestiges such as goose bumps and primitive reflexes. However, many traits that appear to be simple adaptations are in fact exaptations: structures originally adapted for one function, but which coincidentally became somewhat useful for some other function in the process. One example is the African lizard Holaspis guentheri, which developed an extremely flat head for hiding in crevices, as can be seen by looking at its near relatives. However, in this species, the head has become so flattened that it assists in gliding from tree to tree—an exaptation. Within cells, molecular machines such as the bacterial flagella and protein sorting machinery evolved by the recruitment of several pre-existing proteins that previously had different functions. Another example is the recruitment of enzymes from glycolysis and xenobiotic metabolism to serve as structural proteins called crystallins within the lenses of organisms' eyes. An area of current investigation in evolutionary developmental biology is the developmental basis of adaptations and exaptations. This research addresses the origin and evolution of embryonic development and how modifications of development and developmental processes produce novel features. These studies have shown that evolution can alter development to produce new structures, such as embryonic bone structures that develop into the jaw in other animals instead forming part of the middle ear in mammals. It is also possible for structures that have been lost in evolution to reappear due to changes in developmental genes, such as a mutation in chickens causing embryos to grow teeth similar to those of crocodiles. It is now becoming clear that most alterations in the form of organisms are due to changes in a small set of conserved genes. Interactions between organisms can produce both conflict and cooperation. When the interaction is between pairs of species, such as a pathogen and a host, or a predator and its prey, these species can develop matched sets of adaptations. Here, the evolution of one species causes adaptations in a second species. These changes in the second species then, in turn, cause new adaptations in the first species. This cycle of selection and response is called coevolution. An example is the production of tetrodotoxin in the rough-skinned newt and the evolution of tetrodotoxin resistance in its predator, the common garter snake. In this predator-prey pair, an evolutionary arms race has produced high levels of toxin in the newt and correspondingly high levels of toxin resistance in the snake. Not all co-evolved interactions between species involve conflict. Many cases of mutually beneficial interactions have evolved. For instance, an extreme cooperation exists between plants and the mycorrhizal fungi that grow on their roots and aid the plant in absorbing nutrients from the soil. This is a reciprocal relationship as the plants provide the fungi with sugars from photosynthesis. Here, the fungi actually grow inside plant cells, allowing them to exchange nutrients with their hosts, while sending signals that suppress the plant immune system. Coalitions between organisms of the same species have also evolved. An extreme case is the eusociality found in social insects, such as bees, termites and ants, where sterile insects feed and guard the small number of organisms in a colony that are able to reproduce. On an even smaller scale, the somatic cells that make up the body of an animal limit their reproduction so they can maintain a stable organism, which then supports a small number of the animal's germ cells to produce offspring. Here, somatic cells respond to specific signals that instruct them whether to grow, remain as they are, or die. If cells ignore these signals and multiply inappropriately, their uncontrolled growth causes cancer. Such cooperation within species may have evolved through the process of kin selection, which is where one organism acts to help raise a relative's offspring. This activity is selected for because if the helping individual contains alleles which promote the helping activity, it is likely that its kin will also contain these alleles and thus those alleles will be passed on. Other processes that may promote cooperation include group selection, where cooperation provides benefits to a group of organisms. Speciation is the process where a species diverges into two or more descendant species. There are multiple ways to define the concept of "species." The choice of definition is dependent on the particularities of the species concerned. For example, some species concepts apply more readily toward sexually reproducing organisms while others lend themselves better toward asexual organisms. Despite the diversity of various species concepts, these various concepts can be placed into one of three broad philosophical approaches: interbreeding, ecological and phylogenetic. The Biological Species Concept (BSC) is a classic example of the interbreeding approach. Defined by evolutionary biologist Ernst Mayr in 1942, the BSC states that "species are groups of actually or potentially interbreeding natural populations, which are reproductively isolated from other such groups." Despite its wide and long-term use, the BSC like others is not without controversy, for example because these concepts cannot be applied to prokaryotes, and this is called the species problem. Some researchers have attempted a unifying monistic definition of species, while others adopt a pluralistic approach and suggest that there may be different ways to logically interpret the definition of a species. Barriers to reproduction between two diverging sexual populations are required for the populations to become new species. Gene flow may slow this process by spreading the new genetic variants also to the other populations. Depending on how far two species have diverged since their most recent common ancestor, it may still be possible for them to produce offspring, as with horses and donkeys mating to produce mules. Such hybrids are generally infertile. In this case, closely related species may regularly interbreed, but hybrids will be selected against and the species will remain distinct. However, viable hybrids are occasionally formed and these new species can either have properties intermediate between their parent species, or possess a totally new phenotype. The importance of hybridisation in producing new species of animals is unclear, although cases have been seen in many types of animals, with the gray tree frog being a particularly well-studied example. Speciation has been observed multiple times under both controlled laboratory conditions (see laboratory experiments of speciation) and in nature. In sexually reproducing organisms, speciation results from reproductive isolation followed by genealogical divergence. There are four primary geographic modes of speciation. The most common in animals is allopatric speciation, which occurs in populations initially isolated geographically, such as by habitat fragmentation or migration. Selection under these conditions can produce very rapid changes in the appearance and behaviour of organisms. As selection and drift act independently on populations isolated from the rest of their species, separation may eventually produce organisms that cannot interbreed. The second mode of speciation is peripatric speciation, which occurs when small populations of organisms become isolated in a new environment. This differs from allopatric speciation in that the isolated populations are numerically much smaller than the parental population. Here, the founder effect causes rapid speciation after an increase in inbreeding increases selection on homozygotes, leading to rapid genetic change. The third mode is parapatric speciation. This is similar to peripatric speciation in that a small population enters a new habitat, but differs in that there is no physical separation between these two populations. Instead, speciation results from the evolution of mechanisms that reduce gene flow between the two populations. Generally this occurs when there has been a drastic change in the environment within the parental species' habitat. One example is the grass Anthoxanthum odoratum, which can undergo parapatric speciation in response to localised metal pollution from mines. Here, plants evolve that have resistance to high levels of metals in the soil. Selection against interbreeding with the metal-sensitive parental population produced a gradual change in the flowering time of the metal-resistant plants, which eventually produced complete reproductive isolation. Selection against hybrids between the two populations may cause reinforcement, which is the evolution of traits that promote mating within a species, as well as character displacement, which is when two species become more distinct in appearance. Finally, in sympatric speciation species diverge without geographic isolation or changes in habitat. This form is rare since even a small amount of gene flow may remove genetic differences between parts of a population. Generally, sympatric speciation in animals requires the evolution of both genetic differences and nonrandom mating, to allow reproductive isolation to evolve. One type of sympatric speciation involves crossbreeding of two related species to produce a new hybrid species. This is not common in animals as animal hybrids are usually sterile. This is because during meiosis the homologous chromosomes from each parent are from different species and cannot successfully pair. However, it is more common in plants because plants often double their number of chromosomes, to form polyploids. This allows the chromosomes from each parental species to form matching pairs during meiosis, since each parent's chromosomes are represented by a pair already. An example of such a speciation event is when the plant species Arabidopsis thaliana and Arabidopsis arenosa crossbred to give the new species Arabidopsis suecica. This happened about 20,000 years ago, and the speciation process has been repeated in the laboratory, which allows the study of the genetic mechanisms involved in this process. Indeed, chromosome doubling within a species may be a common cause of reproductive isolation, as half the doubled chromosomes will be unmatched when breeding with undoubled organisms. Speciation events are important in the theory of punctuated equilibrium, which accounts for the pattern in the fossil record of short "bursts" of evolution interspersed with relatively long periods of stasis, where species remain relatively unchanged. In this theory, speciation and rapid evolution are linked, with natural selection and genetic drift acting most strongly on organisms undergoing speciation in novel habitats or small populations. As a result, the periods of stasis in the fossil record correspond to the parental population and the organisms undergoing speciation and rapid evolution are found in small populations or geographically restricted habitats and therefore rarely being preserved as fossils. Extinction is the disappearance of an entire species. Extinction is not an unusual event, as species regularly appear through speciation and disappear through extinction. Nearly all animal and plant species that have lived on Earth are now extinct, and extinction appears to be the ultimate fate of all species. These extinctions have happened continuously throughout the history of life, although the rate of extinction spikes in occasional mass extinction events. The Cretaceous–Paleogene extinction event, during which the non-avian dinosaurs became extinct, is the most well-known, but the earlier Permian–Triassic extinction event was even more severe, with approximately 96% of all marine species driven to extinction. The Holocene extinction event is an ongoing mass extinction associated with humanity's expansion across the globe over the past few thousand years. Present-day extinction rates are 100–1000 times greater than the background rate and up to 30% of current species may be extinct by the mid 21st century. Human activities are now the primary cause of the ongoing extinction event; global warming may further accelerate it in the future. Despite the estimated extinction of more than 99 percent of all species that ever lived on Earth, about 1 trillion species are estimated to be on Earth currently with only one-thousandth of one percent described. The role of extinction in evolution is not very well understood and may depend on which type of extinction is considered. The causes of the continuous "low-level" extinction events, which form the majority of extinctions, may be the result of competition between species for limited resources (the competitive exclusion principle). If one species can out-compete another, this could produce species selection, with the fitter species surviving and the other species being driven to extinction. The intermittent mass extinctions are also important, but instead of acting as a selective force, they drastically reduce diversity in a nonspecific manner and promote bursts of rapid evolution and speciation in survivors. Evolutionary history of life Origin of life The Earth is about 4.54 billion years old. The earliest undisputed evidence of life on Earth dates from at least 3.5 billion years ago, during the Eoarchean Era after a geological crust started to solidify following the earlier molten Hadean Eon. Microbial mat fossils have been found in 3.48 billion-year-old sandstone in Western Australia. Other early physical evidence of a biogenic substance is graphite in 3.7 billion-year-old metasedimentary rocks discovered in Western Greenland as well as "remains of biotic life" found in 4.1 billion-year-old rocks in Western Australia. Commenting on the Australian findings, Stephen Blair Hedges wrote, "If life arose relatively quickly on Earth, then it could be common in the universe." In July 2016, scientists reported identifying a set of 355 genes from the last universal common ancestor (LUCA) of all organisms living on Earth. More than 99 percent of all species, amounting to over five billion species, that ever lived on Earth are estimated to be extinct. Estimates on the number of Earth's current species range from 10 million to 14 million, of which about 1.9 million are estimated to have been named and 1.6 million documented in a central database to date, leaving at least 80 percent not yet described. Highly energetic chemistry is thought to have produced a self-replicating molecule around 4 billion years ago, and half a billion years later the last common ancestor of all life existed. The current scientific consensus is that the complex biochemistry that makes up life came from simpler chemical reactions. The beginning of life may have included self-replicating molecules such as RNA and the assembly of simple cells. All organisms on Earth are descended from a common ancestor or ancestral gene pool. Current species are a stage in the process of evolution, with their diversity the product of a long series of speciation and extinction events. The common descent of organisms was first deduced from four simple facts about organisms: First, they have geographic distributions that cannot be explained by local adaptation. Second, the diversity of life is not a set of completely unique organisms, but organisms that share morphological similarities. Third, vestigial traits with no clear purpose resemble functional ancestral traits and finally, that organisms can be classified using these similarities into a hierarchy of nested groups—similar to a family tree. However, modern research has suggested that, due to horizontal gene transfer, this "tree of life" may be more complicated than a simple branching tree since some genes have spread independently between distantly related species. Past species have also left records of their evolutionary history. Fossils, along with the comparative anatomy of present-day organisms, constitute the morphological, or anatomical, record. By comparing the anatomies of both modern and extinct species, paleontologists can infer the lineages of those species. However, this approach is most successful for organisms that had hard body parts, such as shells, bones or teeth. Further, as prokaryotes such as bacteria and archaea share a limited set of common morphologies, their fossils do not provide information on their ancestry. More recently, evidence for common descent has come from the study of biochemical similarities between organisms. For example, all living cells use the same basic set of nucleotides and amino acids. The development of molecular genetics has revealed the record of evolution left in organisms' genomes: dating when species diverged through the molecular clock produced by mutations. For example, these DNA sequence comparisons have revealed that humans and chimpanzees share 98% of their genomes and analysing the few areas where they differ helps shed light on when the common ancestor of these species existed. Evolution of life Prokaryotes inhabited the Earth from approximately 3–4 billion years ago. No obvious changes in morphology or cellular organisation occurred in these organisms over the next few billion years. The eukaryotic cells emerged between 1.6–2.7 billion years ago. The next major change in cell structure came when bacteria were engulfed by eukaryotic cells, in a cooperative association called endosymbiosis. The engulfed bacteria and the host cell then underwent coevolution, with the bacteria evolving into either mitochondria or hydrogenosomes. Another engulfment of cyanobacterial-like organisms led to the formation of chloroplasts in algae and plants. The history of life was that of the unicellular eukaryotes, prokaryotes and archaea until about 610 million years ago when multicellular organisms began to appear in the oceans in the Ediacaran period. The evolution of multicellularity occurred in multiple independent events, in organisms as diverse as sponges, brown algae, cyanobacteria, slime moulds and myxobacteria. In January 2016, scientists reported that, about 800 million years ago, a minor genetic change in a single molecule called GK-PID may have allowed organisms to go from a single cell organism to one of many cells. Soon after the emergence of these first multicellular organisms, a remarkable amount of biological diversity appeared over approximately 10 million years, in an event called the Cambrian explosion. Here, the majority of types of modern animals appeared in the fossil record, as well as unique lineages that subsequently became extinct. Various triggers for the Cambrian explosion have been proposed, including the accumulation of oxygen in the atmosphere from photosynthesis. About 500 million years ago, plants and fungi colonised the land and were soon followed by arthropods and other animals. Insects were particularly successful and even today make up the majority of animal species. Amphibians first appeared around 364 million years ago, followed by early amniotes and birds around 155 million years ago (both from "reptile"-like lineages), mammals around 129 million years ago, homininae around 10 million years ago and modern humans around 250,000 years ago. However, despite the evolution of these large animals, smaller organisms similar to the types that evolved early in this process continue to be highly successful and dominate the Earth, with the majority of both biomass and species being prokaryotes. Concepts and models used in evolutionary biology, such as natural selection, have many applications. Artificial selection is the intentional selection of traits in a population of organisms. This has been used for thousands of years in the domestication of plants and animals. More recently, such selection has become a vital part of genetic engineering, with selectable markers such as antibiotic resistance genes being used to manipulate DNA. Proteins with valuable properties have evolved by repeated rounds of mutation and selection (for example modified enzymes and new antibodies) in a process called directed evolution. Understanding the changes that have occurred during an organism's evolution can reveal the genes needed to construct parts of the body, genes which may be involved in human genetic disorders. For example, the Mexican tetra is an albino cavefish that lost its eyesight during evolution. Breeding together different populations of this blind fish produced some offspring with functional eyes, since different mutations had occurred in the isolated populations that had evolved in different caves. This helped identify genes required for vision and pigmentation. Evolutionary theory has many applications in medicine. Many human diseases are not static phenomena, but capable of evolution. Viruses, bacteria, fungi and cancers evolve to be resistant to host immune defences, as well as pharmaceutical drugs. These same problems occur in agriculture with pesticide and herbicide resistance. It is possible that we are facing the end of the effective life of most of available antibiotics and predicting the evolution and evolvability of our pathogens and devising strategies to slow or circumvent it is requiring deeper knowledge of the complex forces driving evolution at the molecular level. In computer science, simulations of evolution using evolutionary algorithms and artificial life started in the 1960s and were extended with simulation of artificial selection. Artificial evolution became a widely recognised optimisation method as a result of the work of Ingo Rechenberg in the 1960s. He used evolution strategies to solve complex engineering problems. Genetic algorithms in particular became popular through the writing of John Henry Holland. Practical applications also include automatic evolution of computer programmes. Evolutionary algorithms are now used to solve multi-dimensional problems more efficiently than software produced by human designers and also to optimise the design of systems. Social and cultural responses In the 19th century, particularly after the publication of On the Origin of Species in 1859, the idea that life had evolved was an active source of academic debate centred on the philosophical, social and religious implications of evolution. Today, the modern evolutionary synthesis is accepted by a vast majority of scientists. However, evolution remains a contentious concept for some theists. While various religions and denominations have reconciled their beliefs with evolution through concepts such as theistic evolution, there are creationists who believe that evolution is contradicted by the creation myths found in their religions and who raise various objections to evolution. As had been demonstrated by responses to the publication of Vestiges of the Natural History of Creation in 1844, the most controversial aspect of evolutionary biology is the implication of human evolution that humans share common ancestry with apes and that the mental and moral faculties of humanity have the same types of natural causes as other inherited traits in animals. In some countries, notably the United States, these tensions between science and religion have fuelled the current creation–evolution controversy, a religious conflict focusing on politics and public education. While other scientific fields such as cosmology and Earth science also conflict with literal interpretations of many religious texts, evolutionary biology experiences significantly more opposition from religious literalists. The teaching of evolution in American secondary school biology classes was uncommon in most of the first half of the 20th century. The Scopes Trial decision of 1925 caused the subject to become very rare in American secondary biology textbooks for a generation, but it was gradually re-introduced later and became legally protected with the 1968 Epperson v. Arkansas decision. Since then, the competing religious belief of creationism was legally disallowed in secondary school curricula in various decisions in the 1970s and 1980s, but it returned in pseudoscientific form as intelligent design (ID), to be excluded once again in the 2005 Kitzmiller v. Dover Area School District case. - Argument from poor design - Biocultural evolution - Biological classification - Evidence of common descent - Evolutionary anthropology - Evolutionary ecology - Evolutionary epistemology - Evolutionary neuroscience - Evolution of biological complexity - Evolution of plants - Project Steve - Timeline of the evolutionary history of life - Universal Darwinism - Hall & Hallgrímsson 2008, pp. 4–6 - "Evolution Resources". Washington, DC: National Academies of Sciences, Engineering, and Medicine. 2016. Archived from the original on 2016-06-03. - Futuyma, Douglas J.; Kirkpatrick, Mark (2017). "Mutation and variation". Evolution (Fourth ed.). 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OCLC 86090399. - Coyne, Jerry A.; Orr, H. Allen (2004). Speciation. Sunderland, Massachusetts: Sinauer Associates. ISBN 978-0-87893-089-0. LCCN 2004009505. OCLC 55078441. - Bergstrom, Carl T.; Dugatkin, Lee Alan (2012). Evolution (1st ed.). New York: W.W. Norton & Company. ISBN 978-0-393-91341-5. LCCN 2011036572. OCLC 729341924. - Gould, Stephen Jay (2002). The Structure of Evolutionary Theory. Cambridge, Massachusetts: Belknap Press of Harvard University Press. ISBN 978-0-674-00613-3. LCCN 2001043556. OCLC 47869352. - Hall, Brian K.; Olson, Wendy, eds. (2003). Keywords and Concepts in Evolutionary Developmental Biology. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-00904-2. LCCN 2002192201. OCLC 50761342. - Kauffman, Stuart A. (1993). The Origins of Order: Self-organization and Selection in Evolution. New York; Oxford: Oxford University Press. ISBN 978-0-19-507951-7. LCCN 91011148. OCLC 895048122. - Maynard Smith, John; Szathmáry, Eörs (1995). The Major Transitions in Evolution. Oxford; New York: W.H. Freeman Spektrum. ISBN 978-0-7167-4525-9. LCCN 94026965. OCLC 30894392. - Mayr, Ernst (2001). What Evolution Is. New York: Basic Books. ISBN 978-0-465-04426-9. LCCN 2001036562. OCLC 47443814. - Minelli, Alessandro (2009). Forms of Becoming: The Evolutionary Biology of Development. Translation by Mark Epstein. Princeton, New Jersey; Oxford: Princeton University Press. ISBN 978-0-691-13568-7. LCCN 2008028825. OCLC 233030259. - General information - "Evolution" on In Our Time at the BBC - "Evolution". New Scientist. ISSN 0262-4079. Retrieved 2011-05-30. - "Evolution Resources from the National Academies". Washington, DC: National Academy of Sciences. Retrieved 2011-05-30. - "Understanding Evolution: your one-stop resource for information on evolution". Berkeley, California: University of California, Berkeley. Retrieved 2011-05-30. - "Evolution of Evolution – 150 Years of Darwin's 'On the Origin of Species'". Arlington County, Virginia: National Science Foundation. Retrieved 2011-05-30. - "Human Evolution Timeline Interactive". Smithsonian Institution, National Museum of Natural History. 2010-01-28. Retrieved 2018-07-14. Adobe Flash required. - Experiments concerning the process of biological evolution - Lenski, Richard E. "Experimental Evolution". East Lansing, Michigan: Michigan State University. Retrieved 2013-07-31. - Chastain, Erick; Livnat, Adi; Papadimitriou, Christos; Vazirani, Umesh (July 22, 2014). "Algorithms, games, and evolution". Proc. Natl. Acad. Sci. U.S.A. 111 (29): 10620–10623. Bibcode:2014PNAS..11110620C. doi:10.1073/pnas.1406556111. ISSN 0027-8424. PMC 4115542. PMID 24979793. Retrieved 2015-01-03. - Online lectures - "Evolution Matters Lecture Series". Harvard Online Learning Portal. Cambridge, Massachusetts: Harvard University. Archived from the original on 2017-12-18. Retrieved 2018-07-15. - Stearns, Stephen C. "EEB 122: Principles of Evolution, Ecology and Behavior". Open Yale Courses. New Haven, Connecticut: Yale University. Archived from the original on 2017-12-01. Retrieved 2018-07-14.
In mathematics, the spherical coordinate system is a coordinate system for representing geometric figures in three dimensions using three coordinates: the radial distance of a point from a fixed origin, the zenith angle from the positive z-axis to the point, and the azimuth angle from the positive x-axis to the orthogonal projection of the point in the x-y plane. Several different conventions exist for representing the three coordinates. In accordance with the International Organisation for Standardisation (ISO 31-11), in physics they are typically notated as (r, θ, φ) for radial distance, zenith, and azimuth, respectively. In (American) mathematics, the notation for zenith and azimuth are reversed as φ is used to denote the zenith angle and θ is used to denote the azimuthal angle. A further complication is that some mathematics texts list the azimuth before the zenith, but this convention is left-handed and should be avoided. The mathematical convention has the advantage of being most compatible in the meaning of θ with the traditional notation for the two-dimensional polar coordinate system and the three-dimensional cylindrical coordinate system, while the "physics" convention has broader acceptance geographically. Some users of the "physics" convention also use φ for polar coordinates to avoid the first problem (as is the standard ISO for cylindrical coordinates). Other notation uses ρ for radial distance. The notation convention of the author of any work pertaining to spherical coordinates should always be checked before using the formulas and equations of that author. This article uses the standard physics convention. The three coordinates (r, θ, φ) are defined as: - r ≥ 0 is the distance from the origin to a given point P. - 0 ≤ θ ≤ π is the angle between the positive z-axis and the line formed between the origin and P. - 0 ≤ φ < 2π is the angle between the positive x-axis and the line from the origin to the P projected onto the xy-plane. φ is referred to as the azimuth, while θ is referred to as the zenith, colatitude or polar angle. θ and φ lose significance when r = 0 and φ loses significance when sin(θ) = 0 (at θ = 0 and θ = π). To plot a point from its spherical coordinates, go r units from the origin along the positive z-axis, rotate θ about the y-axis in the direction of the positive x-axis and rotate φ about the z-axis in the direction of the positive y-axis. Coordinate system conversions As the spherical coordinate system is only one of many three-dimensional coordinate systems, there exist equations for converting coordinates between the spherical coordinate system and others. Cartesian coordinate system - Further information: Cartesian coordinate system The three spherical coordinates are obtained from Cartesian coordinates by: where atan2(y,x) is a variant of the arctangent function that can return angles outside the range [ − π / 2,π / 2]. Conversely, Cartesian coordinates may be retrieved from spherical coordinates by: Geographic coordinate system - Further information: Geographic coordinate system The geographic coordinate system is an alternate version of the spherical coordinate system, used primarily in geography though also in mathematics and physics applications. In geography, ρ is usually dropped or replaced with a value representing elevation or altitude. Latitude is the complement of the zenith or colatitude, and can be converted by: - , or though latitude is typically represented by θ as well. This represents a zenith angle originating from the xy-plane with a domain -90° ≤ θ ≤ 90°. The longitude is measured in degrees east or west from 0°, so its domain is -180° ≤ φ ≤ 180°. Cylindrical coordinate system - Further information: Cylindrical coordinate system The cylindrical coordinate system is a three-dimensional extrusion of the polar coordinate system, with an z coordinate to describe a point's height above or below the xy-plane. The full coordinate tuple is (ρ, φ, z). Cylindrical coordinates may be converted into spherical coordinates by: Spherical coordinates may be converted into cylindrical coordinates by: The geographic coordinate system applies the two angles of the spherical coordinate system to express locations on Earth, calling them latitude and longitude. Just as the two-dimensional Cartesian coordinate system is useful on the plane, a two-dimensional spherical coordinate system is useful on the surface of a sphere. In this system, the sphere is taken as a unit sphere, so the radius is unity and can generally be ignored. This simplification can also be very useful when dealing with objects such as rotational matrices. Spherical coordinates are useful in analyzing systems that are symmetrical about a point; a sphere that has the Cartesian equation x2 + y2 + z2 = c2 has the very simple equation r = c in spherical coordinates. An example is in solving a triple integral with a sphere as its domain. The surface element for a spherical surface is The volume element is Spherical coordinates are the natural coordinates for describing and analyzing physical situations where there is spherical symmetry, such as the potential energy field surrounding a sphere (or point) with mass or charge. Two important partial differential equations, Laplace's equation and the Helmholtz equation, allow a separation of variables in spherical coordinates. The angular portions of the solutions to such equations take the form of spherical harmonics. Another application is ergonomic design, where r is the arm length of a stationary person and the angles describe the direction of the arm as it reaches out. The concept of spherical coordinates can be extended to higher dimensional spaces and are then referred to as hyperspherical coordinates. The del operator in this system is written as In spherical coordinates the position of a point is written, its velocity is then, and its acceleration is, See also - Vector fields in cylindrical and spherical coordinates - Del in cylindrical and spherical coordinates - List of canonical coordinate transformations - Orthogonal coordinates - Two dimensional orthogonal coordinate systems - Three dimensional orthogonal coordinate systems - Cartesian coordinate system - Cylindrical coordinate system - Spherical coordinate system - Parabolic coordinate system - Parabolic cylindrical coordinates - Paraboloidal coordinates - Oblate spheroidal coordinates - Prolate spheroidal coordinates - Ellipsoidal coordinates - Elliptic cylindrical coordinates - Toroidal coordinates - Bispherical coordinates - Bipolar cylindrical coordinates - Conical coordinates - Flat-ring cyclide coordinates - Flat-disk cyclide coordinates - Bi-cyclide coordinates - Cap-cyclide coordinates - Morse PM, Feshbach H (1953). Methods of Theoretical Physics, Part I. New York: McGraw-Hill. pp. 658. ISBN 0-07-043316-X, LCCN 52-11515. - Margenau H, Murphy GM (1956). The Mathematics of Physics and Chemistry. New York: D. van Nostrand. pp. 177–178. LCCN 55-10911. - Korn GA, Korn TM (1961). Mathematical Handbook for Scientists and Engineers. New York: McGraw-Hill. pp. 174–175. LCCN 59-14456, ASIN B0000CKZX7. - Sauer R, Szabó I (1967). Mathematische Hilfsmittel des Ingenieurs. New York: Springer Verlag. pp. 95–96. LCCN 67-25285. - Moon P, Spencer DE (1988). "Spherical Coordinates (r, θ, ψ)". Field Theory Handbook, Including Coordinate Systems, Differential Equations, and Their Solutions (corrected 2nd ed., 3rd print ed. ed.). New York: Springer-Verlag. pp. 24–27 (Table 1.05). ISBN 978-0387184302. External links - MathWorld description of spherical coordinates - Coordinate Converter - converts between polar, Cartisian and spherical coordinates
This Understanding Subtraction worksheet also includes: - Answer Key - Join to access all included materials In this subtraction worksheet, students examine 4 pictures which show subtraction involving numbers less than 5, then write a subtraction equation for each picture. 3 Views 8 Downloads - Activities & Projects - Graphics & Images - Lab Resources - Learning Games - Lesson Plans - Primary Sources - Printables & Templates - Professional Documents - Study Guides - Writing Prompts - AP Test Preps - Lesson Planet Articles - Interactive Whiteboards - All Resource Types - Show All See similar resources: Subtraction with 3-Digits Numbers #1 Looking for a simple way to practice 3-digit subtraction? Use this review page to reinforce your second and third graders' subtraction skills. It includes twenty problems for them to solve, as well as five problems using money. Useful as... 2nd - 3rd Math CCSS: Designed Study Jams! Relate Addition & Subtraction Understanding the inverse relationship between addition and subtraction is essential for developing fluency in young mathematicians. Zoe and RJ explain how three numbers can form fact families that make two addition and two subtraction... 1st - 4th Math CCSS: Adaptable Solve Subtraction Problems: Using Key Vocabulary The first step to solving any word problem is understanding what the question is asking. The fourth video in this series discusses key terms associated with subtraction, modeling how to identify these phrases with multiple examples.... 5 mins 2nd - 4th Math CCSS: Designed Study Jams! Subtraction with Regrouping Learning how to regroup when subtracting numbers can be challenging and requires a solid understanding of place value. Walk your class through the steps with a clear and explicit presentation that addresses standard regrouping and... 2nd - 4th Math CCSS: Adaptable
Newton’s Laws and two body problems • Our problems so far has been restricted to one objects moving by a force. But what happens if there are two objects connected together in one way or another? • We will find that the problem is solved in the same general manner as when there is one object - through the use of free-body diagrams and Newton's laws. Example problem 1: • A 5.0-kg and a 10.0-kg box are touching each other. A 45.0-N horizontal force is applied to the 5.0-kg box in order to accelerate both boxes across the floor. Ignore friction and determine the acceleration of the boxes and the force acting between the boxes. (Contact Force) Note that there are four forces on the 5.0-kg object at the rear. • Using Fnet = m•a with the free-body diagram for the 5.0-kg object will yield the Equation below: • 45.0 - Fcontact = 5.0•a • Using Fnet = m•a with the free-body diagram for the 10.0-kg object will yield the Equation below: • Fcontact = 10.0•a If the expression 10.0•a is substituted into Equation 1 for Fcontact, then Equation 1 becomes reduced to a single equation with a single unknown. The equation becomes • 45.0 - 10.0•a = 5.0•a • A couple of steps of algebra lead to an acceleration value of 3.0 m/s2 This value of a can be substituted back into Equation 2 in order to determine the contact force: • Fcontact = 10.0•a = 10.0 •3.0Fcontact = 30.0 N Example Problem 2: • A man enters an elevator holding two boxes - one on top of the other. The top box has a mass of 6.0 kg and the bottom box has a mass of 8.0 kg. The man sets the two boxes on a metric scale sitting on the floor. When accelerating upward from rest, the man observes that the scale reads a value of 166 N; this is the upward force upon the bottom box. Determine the acceleration of the elevator (and boxes) and determine the forces acting between the boxes. The force of gravity is calculated in the usual manner using 14.0 kg as the mass. • Fgrav = m•g = 14.0 kg • 9.8 N/kg = 137.2 N • Since there is a vertical acceleration, the vertical forces will not be balanced; the Fgrav is not equal to the Fnorm value. • The net force is the vector sum of these two forces. So • Fnet = 166 N, up + 137.2 N, down = 28.8 N, up The acceleration can be calculated using Newton's second law: • a = Fnet /m = 28.8 N/14.0 kg = 2.0571 m/s2 • Now that acceleration has been determined, using an individual object, either box, we can determine the force acting between them. • Fcontact - 58.8 N = (6.0 kg)•(2.0571 m/s2) Pulley Problems (omg) • 1. Consider the two-body situation below. A 100.0-gram hanging mass (m2) is attached to a 325.0-gram mass (m1) at rest on the table. The coefficient of friction between the 325.0-gram mass and the table is 0.215. Determine the acceleration of the system and the tension in the string. a = 0.695 m/s2 and Ftens = 0.911 N • The solution here will use the approach of a free-body diagram and Newton's second law analysis of each individual mass. For mass m1:Fgrav = m1•g = (0.3250 kg)•(9.8 N/kg) = 3.185 NFnorm = Fgrav = 3.185 NFfrict = µ•Fnorm = (.215)•(3.185 N) = 0.68478 N • Applying Newton's second law to m1:Ftens - 0.68478 = 0.3250•a • For mass m2:Fgrav = m2•g = (0.1000 kg)•(9.8 N/kg) = 0.9800 N • Applying Newton's second law to m2:0.9800 - Ftens = 0.1000•a Combining the two equations leads to the answers:a = 0.69464 m/s2 = ~0.695 m/s2Ftens = 0.91054 N = ~0.911 N Example 2 Pulley • Consider the two-body situation at the right. A 3.50x103-kg crate (m1) rests on an inclined plane and is connected by a cable to a 1.00x103-kg mass (m2). This second mass (m2) is suspended over a pulley. The incline angle is 30.0° and the surface has a coefficient of friction of 0.210. Determine the acceleration of the system and the tension in the cable. Because the parallel component of gravity on m1 exceeds the sum of the force of gravity on m2 and the force of friction, the mass on the inclined plane (m1) will accelerate down it and the hanging mass (m2) will accelerate upward. • For mass m1:Fgrav = m1•g = (3500 kg)•(9.8 N/kg) = 34300 NFparallel = m1•g•sine(θ) = 34300 N • sine(30°) = 17150 NFperpendicular = m1•g•cosine(θ) = 34300 N • cosine(30°) = 29704.67 NFnorm = Fperpendicular = 29704.67 NFfrict = µ•Fnorm = (.210)•(29704.67 N) = 6237.98 N Applying Newton's second law to m1:17150 N - 6237.98 N - Ftens = (3500 kg)•a • For mass m2:Fgrav = m2•g = (1000 kg)•(9.8 N/kg) = 9800 N • Applying Newton's second law to m2:Ftens - 9800 N - = (1000 kg)•a • Combining the two equations leads to the answers:a = 0.24712 m/s2 = ~0.247 m/s2Ftens = 10047 N = ~1.00x104 N
Fast radio bursts (FRBs), the enigmatic astronomical phenomena, have generated unparalleled excitement in recent years. These fleeting and intense flashes of light, observed in the radio spectrum, manifest spontaneously and unpredictably in space. Speculated to emanate from sources such as black holes, neutron stars, or even extraterrestrial civilizations, FRBs typically last from a fraction of a millisecond to a few seconds before disappearing without a trace. Scientists have recently reported the detection of five fresh FRBs utilizing the upgraded Westerbork Synthesis Radio Telescope in the Netherlands. Remarkably, three of these FRBs penetrated our neighboring Triangulum Galaxy, a spiral galaxy situated approximately 2.73 million light years away, as they traveled through space to reach Earth. Although the new FRBs were initially detected in 2019, it is only now that they have been described in a recent paper authored by an international team led by Joeri van Leeuwen from the University of Amsterdam. The team’s paper states, ‘Fast radio bursts (FRBs) must be powered by uniquely energetic emission mechanisms.’ The researchers have uncovered five new FRBs, a noteworthy addition to the approximately 100 previously published at that time. Although FRBs are not visible to the human eye as they are radio waves, they are not rare. These mysterious bursts originate from various directions in the sky, leaving scientists puzzled about their origin. One leading hypothesis is that FRBs could be emitted by neutron stars, which are the incredibly dense remnants of massive stars that pack the mass of our sun into a small city-sized region. However, some scientists have also proposed the intriguing possibility that FRBs could be artificially created by intelligent beings. In 2017, researchers at the Harvard-Smithsonian Center for Astrophysics suggested that FRBs could be signals from distant alien transmitters powering interstellar probes, an idea supported by Professor Avi Loeb at the time. The energy emitted by a single FRB is estimated to be 10 trillion times the annual energy consumption of the entire human population. These bursts are so powerful that radio telescopes can detect them from over four billion light-years away. However, studying FRBs is challenging due to their unpredictable nature, as their occurrence in the sky is unknown in advance. Furthermore, each FRB typically lasts only a millisecond, although a longer-lasting FRB lasting three seconds was discovered last year, which was 1,000 times longer than the average duration. To detect these fleeting radio pulses, researchers depend on ground-based telescopes strategically positioned across the globe, ready to capture the elusive nature of FRBs whenever they occur. A team of astronomers has successfully upgraded the radio telescope array at Westerbork with a cutting-edge supercomputer called the Apertif Radio Transient System (ARTS). Located on the site of a former World War II Nazi detention camp, Westerbork features 14 dishes, each measuring 82 feet (25 meters) in diameter. The upgrade has dramatically improved the array’s vision, likened to a transformation from that of a fly to an eagle, as stated by the team. Study author Eric Kooistra from the Netherlands Institute for Radio Astronomy explained that the complex electronics required for this upgrade were not readily available for purchase, and the system was mostly designed in-house by a large team of researchers, resulting in a state-of-the-art machine that is now one of the most powerful in the world. With the integration of the ARTS supercomputer, the radio telescope array at Westerbork can now continuously combine the images from 12 dishes to create high-resolution images over a vast field of view. Unlike before, when radio telescopes could only provide rough estimates of the location of Fast Radio Bursts (FRBs), ARTS enables experts to accurately pinpoint the exact location of FRBs, marking a significant advancement in our ability to study these mysterious cosmic phenomena. As Fast Radio Bursts (FRBs) travel through space and pierce other galaxies before reaching Earth, the electrons in those galaxies, which are typically invisible, can distort the FRB signals. The ability to track these elusive electrons, along with their associated atoms, is crucial as the majority of matter in the universe is dark and our understanding of it remains limited.
You are searching about Common Core Math Addition And Subtraction, today we will share with you article about Common Core Math Addition And Subtraction was compiled and edited by our team from many sources on the internet. Hope this article on the topic Common Core Math Addition And Subtraction is useful to you. ZeroSum Ruler: Finding Success With Negative Numbers As an algebra teacher, I assumed my students had already mastered certain things: fractions, multiplication, addition and subtraction, solving simple equations. As I learned, reality barely follows theory! My ninth graders struggled to solve equations. At first I thought it was because the equations were relatively new, but looking at their work more closely it wasn’t the equations that they had trouble with, it was the addition and subtraction. How is it possible ? After about a year of telling myself that it just couldn’t be, I gave in to the fact that my students were really struggling. They told me that “-22 + 5 = -27” and “8 – 12 = 4”. These errors appeared in the equations we were making where terms had to be added or subtracted from either side, and my students made all sorts of simple mistakes. In the summer of 2007, the first prototype of the ZeroSum rule was created. It was rough – two paper number lines hinged to zero with an earring – and by no means was classroom-ready yet. Over the years, the manipulator went through many incarnations until his final form was achieved and tested in the classroom with excellent results. A few years later, I had to teach advanced algebra to 11th graders, who were making the same mistakes! My students could solve complex logarithms but would make mistakes on the latter parts of the problems – the parts involving, you guessed it, the addition and subtraction of whole numbers! At that time, the ZeroSum rule was in its final form and ready for use in the classroom. I gave my eleventh graders a pre-test of eight simple addition and subtraction problems. Over the next few weeks, I gave each student a ZeroSum Ruler to use when solving each of three sets of nine simple equations. Immediately after the last set I did a post-test, and a month later I gave my students their delayed retention test. The posttest and delayed retention tests were set up exactly like the pretest, but with different simple integer problems. To my surprise, there was not much difference in scores between the post-test and the delayed retention test. However, there was a huge difference in score between these two tests and the pre-test. 62%! My students had made 62% fewer errors. As part of my research, I looked at the curriculum my students had in elementary and middle school. It seemed like they only ever had 16 days to learn integer addition and subtraction. No wonder they needed help! The ZeroSum Rule has helped my students. I hope to bring this manipulation to more students so they don’t struggle like my students did. There’s nothing like making a simple mistake to shake a child’s math confidence. It is my goal to prevent this from happening. Video about Common Core Math Addition And Subtraction You can see more content about Common Core Math Addition And Subtraction on our youtube channel: Click Here Question about Common Core Math Addition And Subtraction If you have any questions about Common Core Math Addition And Subtraction, please let us know, all your questions or suggestions will help us improve in the following articles! The article Common Core Math Addition And Subtraction was compiled by me and my team from many sources. If you find the article Common Core Math Addition And Subtraction helpful to you, please support the team Like or Share! Rate Articles Common Core Math Addition And Subtraction Rate: 4-5 stars Search keywords Common Core Math Addition And Subtraction Common Core Math Addition And Subtraction way Common Core Math Addition And Subtraction tutorial Common Core Math Addition And Subtraction Common Core Math Addition And Subtraction free #ZeroSum #Ruler #Finding #Success #Negative #Numbers
Nearpod version available Students will be able to: - Create a graph representing a budget line and calculate the trade-offs of moving along the line. - Represent a budget line using an equation in two variables. - Predict transformations of the budget line given changes in income, changes in price of a good, or both. - Calculate an equation for a budget line. - Explain the meaning of the budget line in terms of personal finance. In this personal finance lesson, students explore budget constraints by solving a contextual problem. - Graphing & Interpreting Linear Relationships in the Context of Budgeting Presentation ppt File \| pdf File - Activity 1, Pat and Sam Hangout, one copy per student - Activity 2, Trade-offs and Budget Constraints, one copy per pair of students - Activity 1 Key and Activity 2 Key, one copy for the teacher - Visual 1 Budgets are an important part of personal finance and meeting financial goals. While a budget is a spending and saving plan, based on estimated income and expenses for an individual or an organization over a specific time period, budget constraints are limits. Goods are tangible objects and services are activities that people perform for us. Both satisfy economic wants. The prices of goods and services and the amount of personal income-(i.e., payments earned by households for selling or renting their productive resources which may include salaries, wages, interest and dividends)-limit spending and serve as constraints to budgets. This lesson considers a problem situation in which only two goods can be purchased with a given income. This simplified approach should enable students to extend the decision-making process to more complex (e.g., real-world) challenges virtually everyone faces. The budget line is represented using tables, graphs, and linear functions. Equations use constants and variables to represent relationships between quantities. Variables are symbols used to represent numbers. The impact of shifts in income and prices of goods can be analyzed by exploring transformations of the budget line that represent relationships between these quantities. - Show Slide 1 and tell students they are going to explore the expenses involved in hanging out with friends. - Show Slide 2 and ask: - How much money might students your age have to spend? [Answers will vary.] - How might students earn the money they have to spend? [Answers will vary, but may include allowance or money received from jobs.] - What are some things students your age buy regularly with the money you have earned? [Answers will vary, but may include transportation, food, games, and other entertainment.] - Tell the students that they will investigate the expenses involved with “hanging out” in a problem situation designed to model the relationship between income and prices of goods. - Show Slide 3. Write the following terms on the board: income, budget, budget constraint, and trade-off. Ask the students to share words that could be used to define each term. List the words the students use on the board. - Write the definitions below on the board (or use Slide 4) and circle any of the words used by the students in the definitions. For example, if the students used the term “salaries,” circle the word in the definition of income. - Income: Payments earned by households for selling or renting their productive resources. May include salaries, wages, interest, and dividends. - Budget: A spending-and-saving plan, based on estimated income and expenses for an individual or an organization, over a specific time period. - Budget constraint: All the combinations of goods and services that a consumer may purchase, given current prices, and still be within his or her given income. - Tradeoff: Giving up some of one thing to gain some of something else. - Distribute a copy of Activity 1 to each student. Show Slide 5 and ask volunteers to read the slide. Ask students if they ever hang out with someone. [Answers will vary.] - Show Slide 6. Tell students that Pat rides the bus using the stops in green. Ask students to complete number 1 on Activity 1. - Explain that Pat must use a token to ride to Sam’s bus stop, then get off the bus and go to Sam’s house. Next, Pat and Sam return to the bus stop. They then each use a token to ride together to Freddy’s to have fries. Pat and Sam then must each use a token to ride to Sam’s bus stop. Pat walks with Sam to Sam’s house and returns to the nearest bus stop and rides the bus back home. Ask a student to come up to the slide and trace the route Pat rides to pick up Sam and go to Freddy’s. Note that some students may not know what a token is. Explain that a bus token is a prepaid coin similar to a prepaid bus pass. Ask students if they have suggestions for how Pat might ride the bus using fewer bus tokens. [Students will offer suggestions about how to ride the bus and use fewer bus tokens. Some students may say that Pat does not need to get off the bus, but that the two people can meet at Sam’s bus stop and Pat can just get on the bus. Explain that while they are first hanging out, the two want to ride together for the maximum amount of time.] - Ask students to complete number 2 on Activity 1. - Show Slide 7. Ask students what else they would need to know to find out how much Pat needs to spend in order to hang out with Sam? [Answers will vary. Students will likely say they need to know the price of a bus token and the price of the fries.] - Ask students to complete number 3 on Activity 1. - Show Slide 8. Ask students, “Now that you have more information, what will Pat spend on the bus for both Pat and Sam? What will Pat spend on fries if each gets an order of fries?” [Pat will spend 12 dollars on bus tokens and two dollars on fries.] - Ask the students to share how they found their answers. [If six tokens are needed to hang out and each token is two dollars then you multiply six and two to get 12 dollars (i.e., Pat uses four tokens and Sam uses two). If an order of fries is one dollar and you want to buy two of them, you multiply two and one to get two dollars.] - Show Slide 9. Tell students that the values at the bottom of the table represent the quantities of fries that Pat can buy for a hang out. The values on the left side of the table represent the quantities of bus tokens that Pat can buy for a hang out. Ask students how they can find the total amount that Pat needs for a particular combination. Select a combination such as four fries and 12 tokens and ask what calculation they can do. [One dollar times four plus two dollars times 12 for a total of 28.] - Ask students where the total expense of 28 should go in the table. [Answers will vary. Go to the number 4 along the bottom row and identify the column associated with the expense for 4 fries. Identify the row with 12 bus tokens and see where the row intersects the column. This is the cell that represents the combination of 4 fries and 12 tokens.] - Instruct students to complete the table in number 4 on Activity 1. (Note: this is a good place to split this lesson if you want to do it in two days. You can assign the table completion for homework.) - Show Slide 10. Ask students what patterns they notice and what they noticed that helped them fill in the table quickly. [Answers will vary. Students may notice constant differences in rows (2) or columns (4). They may also notice diagonal differences are constant (6).] Point out that this table represents the amount Pat would spend on different combinations of fries and tokens. - Ask students to answer number 5 a-c on Activity 1. Review answers using the Activity 1 Answer Key. - Refer to Slide 10. Discuss: - Which cells in the table show the number of fries and tokens you can buy for 32 dollars? Tell students to circle them. [Student answers will vary, but they will identify all the cells in the table with 32 in the cell.] - Each of these cells shows us one combination of fries and tokens on which Pat could spend 32 dollars. How many different combinations are there? [Eight] - How can you be sure there will not be other combinations as the number of fries and tokens increases? [Answers will vary. Students may share that since both quantities are increasing, the total amount spent must also increase.] - Show Slide 11 to verify student answers. Tell students that now they will find an equation for all of the possible combinations. - Show Slide 12. Put students into pairs. Give each pair a copy of Activity 2. Ask students to work with their partner and fill in the table in problem number 1 on Activity 2. - Display Visual 1. When students complete this task, ask for volunteers to share their answers but be sure to write answers on Visual 1 in order so that patterns can be identified easily. Otherwise, show Slide 13 and ask what equation they could write if x is the number of fries Pat buys and y is the number of tokens and the total must be 32 dollars. [$1x+$2y=$32] - Tell students they have now represented all of the possible combinations of fries and tokens Pat can buy with 32 dollars. Tell students this is an example of a budget constraint or all the combinations of goods and services that a consumer may purchase, given current prices, within his or her given income. - Tell students they will now investigate how a graph can show all the possibilities if Pat wants to buy only bus tokens and fries with the 32 dollars. Point out to students that with an income of $32, Pat cannot buy all the fries and all the tokens that Pat may want. Pat must make a choice and when Pat determines how many fries and tokens to buy with 32 dollars, Pat makes a trade-off. Tell students that a trade-off is giving up some of one thing to gain some of something else. Ask students what trade-offs are made for the different combinations. For example, to go from 16 to 20 fries, Pat gains four fries, but what does Pat have to give up? [Two tokens] To gain six tokens, how many fries does Pat have to give up? [12.] - Show Slide 14. Tell students to work with their partner to complete numbers 2-4 and the table in number 5 on Activity 2. Give the students 10 minutes to finish this task. Review answers using the Activity 2 Answer Key. - Tell students they are going to represent Pat’s budget and constraints on that budget with a graph. Ask for volunteers to suggest points you need to plot on the graph. Ask students to plot the points on the graph in number 5 on Activity 2. - Tell students they can represent the limit of Pat’s budget with a line. Points below the line represent quantities of fries and tokens Pat can buy. Ask students to draw the budget line in number 6 on Activity 2. - Display slide 15 and ask students to check their graph for accuracy. - Ask students to complete numbers 7-12 on Activity 2. Give students 10 minutes to complete this work. - As the students are completing the activity, circulate and ask them to share their ideas about the addends in the equation and the meaning of points above, on, and below the budget constraint line. [Answers will vary, but students are expected to say that points above the line represent combinations that Pat’s budget will not allow and combinations below the line represent combinations Pat can afford. Addends (i.e., numbers added together) represent the total cost of fries and the total cost of bus tokens. Those points on the line represent combinations Pat can afford, but that will require Pat to spend all of the income.] - Show Slide 16. Discuss: - What is the equation of the line? [Answers will vary, but students should be able to see that the equation of the line is the same as the equation from the table they created namely 1x+2y=32.] Note that the goal is to build a link between the computations and the graph as a representation of Pat’s budget and its constraints for hang outs. - What does 1x represent in the equation? [Money spent on fries is represented by 1x.] - What does 2y represent in the equation? [Money spent on bus tokens is represented by 2y.] - What does the point (6, 10) on your graph represent? [The point represents six fries and 10 bus tokens for a total cost of 26 dollars.] - Can Pat purchase 10 fries and 10 bus tokens? How do you know? [Yes, since the point (10, 10) is below the budget constraint line.] - Can Pat purchase 10 fries and 20 bus tokens? How do you know? [No, since the point (10, 20) is above the budget constraint line.] - What do the points above the line represent? [Answers will vary. They represent combinations that Pat cannot purchase with his income.] - Call the students back together and tell them that Pat just got some news. Show Slide 17. Ask students how this news will impact the budget constraint graph. Ask students to work with their partner to complete number 13 on Activity 2 and to create a new graph to represent the effect of the news. Give the students five minutes for this task. - Call the students back together and ask what they found. [Answers will vary. They may say the line decreases at a faster rate than the original budget constraint line.] - Show Slide 18 and ask students to explain the difference between the original line and the new line in terms of fries and bus tokens. [Answers will vary, but students should say that the new price of fries means that fewer bus tokens can be purchased for a given quantity of fries, so all the y values for the points will be lower than they were before the increase in the price of fries.] - Ask students to complete number 14 on Activity 2. - Show Slide 19 and ask the students how many times each month Pat can hang out with Sam if fries are two dollars and bus tokens are two dollars. [Answers will vary, but students should find a maximum number of two times. Each bus round trip for both costs $12. Thus, with an income of $32, only two round trips can be purchased.] Review the key points of the lesson using the following questions: - What is a budget? [A spending and saving plan based on estimated income and expenses for an individual or an organization, over a specific time period.] - What is income? [Payments earned by households for selling or renting their productive resources. This may include salaries, wages, interest, and dividends.] - When have you earned income? [Answers will vary but students should recognize that they have earned income when they have been paid for work that they have done.] - What is a budget constraint? [All the combinations of goods and services that a consumer may purchase, given current prices, within his or her given income.] - What is a trade-off? [Giving up some of one thing to get some of something else.] - Given the budget constraint line has the equation 32 = 1x + 2y, x is the number of fries Pat can buy, and y is the number of tokens, what is the meaning of 32 in the equation? [32 is Pat’s total income.] - Given the budget constraint line has the equation 32 = 1x + 2y, x is the number of fries Pat can buy, and y is the number of tokens, what is the meaning of 2 in the equation? [$2 is the price of a token.] - Given the budget constraint line has the equation 32 = 1x + 2y, x is the number of fries Pat can buy, and y is the number of tokens, what is the meaning of 1x in the equation? [$ 1 is the price of an order of fries and x is the number of order of fries. So 1x is the total amount Pat can spend on fries.] - Explain how to find the equation for a budget constraint line if you know that your total income is $20 and you can purchase soda and hotdogs. The price of each soda is $2.00 and the price of each hotdog is $4.00. [First decide whether the number of sodas or hotdogs will be x. Second write your equation using the following approach: if the number of sodas is represented by x, then the number of hotdogs will be represented by y. The price of soda is $2 and 2x represents the amount spent on sodas. The price of a hotdog is $4 and 4y is the amount spent on hotdogs. So the total amount spent on hotdogs and soda is 2x + 4y = 20.] - Explain how to create the graph for the budget constraint line if you know that the total income is $20, the price of each soda is $2.00 and the price of each hotdog is $4.00. [First find the number of sodas you could purchase if you bought no hotdogs. Second, find the number of hotdogs you could purchase if you bought no sodas. Third, putting the number of sodas on the x axis, plot the point (10, 0) representing 10 sodas and 0 hotdogs. All your money is spent on soda. Fourth, putting the number of hotdogs on the y-axis, plot the point (0, 5), representing zero sodas and five hotdogs. All your money is spent on hotdogs. Now draw the segment between the two points. This is the budget line that represents the limit for your income. ] - How can we represent the relationship between income and prices of goods? [This relationship can be represented by a line called the budget constraint line.] - Bill has $10 dollars to spend on chips and soda. If the price of chips is $1 and the price of a soda is $2, which equation represents the relationship between Bill’s income and the quantity of chips (x) and soda (y) he can purchase with his money? - 10 = 2x + 1y - [10 = 1x + 2y] - 10 = x + y - 10 = ½ x + y - Bill has $10 dollars to spend on chips and soda. If the price of chips is $1 and the price of a soda is $2, which graph represents the relationship between Bill’s income and the quantity of chips (x) and soda (y) he can purchase with his money? - Create a graph of the budget constraint line if Pat’s income is 12 dollars, bus tokens are four dollars, and fries are two dollars. Grades 6-8, 9-12
Listen to part of a lecture in a botany class. OK, last time we talked about photosynthesis, the process by which plants use light to convert carbon dioxide and water into food. Today, I want to talk about another way light affects plants. I'm sure you all know from physics class about how light moves in microscopic waves, and that we can only see light when the wavelength of that light is in a specific range; plus, depending on the wavelength, we see different colors. Well, plants are also capable of distinguishing between different wavelengths of light. Now I don't want to confuse you-it's not like plants have eyes-plants don't see in the sense that humans or animals do-but they do have photoreceptors. Photoreceptors are cells that respond to light by sending out a chemical signal. And the organism- the plant- reacts to this signal; in fact, the signals that plants get from their photoreceptors sometimes cause significant reactions. And many plants are seasonal, and one way they know when winter is ending and spring is beginning is by sensing the change in light. The time when an adult plant flowers is based on the amount of light the plant senses. Certain plant species won't flower if they sense too much light, and some plants will only flower if they sense a specific amount of light. Of course, these aren't conscious reactions-these plants just automatically respond to light in certain ways. Plants are also able to distinguish between specific wavelengths of light that the human eye cannot even see. Specifically, there's a wavelength called far-red. [realizing that the name is actually inappropriate] Although why they call it "far-red"... I mean, it's not really red at all. It lies in the infrared range of the spectrum. We can't see it, but plants can sense it as a different wavelength. OK, now I need to mention another thing about photosynthesis. I didn't explain how different wavelengths of light affect photosynthesis. When a plant absorbs light for performing photosynthesis, it only absorbs some wavelengths of light and reflects others. Plants absorb most of the red light that hits them. But plants only absorb some of the far-red light that hits them-they reflect the rest. Remember this, because it's going to be relevant in an experiment I want to discuss. This fascinating experiment showed that plants not only detect and react to specific wavelengths of light-plants can also detect and react to changes in the ratio of one wavelength to another. This experiment was called the Pampas experiment. The idea behind the Pampas experiment had to do with the response of plants to changes in the ratio of red light to far-red light that the plants sensed with their photoreceptors. Some biologists hypothesized that a plant will stop growing if it's in the shade of another plant-a reaction that's triggered when it senses an unusual ratio of red light to far-red light. OK, imagine there are two plants, one below the other. The plant on top would absorb most of the red light for photosynthesis but reflect most of the far-red light. That would lead to the plant in its shade sensing an unusual ratio-there would be less red light and more far-red light than normal. What that ratio signifies is important-a ratio of less red light to more far-red light would cause a reaction from the plant: it would stop growing taller-because that plant could sense it wasn't going to get enough sunlight to provide the energy to grow large. To test their hypothesis, researchers took some electrical lights-um, actually they were light-emitting diodes, or LEDs. These light-emitting diodes could simulate red light. So they put these LEDs around some plants that were in the shade. The LEDs produced light that the plants sensed as red-but, unlike sunlight, the light from these LEDs did not support photosynthesis. So the plants sensed a proper ratio of red light to far-red light and reacted by continuing to grow taller, while in reality, these plants were not getting enough energy from photosynthesis to support all of that growth. And because they weren't getting enough energy to support their growth, most of the shaded plants died after a short time.
The cosmic microwave background (CMB, CMBR) is electromagnetic radiation as a remnant from an early stage of the universe in Big Bangcosmology. In older literature, the CMB is also variously known as cosmic microwave background radiation (CMBR) or “relic radiation”. The CMB is a faint cosmic background radiation filling all space that is an important source of data on the early universe because it is the oldest electromagnetic radiation in the universe, dating to the epoch of recombination. With a traditional optical telescope, the space between stars and galaxies (the background) is completely dark. However, a sufficiently sensitive radio telescope shows a faint background noise, or glow, almost isotropic, that is not associated with any star, galaxy, or other object. This glow is strongest in the microwave region of the radio spectrum. The accidental discovery of the CMB in 1964 by American radio astronomers Arno Penzias and Robert Wilson was the culmination of work initiated in the 1940s, and earned the discoverers the 1978 Nobel Prize in Physics. The discovery of CMB is landmark evidence of the Big Bang origin of the universe. When the universe was young, before the formation of stars and planets, it was denser, much hotter, and filled with a uniform glow from a white-hot fog of hydrogen plasma. As the universe expanded, both the plasma and the radiation filling it grew cooler. When the universe cooled enough, protons and electrons combined to form neutral hydrogen atoms. Unlike the uncombined protons and electrons, these newly conceived atoms could not absorb the thermal radiation, and so the universe became transparent instead of being an opaque fog. Cosmologists refer to the time period when neutral atoms first formed as the recombination epoch, and the event shortly afterwards when photons started to travel freely through space rather than constantly being scattered by electrons and protons in plasma is referred to as photon decoupling. The photons that existed at the time of photon decoupling have been propagating ever since, though growing fainter and less energetic, since the expansion of space causes their wavelength to increase over time (and wavelength is inversely proportional to energy according to Planck’s relation). This is the source of the alternative term relic radiation. The surface of last scattering refers to the set of points in space at the right distance from us so that we are now receiving photons originally emitted from those points at the time of photon decoupling. Precise measurements of the CMB are critical to cosmology, since any proposed model of the universe must explain this radiation. The CMB has a thermal black body spectrum at a temperature of 2.72548±0.00057 K. The spectral radiance dEν/dν peaks at 160.23 GHz, in the microwave range of frequencies, corresponding to a photon energy of about 6.626 × 10−4 eV. Alternatively, if spectral radiance is defined as dEλ/dλ, then the peak wavelength is 1.063 mm (282 GHz, 1.168 x 10−3 eV photons). The glow is very nearly uniform in all directions, but the tiny residual variations show a very specific pattern, the same as that expected of a fairly uniformly distributed hot gas that has expanded to the current size of the universe. In particular, the spectral radiance at different angles of observation in the sky contains small anisotropies, or irregularities, which vary with the size of the region examined. They have been measured in detail, and match what would be expected if small thermal variations, generated by quantum fluctuations of matter in a very tiny space, had expanded to the size of the observable universe we see today. This is a very active field of study, with scientists seeking both better data (for example, the Planck spacecraft) and better interpretations of the initial conditions of expansion. Although many different processes might produce the general form of a black body spectrum, no model other than the Big Bang has yet explained the fluctuations. As a result, most cosmologists consider the Big Bang model of the universe to be the best explanation for the CMB. The high degree of uniformity throughout the observable universe and its faint but measured anisotropy lend strong support for the Big Bang model in general and the ΛCDM (“Lambda Cold Dark Matter”) model in particular. Moreover, the fluctuations are coherent on angular scales that are larger than the apparent cosmological horizon at recombination. Either such coherence is acausally fine-tuned, or cosmic inflation occurred. - 3Relationship to the Big Bang - 5Microwave background observations - 6Data reduction and analysis - 7Future evolution - 8Timeline of prediction, discovery and interpretation - 9In popular culture - 10See also - 12Further reading - 13External links The cosmic microwave background radiation is an emission of uniform, black body thermal energy coming from all parts of the sky. The radiation is isotropic to roughly one part in 100,000: the root mean square variations are only 18 µK, after subtracting out a dipole anisotropy from the Doppler shift of the background radiation. The latter is caused by the peculiar velocity of the Earth relative to the comoving cosmic rest frame as our planet moves at some 371 km/s towards the constellation Leo. The CMB dipole as well as aberration at higher multipoles have been measured, consistent with galactic motion. In the Big Bang model for the formation of the universe, inflationary cosmology predicts that after about 10−37 seconds the nascent universe underwent exponential growth that smoothed out nearly all irregularities. The remaining irregularities were caused by quantum fluctuations in the inflaton field that caused the inflation event. Before the formation of stars and planets (after 10−6 seconds), the early universe was smaller, much hotter, and filled with a uniform glow from its white-hot fog of interacting plasma of photons, electrons, and baryons. As the universe expanded, adiabatic cooling caused the energy density of the plasma to decrease until it became favorable for electrons to combine with protons, forming hydrogen atoms. This recombination event happened when the temperature was around 3000 K or when the universe was approximately 379,000 years old. As photons did not interact with these electrically neutral atoms, the former began to travel freely through space, resulting in the decoupling of matter and radiation. The color temperature of the ensemble of decoupled photons has continued to diminish ever since; now down to 2.7260±0.0013 K, it will continue to drop as the universe expands. The intensity of the radiation also corresponds to black-body radiation at 2.726 K because red-shifted black-body radiation is just like black-body radiation at a lower temperature. According to the Big Bang model, the radiation from the sky we measure today comes from a spherical surface called the surface of last scattering. This represents the set of locations in space at which the decoupling event is estimated to have occurred and at a point in time such that the photons from that distance have just reached observers. Most of the radiation energy in the universe is in the cosmic microwave background, making up a fraction of roughly 6×10−5 of the total density of the universe. Two of the greatest successes of the Big Bang theory are its prediction of the almost perfect black body spectrum and its detailed prediction of the anisotropies in the cosmic microwave background. The CMB spectrum has become the most precisely measured black body spectrum in nature. The cosmic microwave background was first predicted in 1948 by Ralph Alpher and Robert Herman. Alpher and Herman were able to estimate the temperature of the cosmic microwave background to be 5 K, though two years later they re-estimated it at 28 K. This high estimate was due to a mis-estimate of the Hubble constant by Alfred Behr, which could not be replicated and was later abandoned for the earlier estimate. Although there were several previous estimates of the temperature of space, these suffered from two flaws. First, they were measurements of the effective temperature of space and did not suggest that space was filled with a thermal Planck spectrum. Next, they depend on our being at a special spot at the edge of the Milky Way galaxy and they did not suggest the radiation is isotropic. The estimates would yield very different predictions if Earth happened to be located elsewhere in the universe. The 1948 results of Alpher and Herman were discussed in many physics settings through about 1955, when both left the Applied Physics Laboratory at Johns Hopkins University. The mainstream astronomical community, however, was not intrigued at the time by cosmology. Alpher and Herman’s prediction was rediscovered by Yakov Zel’dovich in the early 1960s, and independently predicted by Robert Dicke at the same time. The first published recognition of the CMB radiation as a detectable phenomenon appeared in a brief paper by Soviet astrophysicists A. G. Doroshkevich and Igor Novikov, in the spring of 1964. In 1964, David Todd Wilkinson and Peter Roll, Dicke’s colleagues at Princeton University, began constructing a Dicke radiometer to measure the cosmic microwave background. In 1964, Arno Penzias and Robert Woodrow Wilson at the Crawford Hill location of Bell Telephone Laboratories in nearby Holmdel Township, New Jersey had built a Dicke radiometer that they intended to use for radio astronomy and satellite communication experiments. On 20 May 1964 they made their first measurement clearly showing the presence of the microwave background, with their instrument having an excess 4.2K antenna temperature which they could not account for. After receiving a telephone call from Crawford Hill, Dicke said “Boys, we’ve been scooped.” A meeting between the Princeton and Crawford Hill groups determined that the antenna temperature was indeed due to the microwave background. Penzias and Wilson received the 1978 Nobel Prize in Physics for their discovery. The interpretation of the cosmic microwave background was a controversial issue in the 1960s with some proponents of the steady state theory arguing that the microwave background was the result of scattered starlight from distant galaxies. Using this model, and based on the study of narrow absorption line features in the spectra of stars, the astronomer Andrew McKellar wrote in 1941: “It can be calculated that the ‘rotational temperature‘ of interstellar space is 2 K.” However, during the 1970s the consensus was established that the cosmic microwave background is a remnant of the big bang. This was largely because new measurements at a range of frequencies showed that the spectrum was a thermal, black body spectrum, a result that the steady state model was unable to reproduce. Harrison, Peebles, Yu and Zel’dovich realized that the early universe would have to have inhomogeneities at the level of 10−4 or 10−5. Rashid Sunyaev later calculated the observable imprint that these inhomogeneities would have on the cosmic microwave background. Increasingly stringent limits on the anisotropy of the cosmic microwave background were set by ground-based experiments during the 1980s. RELIKT-1, a Soviet cosmic microwave background anisotropy experiment on board the Prognoz 9 satellite (launched 1 July 1983) gave upper limits on the large-scale anisotropy. The NASA COBE mission clearly confirmed the primary anisotropy with the Differential Microwave Radiometer instrument, publishing their findings in 1992. The team received the Nobel Prize in physics for 2006 for this discovery. Inspired by the COBE results, a series of ground and balloon-based experiments measured cosmic microwave background anisotropies on smaller angular scales over the next decade. The primary goal of these experiments was to measure the scale of the first acoustic peak, which COBE did not have sufficient resolution to resolve. This peak corresponds to large scale density variations in the early universe that are created by gravitational instabilities, resulting in acoustical oscillations in the plasma. The first peak in the anisotropy was tentatively detected by the Toco experiment and the result was confirmed by the BOOMERanG and MAXIMA experiments. These measurements demonstrated that the geometry of the universe is approximately flat, rather than curved. They ruled out cosmic strings as a major component of cosmic structure formation and suggested cosmic inflation was the right theory of structure formation. The second peak was tentatively detected by several experiments before being definitively detected by WMAP, which has also tentatively detected the third peak. As of 2010, several experiments to improve measurements of the polarization and the microwave background on small angular scales are ongoing. These include DASI, WMAP, BOOMERanG, QUaD, Planck spacecraft, Atacama Cosmology Telescope, South Pole Telescope and the QUIET telescope. Relationship to the Big Bang This section may be too technical for most readers to understand. Please help improve it to make it understandable to non-experts, without removing the technical details. (September 2011) (Learn how and when to remove this template message) The cosmic microwave background radiation and the cosmological redshift-distance relation are together regarded as the best available evidence for the Big Bang theory. Measurements of the CMB have made the inflationary Big Bang theory the Standard Cosmological Model.The discovery of the CMB in the mid-1960s curtailed interest in alternatives such as the steady state theory. The CMB essentially confirms the Big Bang theory. In the late 1940s Alpher and Herman reasoned that if there was a big bang, the expansion of the universe would have stretched and cooled the high-energy radiation of the very early universe into the microwave region of the electromagnetic spectrum, and down to a temperature of about 5 K. They were slightly off with their estimate, but they had exactly the right idea. They predicted the CMB. It took another 15 years for Penzias and Wilson to stumble into discovering that the microwave background was actually there. The CMB gives a snapshot of the universe when, according to standard cosmology, the temperature dropped enough to allow electrons and protons to form hydrogen atoms, thereby making the universe nearly transparent to radiation because light was no longer being scattered off free electrons. When it originated some 380,000 years after the Big Bang—this time is generally known as the “time of last scattering” or the period of recombination or decoupling—the temperature of the universe was about 3000 K. This corresponds to an energy of about 0.26 eV,which is much less than the 13.6 eV ionization energy of hydrogen. Since decoupling, the temperature of the background radiation has dropped by a factor of roughly 1,100 due to the expansion of the universe. As the universe expands, the CMB photons are redshifted, causing them to decrease in energy. The temperature of this radiation stays inversely proportional to a parameter that describes the relative expansion of the universe over time, known as the scale length. The temperature Tr of the CMB as a function of redshift, z, can be shown to be proportional to the temperature of the CMB as observed in the present day (2.725 K or 0.2348 meV): - Tr = 2.725(1 + z) For details about the reasoning that the radiation is evidence for the Big Bang, see Cosmic background radiation of the Big Bang. The anisotropy, or directional dependency, of the cosmic microwave background is divided into two types: primary anisotropy, due to effects that occur at the last scattering surface and before; and secondary anisotropy, due to effects such as interactions of the background radiation with hot gas or gravitational potentials, which occur between the last scattering surface and the observer. The structure of the cosmic microwave background anisotropies is principally determined by two effects: acoustic oscillations and diffusion damping (also called collisionless damping or Silk damping). The acoustic oscillations arise because of a conflict in the photon–baryon plasma in the early universe. The pressure of the photons tends to erase anisotropies, whereas the gravitational attraction of the baryons, moving at speeds much slower than light, makes them tend to collapse to form overdensities. These two effects compete to create acoustic oscillations, which give the microwave background its characteristic peak structure. The peaks correspond, roughly, to resonances in which the photons decouple when a particular mode is at its peak amplitude. The peaks contain interesting physical signatures. The angular scale of the first peak determines the curvature of the universe (but not the topology of the universe). The next peak—ratio of the odd peaks to the even peaks—determines the reduced baryon density. The third peak can be used to get information about the dark-matter density. The locations of the peaks also give important information about the nature of the primordial density perturbations. There are two fundamental types of density perturbations called adiabatic and isocurvature. A general density perturbation is a mixture of both, and different theories that purport to explain the primordial density perturbation spectrum predict different mixtures. - Adiabatic density perturbations - In an adiabatic density perturbation, the fractional additional number density of each type of particle (baryons, photons …) is the same. That is, if at one place there is a 1% higher number density of baryons than average, then at that place there is also a 1% higher number density of photons (and a 1% higher number density in neutrinos) than average. Cosmic inflation predicts that the primordial perturbations are adiabatic. - Isocurvature density perturbations - In an isocurvature density perturbation, the sum (over different types of particle) of the fractional additional densities is zero. That is, a perturbation where at some spot there is 1% more energy in baryons than average, 1% more energy in photons than average, and 2% less energy in neutrinos than average, would be a pure isocurvature perturbation. Cosmic strings would produce mostly isocurvature primordial perturbations. The CMB spectrum can distinguish between these two because these two types of perturbations produce different peak locations. Isocurvature density perturbations produce a series of peaks whose angular scales (l values of the peaks) are roughly in the ratio 1:3:5:…, while adiabatic density perturbations produce peaks whose locations are in the ratio 1:2:3:… Observations are consistent with the primordial density perturbations being entirely adiabatic, providing key support for inflation, and ruling out many models of structure formation involving, for example, cosmic strings. Collisionless damping is caused by two effects, when the treatment of the primordial plasma as fluid begins to break down: - the increasing mean free path of the photons as the primordial plasma becomes increasingly rarefied in an expanding universe, - the finite depth of the last scattering surface (LSS), which causes the mean free path to increase rapidly during decoupling, even while some Compton scattering is still occurring. These effects contribute about equally to the suppression of anisotropies at small scales and give rise to the characteristic exponential damping tail seen in the very small angular scale anisotropies. The depth of the LSS refers to the fact that the decoupling of the photons and baryons does not happen instantaneously, but instead requires an appreciable fraction of the age of the universe up to that era. One method of quantifying how long this process took uses the photon visibility function (PVF). This function is defined so that, denoting the PVF by P(t), the probability that a CMB photon last scattered between time t and t + dt is given by P(t) dt. The maximum of the PVF (the time when it is most likely that a given CMB photon last scattered) is known quite precisely. The first-year WMAP results put the time at which P(t) has a maximum as 372,000 years. This is often taken as the “time” at which the CMB formed. However, to figure out how long it took the photons and baryons to decouple, we need a measure of the width of the PVF. The WMAP team finds that the PVF is greater than half of its maximal value (the “full width at half maximum”, or FWHM) over an interval of 115,000 years. By this measure, decoupling took place over roughly 115,000 years, and when it was complete, the universe was roughly 487,000 years old. Late time anisotropy Since the CMB came into existence, it has apparently been modified by several subsequent physical processes, which are collectively referred to as late-time anisotropy, or secondary anisotropy. When the CMB photons became free to travel unimpeded, ordinary matter in the universe was mostly in the form of neutral hydrogen and helium atoms. However, observations of galaxies today seem to indicate that most of the volume of the intergalactic medium (IGM) consists of ionized material (since there are few absorption lines due to hydrogen atoms). This implies a period of reionization during which some of the material of the universe was broken into hydrogen ions. The CMB photons are scattered by free charges such as electrons that are not bound in atoms. In an ionized universe, such charged particles have been liberated from neutral atoms by ionizing (ultraviolet) radiation. Today these free charges are at sufficiently low density in most of the volume of the universe that they do not measurably affect the CMB. However, if the IGM was ionized at very early times when the universe was still denser, then there are two main effects on the CMB: - Small scale anisotropies are erased. (Just as when looking at an object through fog, details of the object appear fuzzy.) - The physics of how photons are scattered by free electrons (Thomson scattering) induces polarization anisotropies on large angular scales. This broad angle polarization is correlated with the broad angle temperature perturbation. Both of these effects have been observed by the WMAP spacecraft, providing evidence that the universe was ionized at very early times, at a redshift more than 17.[clarification needed] The detailed provenance of this early ionizing radiation is still a matter of scientific debate. It may have included starlight from the very first population of stars (population III stars), supernovae when these first stars reached the end of their lives, or the ionizing radiation produced by the accretion disks of massive black holes. The time following the emission of the cosmic microwave background—and before the observation of the first stars—is semi-humorously referred to by cosmologists as the dark age, and is a period which is under intense study by astronomers (see 21 centimeter radiation). Two other effects which occurred between reionization and our observations of the cosmic microwave background, and which appear to cause anisotropies, are the Sunyaev–Zel’dovich effect, where a cloud of high-energy electrons scatters the radiation, transferring some of its energy to the CMB photons, and the Sachs–Wolfe effect, which causes photons from the Cosmic Microwave Background to be gravitationally redshifted or blueshifted due to changing gravitational fields. The cosmic microwave background is polarized at the level of a few microkelvin. There are two types of polarization, called E-modes and B-modes. This is in analogy to electrostatics, in which the electric field (E-field) has a vanishing curl and the magnetic field (B-field) has a vanishing divergence. The E-modes arise naturally from Thomson scattering in a heterogeneous plasma. The B-modes are not produced by standard scalar type perturbations. Instead they can be created by two mechanisms: the first one is by gravitational lensing of E-modes, which has been measured by the South Pole Telescope in 2013; the second one is from gravitational waves arising from cosmic inflation. Detecting the B-modes is extremely difficult, particularly as the degree of foreground contamination is unknown, and the weak gravitational lensing signal mixes the relatively strong E-mode signal with the B-mode signal. E-modes were first seen in 2002 by the Degree Angular Scale Interferometer (DASI). Primordial gravitational waves Primordial gravitational waves are gravitational waves that could be observed in the polarisation of the cosmic microwave background and having their origin in the early universe. Models of cosmic inflation predict that such gravitational waves should appear; thus, their detection supports the theory of inflation, and their strength can confirm and exclude different models of inflation. It is the result of three things: inflationary expansion of space itself, reheating after inflation, and turbulent fluid mixing of matter and radiation. On 17 March 2014 it was announced that the BICEP2 instrument had detected the first type of B-modes, consistent with inflation and gravitational waves in the early universe at the level of r = 0.20+0.07 −0.05, which is the amount of power present in gravitational waves compared to the amount of power present in other scalar density perturbations in the very early universe. Had this been confirmed it would have provided strong evidence of cosmic inflation and the Big Bang, but on 19 June 2014, considerably lowered confidence in confirming the findings was reported and on 19 September 2014 new results of the Planck experiment reported that the results of BICEP2 can be fully attributed to cosmic dust. The second type of B-modes was discovered in 2013 using the South Pole Telescope with help from the Herschel Space Observatory. This discovery may help test theories on the origin of the universe. Scientists are using data from the Planck mission by the European Space Agency, to gain a better understanding of these waves. In October 2014, a measurement of the B-mode polarization at 150 GHz was published by the POLARBEAR experiment. Compared to BICEP2, POLARBEAR focuses on a smaller patch of the sky and is less susceptible to dust effects. The team reported that POLARBEAR’s measured B-mode polarization was of cosmological origin (and not just due to dust) at a 97.2% confidence level. Microwave background observations Subsequent to the discovery of the CMB, hundreds of cosmic microwave background experiments have been conducted to measure and characterize the signatures of the radiation. The most famous experiment is probably the NASA Cosmic Background Explorer (COBE) satellite that orbited in 1989–1996 and which detected and quantified the large scale anisotropies at the limit of its detection capabilities. Inspired by the initial COBE results of an extremely isotropic and homogeneous background, a series of ground- and balloon-based experiments quantified CMB anisotropies on smaller angular scales over the next decade. The primary goal of these experiments was to measure the angular scale of the first acoustic peak, for which COBE did not have sufficient resolution. These measurements were able to rule out cosmic strings as the leading theory of cosmic structure formation, and suggested cosmic inflation was the right theory. During the 1990s, the first peak was measured with increasing sensitivity and by 2000 the BOOMERanG experiment reported that the highest power fluctuations occur at scales of approximately one degree. Together with other cosmological data, these results implied that the geometry of the universe is flat. A number of ground-based interferometers provided measurements of the fluctuations with higher accuracy over the next three years, including the Very Small Array, Degree Angular Scale Interferometer (DASI), and the Cosmic Background Imager (CBI). DASI made the first detection of the polarization of the CMB and the CBI provided the first E-mode polarization spectrum with compelling evidence that it is out of phase with the T-mode spectrum. In June 2001, NASA launched a second CMB space mission, WMAP, to make much more precise measurements of the large scale anisotropies over the full sky. WMAP used symmetric, rapid-multi-modulated scanning, rapid switching radiometers to minimize non-sky signal noise. The first results from this mission, disclosed in 2003, were detailed measurements of the angular power spectrum at a scale of less than one degree, tightly constraining various cosmological parameters. The results are broadly consistent with those expected from cosmic inflation as well as various other competing theories, and are available in detail at NASA’s data bank for Cosmic Microwave Background (CMB) (see links below). Although WMAP provided very accurate measurements of the large scale angular fluctuations in the CMB (structures about as broad in the sky as the moon), it did not have the angular resolution to measure the smaller scale fluctuations which had been observed by former ground-based interferometers. A third space mission, the ESA (European Space Agency) Planck Surveyor, was launched in May 2009 and performed an even more detailed investigation until it was shut down in October 2013. Planck employed both HEMT radiometers and bolometer technology and measured the CMB at a smaller scale than WMAP. Its detectors were trialled in the Antarctic Viper telescope as ACBAR (Arcminute Cosmology Bolometer Array Receiver) experiment—which has produced the most precise measurements at small angular scales to date—and in the Archeops balloon telescope. On 21 March 2013, the European-led research team behind the Planck cosmology probe released the mission’s all-sky map (565×318 jpeg, 3600×1800 jpeg) of the cosmic microwave background. The map suggests the universe is slightly older than researchers expected. According to the map, subtle fluctuations in temperature were imprinted on the deep sky when the cosmos was about 370000 years old. The imprint reflects ripples that arose as early, in the existence of the universe, as the first nonillionth of a second. Apparently, these ripples gave rise to the present vast cosmic web of galaxy clusters and dark matter. Based on the 2013 data, the universe contains 4.9% ordinary matter, 26.8% dark matter and 68.3% dark energy. On 5 February 2015, new data was released by the Planck mission, according to which the age of the universe is 13.799±0.021 billion years old and the Hubble constant was measured to be 67.74±0.46 (km/s)/Mpc. Additional ground-based instruments such as the South Pole Telescope in Antarctica and the proposed Clover Project, Atacama Cosmology Telescope and the QUIET telescope in Chile will provide additional data not available from satellite observations, possibly including the B-mode polarization. Data reduction and analysis Raw CMBR data, even from space vehicles such as WMAP or Planck, contain foreground effects that completely obscure the fine-scale structure of the cosmic microwave background. The fine-scale structure is superimposed on the raw CMBR data but is too small to be seen at the scale of the raw data. The most prominent of the foreground effects is the dipole anisotropy caused by the Sun’s motion relative to the CMBR background. The dipole anisotropy and others due to Earth’s annual motion relative to the Sun and numerous microwave sources in the galactic plane and elsewhere must be subtracted out to reveal the extremely tiny variations characterizing the fine-scale structure of the CMBR background. The detailed analysis of CMBR data to produce maps, an angular power spectrum, and ultimately cosmological parameters is a complicated, computationally difficult problem. Although computing a power spectrum from a map is in principle a simple Fourier transform, decomposing the map of the sky into spherical harmonics, in practice it is hard to take the effects of noise and foreground sources into account. In particular, these foregrounds are dominated by galactic emissions such as Bremsstrahlung, synchrotron, and dust that emit in the microwave band; in practice, the galaxy has to be removed, resulting in a CMB map that is not a full-sky map. In addition, point sources like galaxies and clusters represent another source of foreground which must be removed so as not to distort the short scale structure of the CMB power spectrum. Constraints on many cosmological parameters can be obtained from their effects on the power spectrum, and results are often calculated using Markov Chain Monte Carlo sampling techniques. CMBR dipole anisotropy From the CMB data it is seen that the earth appears to be moving at 368±2 km/s relative to the reference frame of the CMB (also called the CMB rest frame, or the frame of reference in which there is no motion through the CMB). The Local Group (the galaxy group that includes the Milky Way galaxy) appears to be moving at 627±22 km/s in the direction of galactic longitude l = 276°±3°, b = 30°±3°. This motion results in an anisotropy of the data (CMB appearing slightly warmer in the direction of movement than in the opposite direction). From a theoretical point of view, the existence of a CMB rest frame breaks Lorentz invariance even in empty space far away from any galaxy. The standard interpretation of this temperature variation is a simple velocity red shift and blue shift due to motion relative to the CMB, but alternative cosmological models can explain some fraction of the observed dipole temperature distribution in the CMB. Low multipoles and other anomalies With the increasingly precise data provided by WMAP, there have been a number of claims that the CMB exhibits anomalies, such as very large scale anisotropies, anomalous alignments, and non-Gaussian distributions. The most longstanding of these is the low-l multipole controversy. Even in the COBE map, it was observed that the quadrupole (l = 2, spherical harmonic) has a low amplitude compared to the predictions of the Big Bang. In particular, the quadrupole and octupole (l = 3) modes appear to have an unexplained alignment with each other and with both the ecliptic plane and equinoxes, A number of groups have suggested that this could be the signature of new physics at the greatest observable scales; other groups suspect systematic errors in the data. Ultimately, due to the foregrounds and the cosmic variance problem, the greatest modes will never be as well measured as the small angular scale modes. The analyses were performed on two maps that have had the foregrounds removed as far as possible: the “internal linear combination” map of the WMAP collaboration and a similar map prepared by Max Tegmarkand others. Later analyses have pointed out that these are the modes most susceptible to foreground contamination from synchrotron, dust, and Bremsstrahlung emission, and from experimental uncertainty in the monopole and dipole. A full Bayesian analysis of the WMAP power spectrum demonstrates that the quadrupole prediction of Lambda-CDM cosmology is consistent with the data at the 10% level and that the observed octupole is not remarkable. Carefully accounting for the procedure used to remove the foregrounds from the full sky map further reduces the significance of the alignment by ~5%. Recent observations with the Planck telescope, which is very much more sensitive than WMAP and has a larger angular resolution, record the same anomaly, and so instrumental error (but not foreground contamination) appears to be ruled out. Coincidence is a possible explanation, chief scientist from WMAP, Charles L. Bennettsuggested coincidence and human psychology were involved, “I do think there is a bit of a psychological effect; people want to find unusual things.” Assuming the universe keeps expanding and it does not suffer a Big Crunch, a Big Rip, or another similar fate, the cosmic microwave background will continue redshifting until it will no longer be detectable, and will be overtaken first by the one produced by starlight, and later by the background radiation fields of processes that are assumed will take place in the far future of the universe., §VD. Timeline of prediction, discovery and interpretation Thermal (non-microwave background) temperature predictions - 1896 – Charles Édouard Guillaume estimates the “radiation of the stars” to be 5.6K. - 1926 – Sir Arthur Eddington estimates the non-thermal radiation of starlight in the galaxy “… by the formula E = σT4 the effective temperature corresponding to this density is 3.18° absolute … black body” - 1930s – Cosmologist Erich Regener calculates that the non-thermal spectrum of cosmic rays in the galaxy has an effective temperature of 2.8 K - 1931 – Term microwave first used in print: “When trials with wavelengths as low as 18 cm. were made known, there was undisguised surprise+that the problem of the micro-wave had been solved so soon.” Telegraph & Telephone Journal XVII. 179/1 - 1934 – Richard Tolman shows that black-body radiation in an expanding universe cools but remains thermal - 1938 – Nobel Prize winner (1920) Walther Nernst reestimates the cosmic ray temperature as 0.75K - 1946 – Robert Dicke predicts “… radiation from cosmic matter” at <20 K, but did not refer to background radiation - 1946 – George Gamow calculates a temperature of 50 K (assuming a 3-billion year old universe), commenting it “… is in reasonable agreement with the actual temperature of interstellar space”, but does not mention background radiation. - 1953 – Erwin Finlay-Freundlich in support of his tired light theory, derives a blackbody temperature for intergalactic space of 2.3K with comment from Max Born suggesting radio astronomy as the arbitrator between expanding and infinite cosmologies. Microwave background radiation predictions and measurements - 1941 – Andrew McKellar detected the cosmic microwave background as the coldest component of the interstellar medium by using the excitation of CN doublet lines measured by W. S. Adams in a B star, finding an “effective temperature of space” (the average bolometric temperature) of 2.3 K - 1946 – George Gamow calculates a temperature of 50 K (assuming a 3-billion year old universe), commenting it “… is in reasonable agreement with the actual temperature of interstellar space”, but does not mention background radiation. - 1948 – Ralph Alpher and Robert Herman estimate “the temperature in the universe” at 5 K. Although they do not specifically mention microwave background radiation, it may be inferred. - 1949 – Ralph Alpher and Robert Herman re-re-estimate the temperature at 28 K. - 1953 – George Gamow estimates 7 K. - 1956 – George Gamow estimates 6 K. - 1955 – Émile Le Roux of the Nançay Radio Observatory, in a sky survey at λ = 33 cm, reported a near-isotropic background radiation of 3 kelvins, plus or minus 2. - 1957 – Tigran Shmaonov reports that “the absolute effective temperature of the radioemission background … is 4±3 K”. It is noted that the “measurements showed that radiation intensity was independent of either time or direction of observation … it is now clear that Shmaonov did observe the cosmic microwave background at a wavelength of 3.2 cm” - 1960s – Robert Dicke re-estimates a microwave background radiation temperature of 40 K - 1964 – A. G. Doroshkevich and Igor Dmitrievich Novikov publish a brief paper suggesting microwave searches for the black-body radiation predicted by Gamow, Alpher, and Herman, where they name the CMB radiation phenomenon as detectable. - 1964–65 – Arno Penzias and Robert Woodrow Wilson measure the temperature to be approximately 3 K. Robert Dicke, James Peebles, P. G. Roll, and D. T. Wilkinson interpret this radiation as a signature of the big bang. - 1966 – Rainer K. Sachs and Arthur M. Wolfe theoretically predict microwave background fluctuation amplitudes created by gravitational potential variations between observers and the last scattering surface (see Sachs-Wolfe effect) - 1968 – Martin Rees and Dennis Sciama theoretically predict microwave background fluctuation amplitudes created by photons traversing time-dependent potential wells - 1969 – R. A. Sunyaev and Yakov Zel’dovich study the inverse Compton scattering of microwave background photons by hot electrons (see Sunyaev-Zel’dovich effect) - 1983 – Researchers from the Cambridge Radio Astronomy Group and the Owens Valley Radio Observatory first detect the Sunyaev-Zel’dovich effect from clusters of galaxies - 1983 – RELIKT-1 Soviet CMB anisotropy experiment was launched. - 1990 – FIRAS on the Cosmic Background Explorer (COBE) satellite measures the black body form of the CMB spectrum with exquisite precision, and shows that the microwave background has a nearly perfect black-body spectrum and thereby strongly constrains the density of the intergalactic medium. - January 1992 – Scientists that analysed data from the RELIKT-1 report the discovery of anisotropy in the cosmic microwave background at the Moscow astrophysical seminar. - 1992 – Scientists that analysed data from COBE DMR report the discovery of anisotropy in the cosmic microwave background. - 1995 – The Cosmic Anisotropy Telescope performs the first high resolution observations of the cosmic microwave background. - 1999 – First measurements of acoustic oscillations in the CMB anisotropy angular power spectrum from the TOCO, BOOMERANG, and Maxima Experiments. The BOOMERanG experimentmakes higher quality maps at intermediate resolution, and confirms that the universe is “flat”. - 2002 – Polarization discovered by DASI. - 2003 – E-mode polarization spectrum obtained by the CBI. The CBI and the Very Small Array produces yet higher quality maps at high resolution (covering small areas of the sky). - 2003 – The Wilkinson Microwave Anisotropy Probe spacecraft produces an even higher quality map at low and intermediate resolution of the whole sky (WMAP provides no high-resolution data, but improves on the intermediate resolution maps from BOOMERanG). - 2004 – E-mode polarization spectrum obtained by the CBI. - 2004 – The Arcminute Cosmology Bolometer Array Receiver produces a higher quality map of the high resolution structure not mapped by WMAP. - 2005 – The Arcminute Microkelvin Imager and the Sunyaev-Zel’dovich Array begin the first surveys for very high redshift clusters of galaxies using the Sunyaev-Zel’dovich effect. - 2005 – Ralph A. Alpher is awarded the National Medal of Science for his groundbreaking work in nucleosynthesis and prediction that the universe expansion leaves behind background radiation, thus providing a model for the Big Bang theory. - 2006 – The long-awaited three-year WMAP results are released, confirming previous analysis, correcting several points, and including polarization data. - 2006 – Two of COBE’s principal investigators, George Smoot and John Mather, received the Nobel Prize in Physics in 2006 for their work on precision measurement of the CMBR. - 2006–2011 – Improved measurements from WMAP, new supernova surveys ESSENCE and SNLS, and baryon acoustic oscillations from SDSS and WiggleZ, continue to be consistent with the standard Lambda-CDM model. - 2010 – The first all-sky map from the Planck telescope is released. - 2013 – An improved all-sky map from the Planck telescope is released, improving the measurements of WMAP and extending them to much smaller scales. - 2014 – On March 17, 2014, astrophysicists of the BICEP2 collaboration announced the detection of inflationary gravitational waves in the B-mode power spectrum, which if confirmed, would provide clear experimental evidence for the theory of inflation. However, on 19 June 2014, lowered confidence in confirming the cosmic inflation findings was reported. - 2015 – On January 30, 2015, the same team of astronomers from BICEP2 withdrew the claim made on the previous year. Based on the combined data of BICEP2 and Planck, the European Space Agency announced that the signal can be entirely attributed to dust in the Milky Way. In popular culture - In the Stargate Universe TV series, an Ancient spaceship, Destiny, was built to study patterns in the CMBR which indicate that the universe as we know it might have been created by some form of sentient intelligence. - In Wheelers, a novel by Ian Stewart & Jack Cohen, CMBR is explained as the encrypted transmissions of an ancient civilization. This allows the Jovian “blimps” to have a society older than the currently-observed age of the universe. - In The Three-Body Problem, a novel by Liu Cixin, a probe from an alien civilization compromises instruments monitoring the CMBR in order to deceive a character into believing the civilization has the power to manipulate the CMBR itself. - The Swiss 20 francs bill lists several astronomical objects with their distances – the CMB is mentioned with 430 · 1015 light-seconds.
Assign Variables Python String Functions A String Functions is a collection of functions that perform one-dimensional integer division on a given input string. For example, this function computes the expression: g = ‘foo’ n = str(g) where g is the input string. Note that this is a function of only one dimension in the input string, which is the same as the two-dimensional function of the integer division in your example. A function that can take two strings as arguments and return an integer, which is how the function operates on the input string and outputs the result. A function that takes two arguments and returns an integer, but does not take one-dimensional integers in the input input string, so it is not a function of two. A function is a function that takes a single argument and returns an object. Calling a function that is a function Calling function The function of the type String is an example of a function that can be used to perform one- dimensional integer division on the input. While calling a function that does not take two arguments, the function can take several arguments, and return an object of the form: import sys import numpy as np sys.argv = np.random.rand(0,3)6 function to_test() This function will return an integer by default. It takes both arguments, and returns an instance of the class Number that is of type Number. To call a function that returns an integer by using the function name, the function name can be any combination of a number and an integer. Programming Homework Help The function to_test is the class Number. For example, to call a function of the form the_function = to_test to return: the = Number(1) has an integer of type Number, which is of type Integer. This is a very simple function that takes one argument, an integer, and returns a new instance of the new class Number. The function, as you can guess, is not a class. Using the function name Calling the function to_tests Calling to_tests is a function called once you have completed the tests. It’s also called once you’ve finished the read the full info here of the program. The function to_check is also called once your program has finished. It takes two arguments, an integer and an integer with the same name. When using the function to check the return type, the return type is the stringified string of the integer, not the integer. The following example demonstrates how to use the function to to_check to find the return this page of a function: def to_test(x): return x def test_to_check(x): print(‘true’) if x == 1: return 1 else: print(‘false’) When you’re using the function from the function to test the return type to find the result, the result type is not the stringified integer, because it’s not a stringified integer. To test the return value learn the facts here now a function, the return value will be a stringified number, not an integer. For the following example, you’ll find that the returned value of a to_test function is not a string, because it is a function. import stringutils def f(a, b): “”” Return the stringified number of the result “”” i = 0 for i in a: if len(a[i]) < 3: return a[i] + b return False def check_to_test(a,b): if a == 0: check_to = "true" # XXX this might not work if b == 1: check_check = "false" # XXX this could not be the result of this test return False def totest_test(n,a,b,c): return n %% (3 + c) + a %% (3 - cAssign Variables Python This code assumes you have Python 3. Python Homework Assignment Help 6 (hence the name ‘Python’) installed and you are using Python 3.5 (hence your name ‘Python 3.5’). To install Python on your system, select Python version 3.5 from the search box, then click on the ‘Install’ button. Once installed, you will need to follow the instructions and you should be able to use the Python Package Manager software. Install Python Now that you have installed Python on your machine, you need to create your own classes and functions. import os from PYTHON.PYTHON import class MyClass(object): def __init__(self, name): class Application(object): def __init__(): self.name = “MyClass” def main(): def generate(): name = “MyName” print(“generate”) if __name__ == ‘__main__’: main() You will need to create a dictionary object to store your classes and functions and to import them in the main(). Now you can use the dictionary to load your classes and function definitions. Before you create your own instances of the classes, you will have to create a new instance of the class. In your example, you created two classes called My and MyName, and two functions called MyFunction and MyFunctionFunction. Online Python Tutoring You can find the documentation for PyPy in the PyGIS Source Code. Now you can create your own functions from the sources: import pypy class MemberFunction(object): # <-- Python 3.3 def findFunction(self, obj): def function(obj): # <-- Your Class/Function definition # <---- Python Module def func(self): class MyFunction(object, MyFunctionFunction): # <---- Your Class/function definition How do I use this method to get the name of the class and function I have in my class? import PyGIS def findFunction( obj ): #... def function_search(): # You can search for browse around this site the classes and functions in the dictionary, or you can do it yourself, but don’t worry! return “MyFunction” If you want to find the class and its function, you need that name. If I have the class, I want to find all the functions in the class. Please note that the result of the findFunction method is a different one than that of the function keyword. I only found the class name, the class, and the function, I don’t know the functions name, I only found the function definition. Here is the code I used to find the function definition, I can’t help you. def f(obj): # <--- Python Module def func(obj): # What do I do? return "Function" #... def func_search(): // or Just “Function” or “FunctionFunction” def func2(obj): def find2(obj, func): # I’ve found you can check here the classes in the dictionary if func2(m) == “function_search”: func_search() else: find2(m, func) Of course, the class and functions name are different, so you need to use the dictionary function instead of the find2’s findFunction. Assign Variables Python #include
During the early twentieth century, astronomers discovered that galaxies are rushing away from us at huge speeds. The Sombrero galaxy, for instance, was found to be moving away from the Earth at about 1000 km/s. These speeds can be found very accurately from the doppler red shift of spectral lines. Hubble concluded that the speed of a galaxy is proportional to its distance – that is, that if one galaxy is three times further from us than another, then it will be moving away at a speed which is three times greater than the other. This result was a huge step forward for astronomers. It implied that in the beginning, the Universe was very much more dense than it is now, and that since the Big Bang all the matter in the Universe has been flying apart. http://www.aps.org/ publications/apsnews/200801/physicshistory.cfm Using a subset of Edwin Hubble’s original data from the 1920’s, you will plot a graph by hand of velocity against distance and draw a straight line (by eye) to the points which “best fits” the data. Should the line should go through the origin? The slope of the line represents velocity/distance, and is known as the Hubble constant Ho. Use your value of Ho to deduce the age of the Universe. As you prepare this assignment for submission. NOTE: Marks will be deduced for incomplete and poorly presented work. Steps in the calculations need to be described or explained as required, terms in the equations defined. The graph (by hand) needs to be properly titled and axes labeled, i.e., “V versus D” is not a title, a title should be at least a complete sentence which describes what is being shown. An estimate for the age of the Universe, 1/Ho is being derived by a “best fit line” through a set of data points. Ho is the Hubble Constant in Hubbles, Law: V = Ho*D. V is the recessional velocity and D is the distance to far away galaxies. Note that nearby galaxies, our local group, are not necessarily moving away from us but are in mutual gravitation orbits. Also keep in mind, that the data being plotted is from the 1920’s — Hubble’s original data. The age estimate derived has been vastly refined over the decades through more data, but primarily from a better understanding of stellar properties and assumptions made in distance estimates — Hubble’s distance estimates were flawed resulting in considerable activity in the scientific community — both Astronomy and Earth Science. Delivering a high-quality product at a reasonable price is not enough anymore. That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe. You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.Read more Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.Read more Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.Read more Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.Read more By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.Read more
Plant hormones are signal molecules produced within the plant, and occur in extremely low concentrations. Hormones regulate cellular processes in targeted cells locally and, moved to other locations, in other functional parts of the plant. Hormones also determine the formation of flowers, stems, leaves, the shedding of leaves, and the development and ripening of fruit. Plants, unlike animals, lack glands that produce and secrete hormones. Instead, each cell is capable of producing hormones. Plant hormones shape the plant, affecting seed growth, time of flowering, the sex of flowers, senescence of leaves, and fruits. They affect which tissues grow upward and which grow downward, leaf formation and stem growth, fruit development and ripening, plant longevity, and even plant death. Hormones are vital to plant growth, and, lacking them, plants would be mostly a mass of undifferentiated cells. So they are also known as growth factors or growth hormones. The term 'Phytohormone' was coined by Thimann in 1948[clarification needed]. Phytohormones are found not only in higher plants but in algae, showing similar functions, and in microorganisms, such as unicellular fungi and bacteria, but in these cases they play no hormonal or other immediate physiological role in the producing organism and can, thus, be regarded as secondary metabolites. The word hormone is derived from Greek, meaning set in motion. Plant hormones affect gene expression and transcription levels, cellular division, and growth. They are naturally produced within plants, though very similar chemicals are produced by fungi and bacteria that can also affect plant growth. A large number of related chemical compounds are synthesized by humans. They are used to regulate the growth of cultivated plants, weeds, and in vitro-grown plants and plant cells; these manmade compounds are called Plant Growth Regulators or PGRs for short. Early in the study of plant hormones, "phytohormone" was the commonly used term, but its use is less widely applied now. Plant hormones are not nutrients, but chemicals that in small amounts promote and influence the growth, development, and differentiation of cells and tissues. The biosynthesis of plant hormones within plant tissues is often diffuse and not always localized. Plants lack glands to produce and store hormones, because, unlike animals — which have two circulatory systems (lymphatic and cardiovascular) powered by a heart that moves fluids around the body — plants use more passive means to move chemicals around their bodies. Plants utilize simple chemicals as hormones, which move more easily through their tissues. They are often produced and used on a local basis within the plant body. Plant cells produce hormones that affect even different regions of the cell producing the hormone. Hormones are transported within the plant by utilizing four types of movements. For localized movement, cytoplasmic streaming within cells and slow diffusion of ions and molecules between cells are utilized. Vascular tissues are used to move hormones from one part of the plant to another; these include sieve tubes or phloem that move sugars from the leaves to the roots and flowers, and xylem that moves water and mineral solutes from the roots to the foliage. Not all plant cells respond to hormones, but those cells that do are programmed to respond at specific points in their growth cycle. The greatest effects occur at specific stages during the cell's life, with diminished effects occurring before or after this period. Plants need hormones at very specific times during plant growth and at specific locations. They also need to disengage the effects that hormones have when they are no longer needed. The production of hormones occurs very often at sites of active growth within the meristems, before cells have fully differentiated. After production, they are sometimes moved to other parts of the plant, where they cause an immediate effect; or they can be stored in cells to be released later. Plants use different pathways to regulate internal hormone quantities and moderate their effects; they can regulate the amount of chemicals used to biosynthesize hormones. They can store them in cells, inactivate them, or cannibalise already-formed hormones by conjugating them with carbohydrates, amino acids, or peptides. Plants can also break down hormones chemically, effectively destroying them. Plant hormones frequently regulate the concentrations of other plant hormones. Plants also move hormones around the plant diluting their concentrations. The concentration of hormones required for plant responses are very low (10−6 to 10−5 mol/L). Because of these low concentrations, it has been very difficult to study plant hormones, and only since the late 1970s have scientists been able to start piecing together their effects and relationships to plant physiology. Much of the early work on plant hormones involved studying plants that were genetically deficient in one or involved the use of tissue-cultured plants grown in vitro that were subjected to differing ratios of hormones, and the resultant growth compared. The earliest scientific observation and study dates to the 1880s; the determination and observation of plant hormones and their identification was spread-out over the next 70 years. Classes of plant hormones In general, it is accepted that there are five major classes of plant hormones, some of which are made up of many different chemicals that can vary in structure from one plant to the next. The chemicals are each grouped together into one of these classes based on their structural similarities and on their effects on plant physiology. Other plant hormones and growth regulators are not easily grouped into these classes; they exist naturally or are synthesized by humans or other organisms, including chemicals that inhibit plant growth or interrupt the physiological processes within plants. Each class has positive as well as inhibitory functions, and most often work in tandem with each other, with varying ratios of one or more interplaying to affect growth regulation. The five major classes are: Abscisic acid hormone Abscisic acid (also called ABA) is one of the most important plant growth regulators. It was discovered and researched under two different names before its chemical properties were fully known, it was called dormin and abscicin II. Once it was determined that the two compounds are the same, it was named abscisic acid. The name "abscisic acid" was given because it was found in high concentrations in newly abscissed or freshly fallen leaves. This class of PGR is composed of one chemical compound normally produced in the leaves of plants, originating from chloroplasts, especially when plants are under stress. In general, it acts as an inhibitory chemical compound that affects bud growth, and seed and bud dormancy. It mediates changes within the apical meristem, causing bud dormancy and the alteration of the last set of leaves into protective bud covers. Since it was found in freshly abscissed leaves, it was thought to play a role in the processes of natural leaf drop, but further research has disproven this. In plant species from temperate parts of the world, it plays a role in leaf and seed dormancy by inhibiting growth, but, as it is dissipated from seeds or buds, growth begins. In other plants, as ABA levels decrease, growth then commences as gibberellin levels increase. Without ABA, buds and seeds would start to grow during warm periods in winter and be killed when it froze again. Since ABA dissipates slowly from the tissues and its effects take time to be offset by other plant hormones, there is a delay in physiological pathways that provide some protection from premature growth. It accumulates within seeds during fruit maturation, preventing seed germination within the fruit, or seed germination before winter. Abscisic acid's effects are degraded within plant tissues during cold temperatures or by its removal by water washing in out of the tissues, releasing the seeds and buds from dormancy. In plants under water stress, ABA plays a role in closing the stomata. Soon after plants are water-stressed and the roots are deficient in water, a signal moves up to the leaves, causing the formation of ABA precursors there, which then move to the roots. The roots then release ABA, which is translocated to the foliage through the vascular system and modulates the potassium and sodium uptake within the guard cells, which then lose turgidity, closing the stomata. ABA exists in all parts of the plant and its concentration within any tissue seems to mediate its effects and function as a hormone; its degradation, or more properly catabolism, within the plant affects metabolic reactions and cellular growth and production of other hormones. Plants start life as a seed with high ABA levels. Just before the seed germinates, ABA levels decrease; during germination and early growth of the seedling, ABA levels decrease even more. As plants begin to produce shoots with fully functional leaves, ABA levels begin to increase, slowing down cellular growth in more "mature" areas of the plant. Stress from water or predation affects ABA production and catabolism rates, mediating another cascade of effects that trigger specific responses from targeted cells. Scientists are still piecing together the complex interactions and effects of this and other phytohormones. Auxins are compounds that positively influence cell enlargement, bud formation and root initiation. They also promote the production of other hormones and in conjunction with cytokinins, they control the growth of stems, roots, and fruits, and convert stems into flowers. Auxins were the first class of growth regulators discovered. They affect cell elongation by altering cell wall plasticity. They stimulate cambium, a subtype of meristem cells, to divide and in stems cause secondary xylem to differentiate. Auxins act to inhibit the growth of buds lower down the stems (apical dominance), and also to promote lateral and adventitious root development and growth. Leaf abscission is initiated by the growing point of a plant ceasing to produce auxins. Auxins in seeds regulate specific protein synthesis, as they develop within the flower after pollination, causing the flower to develop a fruit to contain the developing seeds. Auxins are toxic to plants in large concentrations; they are most toxic to dicots and less so to monocots. Because of this property, synthetic auxin herbicides including 2,4-D and 2,4,5-T have been developed and used for weed control. Auxins, especially 1-Naphthaleneacetic acid (NAA) and Indole-3-butyric acid (IBA), are also commonly applied to stimulate root growth when taking cuttings of plants. The most common auxin found in plants is indole-3-acetic acid or IAA. The correlation of auxins and cytokinins in the plants is a constant (A/C = const.). Cytokinins or CKs are a group of chemicals that influence cell division and shoot formation. They were called kinins in the past when the first cytokinins were isolated from yeast cells. They also help delay senescence of tissues, are responsible for mediating auxin transport throughout the plant, and affect internodal length and leaf growth. They have a highly synergistic effect in concert with auxins, and the ratios of these two groups of plant hormones affect most major growth periods during a plant's lifetime. Cytokinins counter the apical dominance induced by auxins; they in conjunction with ethylene promote abscission of leaves, flower parts, and fruits. The correlation of auxins and cytokinins in the plants is a constant (A/C = const.). Ethylene is a gas that forms through the breakdown of methionine, which is in all cells. Ethylene has very limited solubility in water and does not accumulate within the cell but diffuses out of the cell and escapes out of the plant. Its effectiveness as a plant hormone is dependent on its rate of production versus its rate of escaping into the atmosphere. Ethylene is produced at a faster rate in rapidly growing and dividing cells, especially in darkness. New growth and newly germinated seedlings produce more ethylene than can escape the plant, which leads to elevated amounts of ethylene, inhibiting leaf expansion (see Hyponastic response). As the new shoot is exposed to light, reactions by phytochrome in the plant's cells produce a signal for ethylene production to decrease, allowing leaf expansion. Ethylene affects cell growth and cell shape; when a growing shoot hits an obstacle while underground, ethylene production greatly increases, preventing cell elongation and causing the stem to swell. The resulting thicker stem can exert more pressure against the object impeding its path to the surface. If the shoot does not reach the surface and the ethylene stimulus becomes prolonged, it affects the stem's natural geotropic response, which is to grow upright, allowing it to grow around an object. Studies seem to indicate that ethylene affects stem diameter and height: When stems of trees are subjected to wind, causing lateral stress, greater ethylene production occurs, resulting in thicker, more sturdy tree trunks and branches. Ethylene affects fruit-ripening: Normally, when the seeds are mature, ethylene production increases and builds-up within the fruit, resulting in a climacteric event just before seed dispersal. The nuclear protein Ethylene Insensitive2 (EIN2) is regulated by ethylene production, and, in turn, regulates other hormones including ABA and stress hormones. Main function: initiate mobilization of storage materials in seeds during germination, cause elongation of stems, stimulate bolting in biennials stimulate pollen tube growth. Gibberellins, or GAs, include a large range of chemicals that are produced naturally within plants and by fungi. They were first discovered when Japanese researchers, including Eiichi Kurosawa, noticed a chemical produced by a fungus called Gibberella fujikuroi that produced abnormal growth in rice plants. Gibberellins are important in seed germination, affecting enzyme production that mobilizes food production used for growth of new cells. This is done by modulating chromosomal transcription. In grain (rice, wheat, corn, etc.) seeds, a layer of cells called the aleurone layer wraps around the endosperm tissue. Absorption of water by the seed causes production of GA. The GA is transported to the aleurone layer, which responds by producing enzymes that break down stored food reserves within the endosperm, which are utilized by the growing seedling. GAs produce bolting of rosette-forming plants, increasing internodal length. They promote flowering, cellular division, and in seeds growth after germination. Gibberellins also reverse the inhibition of shoot growth and dormancy induced by ABA. Other known hormones Other identified plant growth regulators include: - Brassinosteroids - are a class of polyhydroxysteroids, a group of plant growth regulators. Brassinosteroids have been recognized as a sixth class of plant hormones, which stimulate cell elongation and division, gravitropism, resistance to stress, and xylem differentiation. They inhibit root growth and leaf abscission. Brassinolide was the first identified brassinosteroid and was isolated from extracts of rapeseed (Brassica napus) pollen in 1979. - Salicylic acid — activates genes in some plants that produce chemicals that aid in the defense against pathogenic invaders. - Jasmonates — are produced from fatty acids and seem to promote the production of defense proteins that are used to fend off invading organisms. They are believed to also have a role in seed germination, and affect the storage of protein in seeds, and seem to affect root growth. - Plant peptide hormones — encompasses all small secreted peptides that are involved in cell-to-cell signaling. These small peptide hormones play crucial roles in plant growth and development, including defense mechanisms, the control of cell division and expansion, and pollen self-incompatibility. - Polyamines — are strongly basic molecules with low molecular weight that have been found in all organisms studied thus far. They are essential for plant growth and development and affect the process of mitosis and meiosis. - Nitric oxide (NO) — serves as signal in hormonal and defense responses (e.g. stomatal closure, root development, germination, nitrogen fixation, cell death, stress response). NO can be produced by a yet undefined NO synthase, a special type of nitrite reductase, nitrate reductase, mitochondrial cytochrome c oxidase or non enzymatic processes and regulate plant cell organelle functions (e.g. ATP synthesis in chloroplasts and mitochondria). - Strigolactones - implicated in the inhibition of shoot branching. - Karrikins - not plant hormones because they are not made by plants, but are a group of plant growth regulators found in the smoke of burning plant material that have the ability to stimulate the germination of seeds - Triacontanol - a fatty alcohol that acts as a growth stimulant, especially initiating new basal breaks in the rose family. It is found in alfalfa (lucerne), bee's wax, and some waxy leaf cuticles. Potential medical applications Plant stress hormones activate cellular responses, including cell death, to diverse stress situations in plants. Researchers have found that some plant stress hormones share the ability to adversely affect human cancer cells. For example, sodium salicylate has been found to suppress proliferation of lymphoblastic leukemia, prostate, breast, and melanoma human cancer cells. Jasmonic acid, a plant stress hormone that belongs to the jasmonate family, induced death in lymphoblastic leukemia cells. Methyl jasmonate has been found to induce cell death in a number of cancer cell lines. Hormones and plant propagation The propagation of plants by cuttings of fully developed leaves, stems, or roots is performed by gardeners utilizing auxin as a rooting compound applied to the cut surface; the auxins are taken into the plant and promote root initiation. In grafting, auxin promotes callus tissue formation, which joins the surfaces of the graft together. In micropropagation, different PGRs are used to promote multiplication and then rooting of new plantlets. In the tissue-culturing of plant cells, PGRs are used to produce callus growth, multiplication, and rooting. Plant hormones affect seed germination and dormancy by acting on different parts of the seed. Embryo dormancy is characterized by a high ABA:GA ratio, whereas the seed has a high ABA sensitivity and low GA sensitivity. In order to release the seed from this type of dormancy and initiate seed germination, an alteration in hormone biosynthesis and degradation toward a low ABA/GA ratio, along with a decrease in ABA sensitivity and an increase in GA sensitivity, must occur. ABA controls embryo dormancy, and GA embryo germination. Seed coat dormancy involves the mechanical restriction of the seed coat. This, along with a low embryo growth potential, effectively produces seed dormancy. GA releases this dormancy by increasing the embryo growth potential, and/or weakening the seed coat so the radical of the seedling can break through the seed coat. Different types of seed coats can be made up of living or dead cells, and both types can be influenced by hormones; those composed of living cells are acted upon after seed formation, whereas the seed coats composed of dead cells can be influenced by hormones during the formation of the seed coat. ABA affects testa or seed coat growth characteristics, including thickness, and effects the GA-mediated embryo growth potential. These conditions and effects occur during the formation of the seed, often in response to environmental conditions. Hormones also mediate endosperm dormancy: Endosperm in most seeds is composed of living tissue that can actively respond to hormones generated by the embryo. The endosperm often acts as a barrier to seed germination, playing a part in seed coat dormancy or in the germination process. Living cells respond to and also affect the ABA:GA ratio, and mediate cellular sensitivity; GA thus increases the embryo growth potential and can promote endosperm weakening. GA also affects both ABA-independent and ABA-inhibiting processes within the endosperm. - Tarakhovskaya, E. R.; Maslov, Yu; Shishova, M. F. (2007). "Phytohormones in algae". Russian Journal of Plant Physiology. 54 (2): 163–170. doi:10.1134/s1021443707020021. - "Gibberellin formation in microorganisms". Plant Growth Regulation. 15: 303–314. doi:10.1007/BF00029903. - Srivastava, L. M. (2002). Plant growth and development: hormones and environment. Academic Press. p. 140. ISBN 0-12-660570-X. - Öpik, Helgi; Rolfe, Stephen A.; Willis, Arthur John; Street, Herbert Edward (2005). The physiology of flowering plants (4th ed.). Cambridge University Press. p. 191. ISBN 978-0-521-66251-2. - Swarup R, Perry P, Hagenbeek D, et al. (July 2007). "Ethylene upregulates auxin biosynthesis in Arabidopsis seedlings to enhance inhibition of root cell elongation". Plant Cell. 19 (7): 2186–96. doi:10.1105/tpc.107.052100. PMC . PMID 17630275. - Srivastava 2002, p. 143 - Weier, Thomas Elliot; Rost, Thomas L.; Weier, T. Elliot (1979). Botany: a brief introduction to plant biology. New York: Wiley. pp. 155–170. ISBN 0-471-02114-8. - Feurtado JA, Ambrose SJ, Cutler AJ, Ross AR, Abrams SR, Kermode AR (February 2004). "Dormancy termination of western white pine (Pinus monticola Dougl. Ex D. Don) seeds is associated with changes in abscisic acid metabolism". Planta. 218 (4): 630–9. doi:10.1007/s00425-003-1139-8. PMID 14663585. - Ren H, Gao Z, Chen L, et al. (2007). "Dynamic analysis of ABA accumulation in relation to the rate of ABA catabolism in maize tissues under water deficit". J. Exp. Bot. 58 (2): 211–9. doi:10.1093/jxb/erl117. PMID 16982652. - Else M.A.; Coupland D.; Dutton L.; Jackson M.B. (January 2001). "Decreased root hydraulic conductivity reduces leaf water potential, initiates stomatal closure, and slows leaf expansion in flooded plants of castor oil (Ricinus communis) despite diminished delivery of ABA from the roots to shoots in xylem sap". Physiologia Plantarum. 111 (1): 46–54. doi:10.1034/j.1399-3054.2001.1110107.x. - Yan J, Tsuichihara N, Etoh T, Iwai S (October 2007). "Reactive oxygen species and nitric oxide are involved in ABA inhibition of stomatal opening". Plant Cell Environ. 30 (10): 1320–5. doi:10.1111/j.1365-3040.2007.01711.x. PMID 17727421. - Kermode AR (December 2005). "Role of Abscisic Acid in Seed Dormancy". J Plant Growth Regul. 24 (4): 319–344. doi:10.1007/s00344-005-0110-2. - Osborne, Daphné J.; McManus, Michael T. (2005). Hormones, signals and target cells in plant development. Cambridge University Press. p. 158. ISBN 978-0-521-33076-3. - Classification of auxin related compounds based on similarity of their interaction fields: Extension to a new set of compounds Tomic, S.1,2, Gabdoulline, R.R.1, Kojic-Prodic, B.2 and Wade, R.C.11 European Molecular Biology Laboratory, 69012 Heidelberg, Germany 2Institute Rudjer Boskovic, HR-10000 Zagreb, Croatia - Walz A, Park S, Slovin JP, Ludwig-Müller J, Momonoki YS, Cohen JD (February 2002). "A gene encoding a protein modified by the phytohormone indoleacetic acid". Proc. Natl. Acad. Sci. U.S.A. 99 (3): 1718–23. Bibcode:2002PNAS...99.1718W. doi:10.1073/pnas.032450399. PMC . PMID 11830675. - Sipes DL, Einset JW (August 1983). "Cytokinin stimulation of abscission in lemon pistil explants". J Plant Growth Regul. 2 (1–3): 73–80. doi:10.1007/BF02042235. - Wang Y, Liu C, Li K, et al. (August 2007). "Arabidopsis EIN2 modulates stress response through abscisic acid response pathway". Plant Mol. Biol. 64 (6): 633–44. doi:10.1007/s11103-007-9182-7. PMID 17533512. - Grennan, Aleel K (2006). "Gibberellin Metabolism Enzymes in Rice". Plant Physiology. 141 (2): 524–6. doi:10.1104/pp.104.900192. PMC . PMID 16760495. - Tsai F-Y.; Lin C.C.; Kao C.H. (January 1997). "A comparative study of the effects of abscisic acid and methyl jasmonate on seedling growth of rice". Plant Growth Regulation. 21 (1): 37–42. doi:10.1023/A:1005761804191. - Grove, M. D.; Spencer, G. F.; Rohwedder, W. K.; Mandava, N.; Worley, J. F.; Warthen, J. D.; Steffens, G. L.; Flippen-Anderson, J. L.; Cook, J. C. (1979). "Brassinolide, a plant growth-promoting steroid isolated from Brassica napus pollen". Nature. 281 (5728): 216–217. Bibcode:1979Natur.281..216G. doi:10.1038/281216a0. - Lindsey, Keith; Casson, Stuart; Chilley, Paul. (2002). "Peptides:new signalling molecules in plants". Trends in Plant Science. 7 (2): 78–83. doi:10.1016/S0960-9822(01)00435-3. PMID 11832279. - Shapiro AD (2005) Nitric oxide signaling in plants. Vitam Horm. 2005;72:339-98. - Roszer T (2012) Nitric Oxide Synthesis in the Chloroplast. in: Roszer T. The Biology of Subcellular Nitric Oxide. Springer New York, London, Heidelberg. ISBN 978-94-007-2818-9 - Gomez-Roldan V, Fermas S, Brewer PB, et al. (September 2008). "Strigolactone inhibition of shoot branching". Nature. 455 (7210): 189–94. Bibcode:2008Natur.455..189G. doi:10.1038/nature07271. PMID 18690209. - Chiwocha, Sheila D. S.; Dixon, Kingsley W.; Flematti, Gavin R.; Ghisalberti, Emilio L.; Merritt, David J.; Nelson, David C.; Riseborough, Julie-Anne M.; Smith, Steven M.; Stevens, Jason C. (2009-10-01). "Karrikins: A new family of plant growth regulators in smoke". Plant Science. 177 (4): 252–256. doi:10.1016/j.plantsci.2009.06.007. - Fingrut O, Flescher E (April 2002). "Plant stress hormones suppress the proliferation and induce apoptosis in human cancer cells". Leukemia. 16 (4): 608–16. doi:10.1038/sj.leu.2402419. PMID 11960340. - The Seed Biology Place — Seed Dormancy - Another quality guide - Simple plant hormone table with location of synthesis and effects of application — this is the format used in the descriptions at the ends of the Wikipedia articles on individual plant hormones. - Hormonal Regulation of Gene Expression and Development — Detailed intro including genetic information.
3.4 Trade Controls - Describe the ways in which governments and international bodies promote and regulate global trade. The debate about the extent to which countries should control the flow of foreign goods and investments across their borders is as old as international trade itself. Governments continue to control trade. To better understand how and why, let’s examine a hypothetical case. Suppose you’re in charge of a small country in which people do two things—grow food and make clothes. Because the quality of both products is high and the prices are reasonable, your consumers are happy to buy locally made food and clothes. But one day, a farmer from a nearby country crosses your border with several wagonloads of wheat to sell. On the same day, a foreign clothes maker arrives with a large shipment of clothes. These two entrepreneurs want to sell food and clothes in your country at prices below those that local consumers now pay for domestically made food and clothes. At first, this seems like a good deal for your consumers: they won’t have to pay as much for food and clothes. But then you remember all the people in your country who grow food and make clothes. If no one buys their goods (because the imported goods are cheaper), what will happen to their livelihoods? Will everybody be out of work? And if everyone’s unemployed, what will happen to your national economy? That’s when you decide to protect your farmers and clothes makers by setting up trade rules. Maybe you’ll increase the prices of imported goods by adding a tax to them; you might even make the tax so high that they’re more expensive than your homemade goods. Or perhaps you’ll help your farmers grow food more cheaply by giving them financial help to defray their costs. The government payments that you give to the farmers to help offset some of their costs of production are called subsidies. These subsidies will allow the farmers to lower the price of their goods to a point below that of imported competitors’ goods. What’s even better is that the lower costs will allow the farmers to export their own goods at attractive, competitive prices. The United States has a long history of subsidizing farmers. Subsidy programs guarantee farmers (including large corporate farms) a certain price for their crops, regardless of the market price. This guarantee ensures stable income in the farming community but can have a negative impact on the world economy. How? Critics argue that in allowing American farmers to export crops at artificially low prices, U.S. agricultural subsidies permit them to compete unfairly with farmers in developing countries. A reverse situation occurs in the steel industry, in which a number of countries—China, Japan, Russia, Germany, and Brazil—subsidize domestic producers. U.S. trade unions charge that this practice gives an unfair advantage to foreign producers and hurts the American steel industry, which can’t compete on price with subsidized imports. Whether they push up the price of imports or push down the price of local goods, such initiatives will help locally produced goods compete more favorably with foreign goods. Both strategies are forms of trade controls—policies that restrict free trade. Because they protect domestic industries by reducing foreign competition, the use of such controls is often called protectionism. Though there’s considerable debate over the pros and cons of this practice, all countries engage in it to some extent. Before debating the issue, however, let’s learn about the more common types of trade restrictions: tariffs, quotas, and, embargoes. Tariffs are taxes on imports. Because they raise the price of the foreign-made goods, they make them less competitive. The United States, for example, protects domestic makers of synthetic knitted shirts by imposing a stiff tariff of 32.5 percent on imports (Insider Online, 2009). Tariffs are also used to raise revenue for a government. Shoe imports are worth $2 billion annually to the federal government (Carney, 2011). A quota imposes limits on the quantity of a good that can be imported over a period of time. Quotas are used to protect specific industries, usually new industries or those facing strong competitive pressure from foreign firms. U.S. import quotas take two forms. An absolute quota fixes an upper limit on the amount of a good that can be imported during the given period. A tariff-rate quota permits the import of a specified quantity and then adds a high import tax once the limit is reached. Sometimes quotas protect one group at the expense of another. To protect sugar beet and sugar cane growers, for instance, the United States imposes a tariff-rate quota on the importation of sugar—a policy that has driven up the cost of sugar to two to three times world prices (Edwards, 2007). These artificially high prices push up costs for American candy makers, some of whom have moved their operations elsewhere, taking high-paying manufacturing jobs with them. Life Savers, for example, were made in the United States for ninety years but are now produced in Canada, where the company saves $10 million annually on the cost of sugar (Will, 2004). An extreme form of quota is the embargo, which, for economic or political reasons, bans the import or export of certain goods to or from a specific country. The United States, for example, bans nearly every commodity originating in Cuba. A common political rationale for establishing tariffs and quotas is the need to combat dumping: the practice of selling exported goods below the price that producers would normally charge in their home markets (and often below the cost of producing the goods). Usually, nations resort to this practice to gain entry and market share in foreign markets, but it can also be used to sell off surplus or obsolete goods. Dumping creates unfair competition for domestic industries, and governments are justifiably concerned when they suspect foreign countries of dumping products on their markets. They often retaliate by imposing punitive tariffs that drive up the price of the imported goods. The Pros and Cons of Trade Controls Opinions vary on government involvement in international trade. Some experts believe that governments should support free trade and refrain from imposing regulations that restrict the free flow of goods and services between nations. Others argue that governments should impose some level of trade regulations on imported goods and services. Proponents of controls contend that there are a number of legitimate reasons why countries engage in protectionism. Sometimes they restrict trade to protect specific industries and their workers from foreign competition—agriculture, for example, or steel making. At other times, they restrict imports to give new or struggling industries a chance to get established. Finally, some countries use protectionism to shield industries that are vital to their national defense, such as shipbuilding and military hardware. Despite valid arguments made by supporters of trade controls, most experts believe that such restrictions as tariffs and quotas—as well as practices that don’t promote level playing fields, such as subsidies and dumping—are detrimental to the world economy. Without impediments to trade, countries can compete freely. Each nation can focus on what it does best and bring its goods to a fair and open world market. When this happens, the world will prosper. Or so the argument goes. International trade hasn’t achieved global prosperity, but it’s certainly heading in the direction of unrestricted markets. - Because they protect domestic industries by reducing foreign competition, the use of controls to restrict free trade is often called protectionism. - Though there’s considerable debate over protectionism, all countries engage in it to some extent. - Tariffs are taxes on imports. Because they raise the price of the foreign-made goods, they make them less competitive. - Quotas are restrictions on imports that impose a limit on the quantity of a good that can be imported over a period of time. They’re used to protect specific industries, usually new industries or those facing strong competitive pressure from foreign firms. - An embargo is a quota that, for economic or political reasons, bans the import or export of certain goods to or from a specific country. - A common rationale for tariffs and quotas is the need to combat dumping—the practice of selling exported goods below the price that producers would normally charge in their home markets (and often below the costs of producing the goods). - Some experts believe that governments should support free trade and refrain from imposing regulations that restrict the free flow of products between nations. - Others argue that governments should impose some level of trade regulations on imported goods and services. Because the United States has placed quotas on textile and apparel imports for the last thirty years, certain countries, such as China and India, have been able to export to the United States only as much clothing as their respective quotas permit. One effect of this policy was spreading textile and apparel manufacture around the world and preventing any single nation from dominating the world market. As a result, many developing countries, such as Vietnam, Cambodia, and Honduras, were able to enter the market and provide much-needed jobs for local workers. The rules, however, have changed: as of January 1, 2005, quotas on U.S. textile imports were eliminated, permitting U.S. companies to import textile supplies from any country they choose. In your opinion, what effect will the new U.S. policy have on each of the following groups: 1. Firms that outsource the manufacture of their apparel 2. Textile manufacturers and workers in the following countries: - United States 3. American consumers Carney, J., “The Affordable Footwear Act Is a Real Thing,” CNBC NetNet, June 1, 2011, http://www.cnbc.com/id/43239340/The_Affordable_Footwear_Act_Is_a_Real_Thing. Edwards, C., “The Sugar Racket,” CATO Institute, Tax and Budget, June 2007, http://www.cato.org/pubs/tbb/tbb_0607_46.pdf (accessed August 24, 2011). Insider Online, “The Protectionist Swindle: How Trade Barriers Cheat the Poor and Middle Class,” Insider Online, December 1, 2009, http://www.insideronline.org/feature.cfm?id=270 (accessed August 24, 2011). Will, G., “Sugar Quotas Produce Sour Results,” Detroit News, February 13, 2004, http://www.detnews.com/2004/editorial/0402/15/all-62634.htm (accessed October 17, 2004).
Titration is a well-established analysis technique taught to each and every chemistry student. Titration is carried out in nearly every analytical laboratory either as manual titration, photometric titration, or potentiometric titration. In this blog entry, I would like to present an additional kind of titration you may not have heard of before – thermometric titration – which can be considered the missing piece of the titration puzzle. Here, I plan to cover the following topics: - What is thermometric titration? - Why consider thermometric titration? - Practical application examples What is thermometric titration? At first glance, thermometric titration (TET) looks like a normal titration and you won’t see much (or any) difference from a short distance. The differences compared to potentiometric titration are in the details. TET is based on the principal of enthalpy change (ΔH). Each chemical reaction is associated with a change in enthalpy which in turn causes a temperature change. During a titration, analyte and titrant react either exothermically (increase in temperature) or endothermically (decrease in temperature). During a thermometric titration, the titrant is added at a constant rate and the change in temperature caused by the reaction between analyte and titrant is measured. By plotting the temperature versus the added titrant volume, the endpoint can be determined by a break within the titration curve. Figure 1 shows idealized thermometric titration curves for both exothermic and endothermic situations. Figure 1. Illustration of exothermic and endothermic titration curves showing clear endpoints where the temperature of the solution changes abruptly. What happens during a thermometric titration? During an exothermic titration reaction, the temperature increases with the titrant addition as long as analyte is still present. When all analyte is consumed, the temperature decreases again as the solution equilibrates with the atmospheric temperature and/or due to the dilution of the solution with titrant (Figure 1, left graph). This temperature decrease results in an exothermic endpoint. On the contrary, for an endothermic titration reaction, the temperature decreases with the titrant addition as long as analyte is still available. When all analyte is consumed, the temperature stabilizes or increases again as the solution equilibrates with the atmospheric temperature and/or due to the dilution of the solution with titrant (Figure 1, right graph). This temperature decrease results in an endothermic endpoint. Knowing the absolute temperature, isolating the titration vessel, or thermostating the titration vessel is thus not required for the titration. Figure 2. Metrohm’s maintenance-free Thermoprobe used for the reliable indication of thermometric endpoints. In order to measure the small temperature changes during the titration, a very fast responding thermistor with a high resolution is required. These sensors are capable of measuring temperature differences of less than 0.001 °C, and allow the collection of a measuring point every 0.3 seconds (Figure 2). Visit the Metrohm website to learn more about the fast, sensitive Thermoprobe products available even for aggressive sample solutions. If you would like to learn more about the theory behind TET, then download our free comprehensive monograph on thermometric titration. Why consider thermometric titration? Potentiometric and photometric titration are already well established as instrumental titration techniques, so why should one consider thermometric titration instead? TET has the same advantages as any instrumental titration technique: - Inexpensive analyses: Titration instruments are inexpensive to purchase and do not have high running and maintenance costs compared to other instruments for elemental analysis (e.g., HPLC or ICP-MS). - Absolute method: Titration is an absolute method, meaning it is not necessary to frequently calibrate the system. - Versatile use: Titration is a universal method, which can be used to determine many different analytes in various industries. - Easy to automate: Titration can be easily automated, increasing reproducibility and efficiency in your lab. In comparison to classical instrumental titration, thermometric titration has several additional advantages: - Fast titrations: Due to the constant titrant addition, thermometric titrations are very fast. Typically, a thermometric titration takes 2–3 minutes. - Single sensor: Regardless of the titration reaction (e.g., acid-base, redox, precipitation, …), the same sensor (Thermoprobe) can be used for all of them. - Maintenance-free sensor: Additionally, the Thermoprobe is maintenance free. It requires no calibration or electrolyte filling and can simply be stored dry. - Less solvent: Typically, thermometric titrations use 30 mL of solvent or even less. The small amount of solvent ensures that the dilution is minimized, and the enthalpy changes can be detected reliably. As a side benefit, less waste is produced. - Additional titrations possible: Because enthalpy change is universal for any chemical reaction, thermometric titration is not bound to finding a suitable color indicator or indication electrode. This allows the possibility of additional titrations which cannot be covered by other kinds of titration. - Easier sample preparation: As TET uses higher titrant concentrations it is possible to use larger sample sizes, reducing weighing and dilution errors. Tedious sample preparation steps such as filtration can be omitted as well. Learn more about the 859 Titrotherm system for the most reliable TET determinations on the Metrohm website. Practical application examples In this section I would like to present you some practical examples where TET can be applied. Acid number and base number The acid number (AN) and base number (BN) are two key parameters in the petroleum industry. They are determined by a nonaqueous acid-base titration using KOH or HClO4, respectively, as titrant. During such determinations, very weak acids (for AN analysis) and bases (for BN analysis) are titrated with only small enthalpy changes. Using a catalytic indicator, these weak acids and bases can also be determined by TET. ASTM D8045 describes the analysis of the AN by thermometric titration. The benefits of carrying out this titration are: - Less solvent (30 mL instead of 60 or 120 mL), meaning less waste - Fast titration (1–3 minutes) - No conditioning of the sensor Using conventional titration, the salt content in foodstuff is usually determined based solely on the chloride content. However, foods usually contain additional sources of sodium, e.g. monosodium glutamate (also known as «MSG»). With TET it becomes possible to titrate the sodium directly, and thus to inexpensively determine the true sodium content in foodstuff, as stipulated in several countries. If you wish to learn more about the sodium determination, watch our Metrohm LabCast video: «Sodium determination in food: Fast and direct thanks to thermometric titration». For more detailed information on the titration itself, download the free Application Bulletin AB-298 here. Fertilizers consists of various nutrients, including phosphorus, nitrogen, and potassium, which are important for plant growth. TET enables the analysis of these nutrients by employing classical gravimetric reactions as the basis for the titration (e.g., precipitation of sulfate with barium). This allows for a rapid determination, without needing to wait hours for a result, as with conventional procedures based on drying and weighing the precipitate. Nutrients which can be analyzed by TET include: - Ammoniacal nitrogen - Urea nitrogen Metal-organic compounds, such as Grignard reagents or butyl lithium compounds, are used for synthetizing active pharmaceutical ingredients (APIs) or manufacturing polymers such as polybutadiene. With TET, the analysis of these sensitive species can be performed rapidly and reliably by titrating them under inert gas with 2-butanol. - TET is an alternative titration method based on enthalpy change - A fast and sensitive Thermoprobe is used to determine exothermic and endothermic endpoints - Thermometric titration is a fast analysis technique providing results in less than 3 minutes - Thermometric titration can be used for various analyses, including titrations which cannot be performed otherwise (e.g., sodium determination) I hope this overview has given you a better idea about thermometric titration – the missing piece of the titration puzzle. For more information Download our free Monograph: Practical thermometric titrimetry Post written by Lucia Meier, Technical Editor at Metrohm International Headquarters, Herisau, Switzerland.
Image Representation in Computer Graphics Image Representation: In computer science, we can represent an image in various forms. Most of the time, it refers to the way that brings information, such as color is coded digitally, and how the image is stored, i.e., how an image file is structured. Several open standards were recommended to create, manipulate, store, and exchange digital images. The rules described the format of image files, the algorithms of image encoding, the form of additional information often named as metadata. A digital image is the composition of individual pixels or picture elements. The pixels are arranged in the form of row and column to form a picture area. The number of pixels in an image is a function of the size of the image and number of pixels per unit length (e.g., inch) in horizontal as well as vertical direction. It is a method to implement some operations on an image. It is also used to get an enhanced image or to access some useful information from an image. It is a type of processing in which the input is an image, and output may be the image or characteristics/features correlated with that image. For example- photographs, frames of video. Most image processing techniques consider the image as a two-dimensional and applying standard signal-processing technique on it. Pixel: “Pixel is the smallest unit of a picture displayed on the computer screen.” A pixel includes its own:- - Name or Address The size of the image is defined as the total number of pixels in the horizontal direction times the total number of pixels in the vertical direction (512 x 512,640 x 480, or 1024 x 768). The ratio of an image’s width to its height, we can measure it in unit length or number of pixels, is known as the aspect ratio of the image. For example- A 2 x 2inch image and a 512 x 512 image have an aspect ratio of 1/1, whereas a 6 x 4inch image and a 1024 x 768 image have an aspect ratio of 4/3. Resolution: It is the number of separate pixels display on a screen expressed in terms of pixels on the horizontal axis and vertical axis. The sharpness of the picture on display depends on the resolution and the size of the monitor. “The number of pixels per unit is called the resolution of the image.” It also includes- - Image Resolution: “The distance between two pixels.” - Screen Resolution: “The number of horizontal and vertical pixels displayed on the screen is called Screen Resolution.” For Example- 640 x 480, 1024 x 768 (Horizontal x Vertical) Aspect Ratio: “The ratio of image’s width to its height is known as the aspect ratio of an image.” The height and width of an image are measured in length or number of pixels. For Example: If a graphics has an aspect ratio of 2:1, it means the width is twice large to height. - Frame aspect ratio: Horizontal /Vertical Size - Pixel aspect ratio: Width of Pixel/Height of Pixel Applications of Image Processing Some application areas of Image Processing are as follow: - Computerized Photography - Space Image Processing (e.g., Hubble space telescope image, Interplanetary probe images) - Medical/ Biological Image Processing - Automatic Character Recognition - Fingerprint/ Face/ Iris Recognition - Remote sensing - Industrial application Format of Image Files There are some different type of images which are mentioned as: - JPEG (Joint Photographic Experts Group): It is used for digital images, especially for those images which are composed of digital photography. The ‘.jpeg’ filename extension is used to save the file. - PNG (Portable Network Graphics): These files are commonly used to store graphics for web images. PNG was developed to enhance the non-registered replacement for Graphics Interchange Format. The ‘.png’ filename extension is used to save the file. - GIF (Graphics Interchange Format): It is a file format for storing graphical images up to 256 colors. PNG is based on a lossless compression method, which makes higher quality output. PNG was created as a more powerful option to the GIF file format. The ‘.gif’ filename extension is used to save the file. - TIFF/ TIF (Tagged Image File): These files can be saved in a collection of color formats and many forms of compression. TIFF file is used to maintain image integrity and clarity. It is often used for professional photography. The ‘.tif’ filename extension is used to save the file. - PSD (Photoshop Document): It is a layered image file used in Adobe PhotoShop. It is a default format that is used by PhotoShop for saving data. PSD is a custody file that allows the user to work with the images' separate layers even after the file has been saved. The ‘.psd’ filename extension is used to save the file. - PDF (Portable Document Format): It is used to share the documents between computers and across operating system platforms when the user needs to save files that cannot be altered. The ‘.pdf’ filename extension is used to save the file. - EPS (Encapsulated Postscript): It is a graphics file format, which is used in vector-based images. In Windows, the user needs graphics software to open the EPS file (i.e., Adobe Illustrator, Coral Draw). The ‘.eps’ filename extension is used to save the file. - AI (Adobe Illustrator Document): It is a file format developed by Adobe system. It is used to represent single-page vector-based drawings in EPS or PDF formats. The ‘.ai’ filename extension is used to save the file. - Homogenous Coordinates in Computer Graphics - Filled Area Primitives Computer Graphics - Scan Conversion in Computer Graphics - Bresenham’s Line Drawing Algorithm in Computer Graphics - Line Drawing Algorithm in Computer Graphics - DDA line Drawing Algorithm in Computer Graphics - Polygon Clipping in Computer Graphics - Line Clipping in Computer Graphics - Clipping in Computer Graphics - 3D Rotation in Computer Graphics
Presentation on theme: "Goal: To learn about Forces"— Presentation transcript: 1Goal: To learn about Forces Objectives:To explore the basics of force and Newton’s first lawTo learn about weight and compare to massTo learn about the Normal forceTo learn about frictional forceTo learn about TensionTo learn about force vectors and net force 2Newton’s First LawAn object in rest or in motion will stay in rest or in motion until acted upon by an outside forceThis is called the law of inertiaIn other words, to change an objects motion (and you can consider at rest a “motion”) you have to do something to it 3Force There are many different forces in the universe. The main 4 are: A) GravityB) ElectromagneticC) StrongD) Weak 4Force is a VECTOR Force is a vector Force has DIRECTION! Force ALWAYS has directionSo, the units of force are Newton directionNewton is NSo, a force could be +3 N up, +2 N down, N forward, N north, ect 5Something we will look at in this class: Gravity near the surface of the Earth.Near the surface of the Earth the force of gravity is fairly straightforwardGravity force = mgIf there are no other vertical forces (other than a Normal force) then the gravity force is the WeightNote that Weight is a FORCE 6Questions 1) What is the unit(s) of Weight? 2) g = 9.8 m/s2 does it have a direction? 7Weight vs MassOn the Earth I have a mass of about 90 kg and a weight of about 205 lbs (880 Newtons).On the moon gravity is 1/6th what it is on the earth.What is my mass and weight on the moon? 8Normal ForceAnytime you contact something there is a Normal Force (Newton’s 3rd law, equal and opposite force)The normal force is the force that pushes you away from a surface and is perpendicular to the plane of that surface.What would happen if you stood on a surface that had no normal force? 9How to find the normal force Find the sum of all the non normal forces.If the object is not moving in the vertical direction (that means there is no total force – which we call a net force) then the normal force is the force needed to cancel out all the other forces.So, if there is just gravity, then the normal force is equal to the weight.If I pull up on something then the normal is less because the total downward force (and up force is effectively a negative down) is less.If I push down then the normal force increases. 10Friction One force you are probably familiar with is friction. Friction is always a force that opposes motion – that is the direction is opposite the direction of motion.There are actually two type of frictional forces.The first is called Static Friction 11Static FrictionStatic Friction is caused because on a microscopic level nothing is perfectly smooth.The bumps and pits of the two objects touching makes things rub and rip off small pieces.This takes energy to do which causes the static friction. 12Kinetic FrictionOnce an object starts to slide across another object it now glides over the top of the bumps and pits.As a result the force of friction is cut in half.A tire is stationary on the ground normally. If a tire slides you loose friction and you loose control. 13Friction Equation F = μ N I am 90 kg. I walk down a sidewalk which has a frictional coefficient of 0.2A) Find my normal forceB) What is the frictional force on meC) What force do my legs need to exert to keep myself walking at a constant velocity and how do you use Newton’s First Law to determine this? 14Tension Forces provided by strings or wires are called Tensions. The Tension in a wire is similar to the normal force except that it pulls an object towards it instead of pushing away.To find tension either:A) compare the total force to all the forces exerted on the string. The difference will be the tension of the string.B) find the force the string is exerting on something else 15Tension exampleA 10 kg mass is tied to the end of a string and allowed to hang.A person pulls down on the string with a force of 150 N.A) What is the tension of the string if the mass does not move (Hint, Newton’s first law)? 16Force VectorsIn reality forces will often times have components in more than 1 dimension.This creates a vector.In order to solve for problems where you have forces in more than 1 dimension you need to create 2 accounts, that is 2 problems that are separate from one another.This is similar to having a checking account and a savings account. 17Calculator noteEveryone use their calculators to find the answer to the following problem (even if you can do this one in your head):(2 * 6) / (3 * 4) 18Vector Break downSince the 2 components will be 90 degrees from each other you can use the following to find each component.Lets call the total force FtThe opposite leg in our right triangle has a length of: Ft sin(theta) where theta is the angleAdjacent is: Ft cos(theta)Finally tan(theta) = Opposite / Adjacent 19One way to remember which is which Sin(0 degrees) = 0So, ask yourself would this value be 0 if the angle is 0? If the answer is yes then use sineCos(0 degrees) = 1Ask yourself, if the angle was 0 would the total force be just this force? If the answer is yes then use the cosine. 20Adding Force vectorsOnce you break a force into its components (for this class we will often use x and y) now you are ready to add them.The x’s add to the x’s because the x direction is a UNIT!Same for the y’s because the y’s are a UNITIf you need a magnitude at the end, which you may for the homework then once you have the total x and total y you can use the Pythagorean Theorem.However, as we get further along we will treat the x and y as separate problems and may have to solve for 1 to get the other. 21Net ForceOnce you add up all the vectors for all the forces you have what is called the Net ForceThe Net Force will determine how the objects motion is changedNote that the Net Force is a vector.It can have x and y components – and if any are non-zero, then its motion in that direction will change.Meanwhile in any direction that the net force is exactly zero the motion in that direction will be constant (even if the motion is zero). 22Net Force Net Force = sum of all forces Net Force = mass * net accelerationFor example, if you have vertical forces, and need to solve the net force, find the net force from mass * net accelerationThen, plug that answer into Net Force = sum of all forces so that you can solve for the Normal force 23Your turn!The 3 Stooges decide to open a moving company and someone is crazy enough to hire them.The 3 are moving a rather large box by pushing it across the floor.Luckily the floor is slippery due to all the banana peals that…. Well that is another show. Anyhow, no frictionLarry pushes on the box from behind. He pushes at an angle 30 degrees below the vertical with a force of 200 N.Curly (who has a mass of 70 kg) sits on the box. Not much help there…Mo pulls on the box at a 45 degree angle with a force of 350 N.The box has a mass of 50 kg.A) What is the net force on the box in the vertical direction (call this the y direction)? Hint, will the box lift off the ground?B) What is the normal force on the box (and no it is not = mg)?C) What is the net force on the box? 24Conclusion We have learned about force. We have learned how to compute gravitational forceWe have learned how to find a normal force.We have learned how to use that normal force to find the frictional forceWe have learned how to find tensionWe have learned how to turn Forces into vectors and add those vectors to create a net force.
THE CO2 DEBATE The discussion and analysis here should be readily understood by most readers, but some of the theory and interpretation behind the discussion might require some understanding of relatively low-level chemistry. The stable forms of carbon at the Earth’s surface are: carbon dioxide CO2, bicarbonate ions in solution HCO3-, carbonates (calcite, limestone etc). These three are the most oxidised and therefor the most stable forms of carbon at the Earth's well-oxygenated surface. Other forms of unstable carbon are more reduced and include methane (CH4), carbon monoxide (CO), elemental carbon it self, and living matter. All of these will ultimately oxidise to one of the more oxidised variants in the presence of an oxygenated atmosphere. CO2 is the most oxidised form of carbon, forming a stable relatively inert gas in the atmosphere (currently just over 400 ppm). Bicarbonate (HCO3-), is the stable form dissolved in water, which contains 60 times more abundant CO2 than does the atmosphere. Carbonates are the stable solid form, mainly as calcite (CaCO3 or limestone) and dolomite (CaMg(CO3)2 another form of limestone). Limestones are 44% CO2 by weight and form a major rock type, often entire mountain ranges. More than 99% of all the CO2 component formerly in the Earth’s early atmosphere is now locked up in carbonate rock. Certain trace gases in the atmosphere are thought to maintain the Earth’s temperature at a fairly constant level. These gases are called greenhouse gases & have the effect of preventing incoming visible radiation escaping as infrared radiation. The trapped radiation wave lengths heat up the atmosphere at the surface, but only to a limited extent, dropping off dramatically as their abundance increases (see later comments). The mean global temperature of the Earth is a warm 15 degrees C . Without these greenhouse gases, all infrared radiation would be lost to space and the global Earth temperature would be considerably lower overall with hot days and very cold nights. Without the atmosphere the Earth’s mean surface temperature would be -18 degrees, rather than the present average of 15 degrees. Variations in greenhouse gases are thought to influence climate, & in the present climate debate CO2 is the greenhouse gas of principal concern. The main greenhouse gases, their abundance, their thermal influences & the contribution by man are presented in the following table. Ranking of greenhouse gases vs CO2 in terms of global heat generation capacity: GREEN HOUSE GAS Heat retention potential (multiple) Carbon Dioxide (CO2) 1 Chloroflourocarbons (CFC’s) 1,300 TO 9,300 Methane (CH4) 21 Nitrous oxide (N2O) 310 Water vapour (this does not include water droplets as in clouds) is a powerful greenhouse gas comprising about 95% of the greenhouse gas inventory & is by far the dominant influence, but does not contribute to what is called the enhanced greenhouse effect because it is not increasing in abundance. A runnaway greenshouse effect is said to occur when increasing greenshouse temperatures are enhanced by positive feedbacks in the environment that also generate more greenhouse components or other forms of atmospheric temperature increase, (eg increasing water vapour) thus accelerating and exacerbating the climatic effect. Positive feedbacks are generally more than compensated by buffering effects which act to minimise any change in systems at equilibrium. Pre industrial revolution levels 1750-1800 1990 levels CO2 280 ppm 353 ppm Methane 0.8 ppm 1.72 ppm CO2 dissolved in the ocean is some 60 times that in the atmosphere with more than 85% as bicarbonate ions (HCO3-). Human activity (fossil fuels & burning biomass), has caused much of the increase. Volcanic gases also produce large amounts of CO2. Burning all the fossil fuels in existence would produce an atmospheric CO2 level of around 2000 ppm. To halve the present levels would probably annihilate all terrestrial vegetation & animal life. Decreasing atmospheric CO2 would be far more disadvantageous than increasing it. Methane is sourced through rice cultivation, ruminating animals, coal mining, natural gas venting, & inefficient biomass oxidation. 95% of warming due to greenhouse gases comes from water vapour in the atmosphere (not water droplets as in clouds), and only 0.28% from human additions. Human activity accounts for about 6% of the non-water vapour component. Atmospheric CO2 levels over recent time, temperature cycle regularity and warming pulse rates The chart below displays the cyclical variations in atmospheric CO2 determined from ice core samples over the last 400,000 years, showing the ”hockey stick effect”, & the remarkable regularity of CO2 increases & reductions following 100, 000 year cycles. If CO2 causes temperature increases, what caused these regular cycles of increasing CO2 lasting about 100,000 years? If however the temperatures where cyclical (due to Milankovitch-cycle style planetary orbit, tilt and wobble variations), and the CO2 variations followed temperature changes (not driving them), this would account for this phenomena. A similar chart shows temperature data from Antarctic ice cores (EPICA C Dome) over the same time interval. The major warming peaks (indicated by the black arrows) are about 100,000 years apart and reflect about 8 degrees of warming. The present position on the larger zig-zag pattern suggests we are about to descend into a 100,000 year global cooling event, representing some 8-10 degrees of cooling. The much smaller peaks are some 1000 years apart and reflect 1-2 degrees of warming. The smaller peaks from the Greenland Ice Core data chart ( refer to the 10,000 year Greenland ice core GISP2 chart below), show 1-2 degree, warming over 100-200 years indicating a warming rate of around 1 degree per hundred years in keeping with present warming estimates for the current warming pulse determined elsewhere by climate science sources. The consistent warming slopes on these shorter cyclical warming pulses suggest that the warming rate it fairly consistent in these 1000 year events, whose regularity suggests a very short-term (1,000 year) minor orbital cyclicity perhaps not previously recognized. Some 10 major warming & cooling cycles in the GISP 2 Greenland ice core are scattered regularly over the last 10,000 year interglacial warming episodes. Calculating global temperatures & warming & cooling rates from Greenland ice core data for warming cycles over the last 10,000 years. The warming appears generally about 2 degrees over about 200-300 year warming event. Warming & cooling appear symmetrical at about 1 degree/100 years. Other significant CO2 and temperature versus time charts across all of geological time are presented and discussed in much more detail elsewhere in this web site. FACTS about CARBON DIOXIDE Of the over 200 billion tons of CO2 that enter earth's atmosphere each year from all sources. Human activities—mostly burning of coal and other fossil fuels, but also cement production, deforestation and other landscape changes—emitted roughly 40 billion metric tons of carbon dioxide in 2015. Approximately 90 billion tons come from biologic activity in earth's oceans and another 90 billion tons from such sources as volcanoes and decaying land plants. According to the U.S. Geological Survey (USGS), the world's volcanoes, both on land and undersea, generate about 200 million tons of carbon dioxide (CO2) annually, while our automotive and industrial activities cause some 24 billion tons of CO2 emissions every year worldwide: www.scientificamerican.com › article › earthtalks-volca.. At 382 parts per million, CO2 is a minor constituent of earth's atmosphere—less than 4/100ths of 1% of all gases present. Compared to former geologic times, earth's current atmosphere is CO2 impoverished. During the Ordovician-Silurian glaciation (450-420 million years ago), atmospheric CO2 was more than 4000 ppm, but did not contribute to any warming. During the Jurassic-Cretaceous glaciation (151-132 million years ago), atmospheric CO2 was more than 2000 ppm and again did not contribute to any warming. If CO2 drives climate, why were there glaciations and not a runaway greenhouse effects during these events? The effect of increasing levels of atmospheric CO2 on plant growth and animal health. The photo below shows a comparison of plant growth achieved in atmospheres of differing CO2 levels. This readily displays the fertilizer effect of increased levels of atmospheric CO2. The numbers in the photo's indicate the amount of additional CO2 that has been introduced into the atmosphere, and the numbers below the total atmospheric CO2 content in parts per million. The table and chart below display the dramatically decreasing greenhouse warming effect of increasing CO2 levels in an atmosphere, a point that is often lost when increasing CO2 levels are being discussed in the media. The data suggests that plants are seriously starved for adequate CO2 for healthy development and optimum growth in the present atmosphere and that significant agricultural productivity may be gained in this area if atmospheric CO2 levels can be substantially increased. Optimal levels of atmospheric CO2 may be around 1000 ppm for many plant species. At present plants find it difficult acquiring sufficient CO2 from the present very thin, CO2-depleted atmosphere. Plants exposed to higher levels of CO2, not only grow more vigorously , they require less water (less evapo-transpiration from smaller stomata required to get adequate CO2). They can grow in drier climates and produce higher yields on smaller acreages. Limiting growth factors such as higher usage of nutrients such as nitrogen, zinc, iron etc (as exist for today''s plants) can be accommodated, as they are today, with fertilizers, supplements and management practices. There are likely to be pros and cons, with increased CO2 levels, but plants developed and thrived under these conditions in the past, they don't need to adapt to new conditions, and they manage on less water and in drier conditions. Even the small man-made CO2 contributions over the last 50 years or so have dramatically greened the earth (see CSIRO global map below). The image below is derived from: Sherwood B Idso, President of the Centre for the study of carbon dioxide and global change. Research Physicist with the U.S. Department of Agriculture's Agricultural Research Service at the U.S. Water Conservation Laboratory in Phoenix, Arizona, where he worked since June 1967. His science citation record: as of July 2000, Dr. Idso’s research papers had been cited in the scientific literature in excess of 6,500 times, more than an order of magnitude above the norm for all scientists of that time period. CO2 & Human Health. CO2 is odorless, colorless, tasteless and slightly heavier than air. Plants absorb CO2 and emit oxygen as a waste product. Humans and animals breathe oxygen and emit CO2 as a waste product. Carbon dioxide is a nutrient, not a pollutant, and for all life, plants and animals alike it is an essential requirement. Atmospheric CO2 is an essential plant fertilizer not a toxin. All animals get their carbon from eating plants, or eating other animals that eat plants. The effect of increased atmospheric CO2 on humans appears minimal at any likely concentrations, even up to 1% (10,000 ppm). Human exhale CO2 at levels of around 38,000 ppm from their lungs, suggesting that even at these levels there is no serious toxicity as long as here is adequate oxygen available for normal respiration. Coral reefs and CO2 CO2 gets into the atmosphere originally through volcanic eruptions. Once in the atmosphere it is continually recycled by terrestrial plant life (through the process of photosynthesis), animal life, the earth's oceans (in the form of the bicarbonate ion, HCO3-), and eventually into calcite (limestones, coral reef structures, marine shells & skeletons), and carbon energy reservoirs of coal, petroleum & gas. The oceans contain more than 60 times as much CO2 as the atmosphere and are in equilibrium with marine limestone deposits. The great retirement home for most terrestrial carbon dioxide is in limestones (44% CO2 by weight), and they make up a considerable proportion of surface and subsurface rock sequences, including all the worlds coral reefs and entire mountain ranges in many parts of the world. Coral reefs are made of CO2 and would not exist without CO2. The coral organisms themselves derive all their cellular carbon from CO2 sourced from bicarbonate ions extracted from the oceans, but ultimately derived from he atmosphere. The carbonate forming chemical reactions depend on the two equilibrium reactions involved: (1) CO2 + H2O <----> HCO3- + H+ (acid) at the atmosphere-ocean interface (2) HCO3- + Ca2+ <----> CaCO3 + H+ (acid) occurring in shallow warm oceans The overall combined reaction is: (3) CO2 + H2O + Ca2+ <------> CaCO3 + 2H+ (acid) Note that although these reactions are equilibrium reactions, the equilibrium strongly favors the reactions moving the the right in each case and downward in the sequence through 1), to 2), and the ultimate removal of all CO2 from the atmosphere, and all HCO3- from the seas, to from voluminous limestone. Eventually all the world''s carbon and all the world's CO2 will end up in limestones, (see later section), and none will be available to maintain or form any life on Earth. Note also that for each molecule of calcite (CACO3) produced (or molecle of CO2 consumed), two hydrogen ions (H+, read acid) are produced, contributing to ocean acidification. Coral reefs themselves are responsible for much of the worlds oceans acidification, although no one is suggesting that we should eliminate coral reefs in order to reduce ocean acidification. Atmospheric CO2 when dissolving in the oceans to produce bicarbonate ions (HCO3- reaction 1 above), does increase ocean acidification, but the removal of bicarbonate ions to form coral reefs and other limestones (reaction 2 above) produces even more acid. CO2 in the oceans and ocean acidification There is about fifty to sixty times as much carbon dissolved in the oceans as exists in the atmosphere. The oceans act as an enormous carbon sink, and have taken up about a third of CO2 emitted by human activity. It has been estimated that the uptake of anthropogenic carbon since 1750 has led to the ocean becoming more acidic with an average decrease in pH of 0.1 units. No mention that coral reef formation as a major cause of ocean acidification, or that hundreds of millions of years when atmospheric CO2/acidification was much higher yet did not cause a problem. The pH of the ocean is around 8.0 (mildly alkaline). The introduction of hydrogen ions in the above reactions causes the ocean pH to lower and become less alkaline. It does not become more acid as the H+ ions immediately react with excess OH- ions and neutralize. Only when the pH is lowered below 7.0 will the ocean become acid and have an excess of H+ ions. Introducing H+ ions at pH 8.00 will make the ocean less corrosive (less caustic) and increasingly more neutral until pH 7.0 is reached. The use of the term ocean acidification is a misnomer until the pH drops below 7.0, which is unlikely in the present circumstances because there are enormous pH buffering reactions with geology (rocks), countering the lowering of pH to anywhere near pH 7. Another contributor to lowering the oceans pH is rainwater. Pure condensed water has a pH of 7.0, but rainwater has a pH between 5-6. Even compared to sea water, pure water is more acid, and rain water far more acid again. Every time fresh rainwater enters the Coal Sea from Queensland flood events it contributes substantially to ocean acidification of the reef environment. We never hear this being stated in ocean acidification discussions, or the fact that coral reef growth itself increases acidification. Many of the low-lying island nations concerned about rising oceans may not realize it but it is the continued growth of coral limestone and its essential CO2 component that formed their island nation in the first place and is keeping their island nations above sea level now and has been for centuries. The reactions above are ultimately responsible for all the worlds coral reefs, all the worlds limestones, dolomites and marble rock sequences including entire mountain ranges and landscapes, all the worlds carbonate shellfish, and all the worlds calcareous soils. Atmospheric CO2 and climate change Global warming began 18,000 years ago, accompanied by a steady rise in atmospheric carbon dioxide. The correlation of CO2 with temperature appears clearly demonstrated. But correlation does not always mean causation. What caused this phenomena is a matter of ongoing debate for some. Clearly, though, global warming and rising CO2 levels in Earth's atmosphere started long before the industrial revolution. In detail there are some surprising contradictions. Time lines (in the red ellipses in the diagram below), reveal that the relationships are not always synchronous or positive. In the highlighted red ellipses there are both positive and negative correlations between temperatures and CO2 levels which should not happen if CO2 is driving temperature. The warming rates are ten times the cooling rates and occur over much shorter periods. In the Vostok ice core data, if gain and loss of CO2 is the cause of warming and cooling, it is difficult to understand where the CO2 is coming from, and going to, in this period in the past on such regular cycles unless the cooling and warming episode came first and are followed by CO2 changes. The rapid warming rate versus the much lower cooling rate also is telling us something. In this instance it appears that if temperature increases first (due to orbital forcing), followed by a delayed change in atmospheric CO2, as CO2 is released (on warming), or reabsorbed (on cooling), in the ocean. This causes an additional feedback affect on temperature with two separate pulses of temperature resulting with a recognizable delay. The temperature should be seen to increase first, followed by an increase in CO2 and further temperature feedback. . However if CO2 levels increased first, temperatures should rise appropriate to the atmospheric CO2 concentration, (with some internal feedback) and a new equilibrium temperature would be eventually reached. There would not be two distinct pulses separated by a delay period. In this case the CO2 should be seen to increase first followed by temperature. Both this and the previous scenario can occur but should be distinguishable. It appears more likely that increasing temperature in the oceans causes increased levels of CO2 to form and to be released into the atmosphere. It is well known that increasing ocean temperatures decreases bicarbonate levels in the ocean (closer to the equator), favouring more CO2 in the atmosphere and more limestone production, while at the same time lower temperature towards the poles favour increasing CO2 solubility in the oceans as bicarbonate ions (HCO3-). This means that there is an atmospheric flow of CO2 from the equator to the poles, and a counter flow of bicarbonate ions in the ocean towards the equator. On approaching the equator, as the oceans warm, some bicarbonate converts to CO2 and escapes into the atmosphere to be recirculated, and some reacts with abundant soluble Ca2+ to be permanently removed from the system in the form of limestone, including coral reefs, according to the equilibrium chemical reactions listed earlier. Global CO2 and Temperature Across the Geological Time Scale The extremely revealing but rather busy chart below displays the relationship of both temperature (as seen on other charts) shown in red, and also atmospheric CO2 levels (in blue), across geological time. The relationship between CO2 levels and the temperature can be seen to be totally inconsistent, varying from being a positive association, to periods where it was entirely antipathetic. During the massive decrease in CO2 over time the mean global temperature has not changed significantly, largely remaining at about 20 degrees (a few degrees warmer than at present). This is yet another demonstration (if one was necessary) that atmospheric CO2 (man-made or otherwise) has not consistently influenced global temperature at any stage in Earth history despite a massive decrease (95% reduction) and did not pose and existential threat during that period. The reason that CO2 is rising is that atmospheric CO2 levels are now so low (having progressively naturally declined over 90% over earth history to present starvation levels), that the very low man-made CO2 contributions (of a few 10's of ppm/year), are now registering. This is an indication of how perilously low atmospheric CO2 actually is. We need to actively restore hugely beneficial CO2 levels by burning fossil fuels. Global vegetation is currently starved of adequate CO2 (around 1000 ppm), for optimum growth. This chart in particular and the other global temperature versus geological time charts displayed in this web site, completely contradict the popular climate change models advanced by climate alarmists where CO2 is purported to dive temperature. The man-induced atmospheric CO2 model appears to have arisen solely as there seemed no other possible explanation for observed warming. No one it seems amongst the cream of world climate science considered the possibility that it might be normal and reflected in the longer term climate history. A history that seems to have been entirely ignored . It appears that IPCC scientists and other climate catastrophists were either entirely ignorant of this information, that has been around for more than 40 years, or chose to ignore it and not reveal it. Either way it displays an appalling lack of quality science by some of the world's leading scientists who have claimed scientific purity and superiority on this issue, howling down those with contrary views for many years. The second chart below displays he dramatic decline in atmospheric CO2 over he last 140 million years, down some 90% over that interval and perilously approaching the 150 ppm survival threshold for vegetation. The decline is of the order to 2-3 ppm CO2 per million years. At this rate there may be only 200 million years of atmospheric CO2 remaining.
Computer Programming Basics Lesson Plan: Tynker Games Grade Levels: 3-5, 6-8, 9-12 In this computer programming basics lesson plan, which is adaptable for grades 3-12, students use BrainPOP resources (including online coding games) to learn about programming. Lesson Plan Common Core State Standards Alignments By the end of year, read and comprehend informational texts, including history/social studies, science, and technical texts, in the grades 4–5 text complexity band proficiently, with scaffolding as needed at the high end of the range. Interpret information presented visually, orally, or quantitatively (e.g., in charts, graphs, diagrams, time lines, animations, or interactive elements on Web pages) and explain how the information contributes to an understanding of the text in which it appears. By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 4–5 text complexity band independently and proficiently. Explain the relationships or interactions between two or more individuals, events, ideas, or concepts in a historical, scientific, or technical text based on specific information in the text. Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks; analyze the specific results based on explanations in the text. Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 11–12 texts and topics. Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., quantitative data, video, multimedia) in order to address a question or solve a problem. Synthesize information from a range of sources (e.g., texts, experiments, simulations) into a coherent understanding of a process, phenomenon, or concept, resolving conflicting information when possible. Grade: 06, 07, 08 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 6–8 texts and topics. Grade: 06, 07, 08 Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table). Grade: 09, 10 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text. Grade: 09, 10 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics. Grade: 09, 10 Analyze the structure of the relationships among concepts in a text, including relationships among key terms (e.g., force, friction, reaction force, energy). Grade: 09, 10 Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words. Preparation:BrainPOP's GameUp offers four interactive games from Tynker to teach students coding and computer programming: - Lost in Space: Students learn to drag function blocks together to build applications of increasing complexity that move an astronaut named Biff and his spaceship toward desired goals. As challenges get harder, students will learn to use logic skills to bundle commands and create algorithms. - Puppy Adventure: Students learn to drag function blocks together to build applications of increasing complexity in order to move a lost puppy named Pixel toward various desired goals. As challenges get harder, students will learn to properly bundle commands and create algorithms. The puzzles are designed to teach students about sequencing, repetition, and conditional logic. - Sketch Racer: Students program a turtle named Snap to mimic geometric shapes and follow set patterns. Each puzzle presents a pattern and a starting position for Snap. Students are required to program the turtle using the tile-based commands such as "move forward," "move backward," "turn to the left" and "turn to the right." Each puzzle may have a number of correct solutions, but players are encouraged to solve them using the fewest possible blocks. With Sketch Racer, students will learn about sequencing, repetition and algorithmic logic. They will need some prior knowledge of angles and geometry to successfully complete the puzzles. - 15 Blocks: Students create a simple computer app using no more than 15 blocks. The activity allows players to work with pre-loaded characters, backgrounds, and movements to create an animation that requires logic and creativity to build. Programming commands are based on the Tynker system of visual programming blocks, which simulate basic coding commands and processes. This lesson plan will help you determine how best to use these resources with your students. You may want to spread out the games and activities over the course of several days. - Play the BrainPOP movie Computer Programming to introduce students to the topic. If students have no background information on programming, you may want to have them complete the activities in our Program Your Partner lesson plan. - Tell students that they will have the chance to explore simple computer programming through four online games. Project the Lost in Space game, and demonstrate how to drag function blocks together to build applications. Introduce the term Logo and explain that it is a simple programming language. - Allow students to explore Lost in Space independently or with a partner for 10-15 minutes. - You can then introduce the Puppy Adventure game. We recommend briefly playing this first as a whole-class demonstration with student volunteers so you can reinforce vocabulary terms (such as 'commands' and 'algorithm') and ensure understanding. Then release students to try on their own. - After 10-15 minutes of game play with Puppy Adventure, have students compare and contrast the game with Lost in Space. How are the commands the same? Different? - Tell students they will now explore a game called Sketch Racer, in which they will program a turtle using the tile-based commands such as "move forward," "move backward," "turn to the left" and "turn to the right." You may want to quickly review students' prior knowledge of related geometry concepts with the BrainPOP Angles movie prior to replacing students to play the game. - Provide at least 10-15 minutes for students to explore Sketch Racer. Challenge students to find the solution that uses the fewest possible blocks. - Afterward, debrief with students on the three games they played and discuss their strategies. You can use the Computer Programming Quiz or any of the game quizzes to assess student learning. - For a cumulative assessment or final project, introduce students to the 15 Blocks game, which requires them to use their creativity as they build with pre-loaded characters, backgrounds, and movements. After they've had some time to experiment with the game, challenge students to pair up and think of their own programs. They can assign a specific program to their partner and challenge them to produce it. You can find more ideas for using this game in the 15 Blocks Lesson Plan. Filed as: 3-5, 6-8, 9-12, Ada Lovelace, Binary, Blended Learning, CCSS.ELA-Literacy.RI.4.10, CCSS.ELA-Literacy.RI.4.7, CCSS.ELA-Literacy.RI.5.10, CCSS.ELA-Literacy.RI.5.3 CCSS.ELA-Literacy.RST.11-12.3, CCSS.ELA-Literacy.RST.11-12.4, CCSS.ELA-Literacy.RST.11-12.7, CCSS.ELA-Literacy.RST.11-12.9, CCSS.ELA-Literacy.RST.6-8.4, CCSS.ELA-Literacy.RST.6-8.7, CCSS.ELA-Literacy.RST.9-10.3, CCSS.ELA-Literacy.RST.9-10.4, CCSS.ELA-Literacy.RST.9-10.5, CCSS.ELA-Literacy.RST.9-10.7, Coding, Computer Programming, Computer Science, Digital Animation, Gaming Lesson Plans, Hour of Code, Lesson Plan, Logic Gates, Science Games, Social Studies, Teacher Support, Tech Games, Technology, Tynker, Tynker: 15-Block Challenge, Tynker: Lost In Space, Tynker: Puppy Adventure, Tynker: Sketch Racer, Video Games
Researchers at the Georgia Institute of Technology have developed a concept that would make Martian rocket fuel, on Mars, that could be used to launch future astronauts back to Earth. Researchers measured the potassium isotope compositions of Martian meteorites in order to estimate the presence, distribution and abundance of volatile elements and compounds, including water, on Mars, finding that Mars has lost more potassium than Earth but retained more potassium than the Moon or the asteroid 4-Vesta; the results suggest that rocky planets with larger mass retain more volatile elements during planetary formation and that Mars and Mars-sized exoplanets fall below a size threshold necessary to retain enough water to enable habitability and plate tectonics. Transporting a single brick to Mars can cost more than a million British pounds – making the future construction of a Martian colony seem prohibitively expensive. Soil on Mars is different than soil on Earth, and exploration is helping us learn more A new study led by University of Chicago planetary scientist Edwin Kite finds Mars could have had a thin layer of icy, high-altitude clouds that caused a greenhouse effect, allowing rivers and lakes to flow. While attention has been focused on the Perseverance rover that landed on Mars last month, its predecessor Curiosity continues to explore the base of Mount Sharp on the red planet and is still making discoveries. Billions of years ago, the Red Planet was far more blue; according to evidence still found on the surface, abundant water flowed across Mars and forming pools, lakes, and deep oceans. The question, then, is where did all that water go? A new study that characterizes the climate of Mars over the planet’s lifetime reveals that in its earliest history it was periodically warmed, yet remained relatively cold in the intervening periods, thus providing opportunities and challenges for any microbial life form that may have been emerging. The new era of space exploration features two Stony Brook University faculty members as part of the development of NASA’s Mars2020 Perseverance rover that recently landed. Distinguished Professor Scott McLennan and Associate Professor Joel Hurowitz both worked on the PIXL (Planetary Instrument for X-ray Lithochemistry) that is attached to the arm of the rover. The PIXL is a micro-focus X-ray fluorescence instrument that rapidly measures elemental chemistry by focusing an X-ray beam to a tiny spot on the target rock or soil, analyzing the induced X-ray fluorescence. Both professors have been working on Mars missions with NASA since 2004. A batch of pills will be on its way into space where they will be placed on the outside of the International Space Station (ISS) to test how they withstand the full effects of zero gravity, extreme temperatures and some of the highest levels of radiation found beyond the Earth’s atmosphere. ALBANY, N.Y. (Feb. 17, 2021) – After having traveled nearly 292.5 million miles, NASA’s Perseverance spacecraft is just about set to touch down on Mars. The landing, scheduled for about 3 p.m. on Thursday, is the culmination of a seven-month… When NASA’s Mars Perseverance rover touches down on the surface of Mars on Feb. 18, a bit of New Mexico will land along with it, thanks to work done at Los Alamos National Laboratory. FOR IMMEDIATE RELEASE Media contact: Neal Buccino, [email protected], 732-668-8439 Scheduled for a Feb. 18 Mars landing, the rover will look for signs of past life New Brunswick, N.J. (Feb. 11, 2021) – Rutgers University-New Brunswick planetary and life scientists are… How did rocks rust on Earth and turn red? A Rutgers-led study has shed new light on the important phenomenon and will help address questions about the Late Triassic climate more than 200 million years ago, when greenhouse gas levels were high enough to be a model for what our planet may be like in the future. Thinking like Earthlings may have caused scientists to overlook the electrochemical effects of Martian dust storms. On Earth, dust particles are viewed mainly in terms of their physical effects, like erosion. But, in exotic locales from Mars to Venus to Jupiter’s icy moon Europa, electrical effects can affect the chemical composition of a planetary body’s surface and atmosphere in a relatively short time, according to research from Washington University in St. Louis. The New York Academy of Sciences is hosting two programs on Space Exploration this week, with topics including legal agreements for “off planet” governance, bioengineering to make space travel safer for astronauts, and questions of bio-ethics related to interplanetary travel. The most habitable region for life on Mars would have been up to several miles below its surface, likely due to subsurface melting of thick ice sheets fueled by geothermal heat, a Rutgers-led study concludes. The study, published in the journal Science Advances, may help resolve what’s known as the faint young sun paradox – a lingering key question in Mars science. A new electrolysis system that makes use of briny water could provide astronauts on Mars with life-supporting oxygen and fuel for the ride home, according to engineers at the McKelvey School of Engineering at Washington University in St. Louis, who developed the system. Floods of unimaginable magnitude once washed through Gale Crater on Mars’ equator around 4 billion years ago – a finding that hints at the possibility that life may have existed there, according to data collected by NASA’s Curiosity rover and analyzed in joint project by scientists from Jackson State University, Cornell University, the Jet Propulsion Laboratory and the University of Hawaii. Diverse microbes discovered in the clay-rich, shallow soil layers in Chile’s dry Atacama Desert suggest that similar deposits below the Martian surface may contain microorganisms, which could be easily found by future rover missions or landing craft. Humankind’s next giant step may be onto Mars. But before those missions can begin, scientists need to make scores of breakthrough advances, including learning how to grow crops on the red planet. For the better part of a decade, an extraordinary tool aboard NASA’s Curiosity rover has been investigating the chemical building blocks of life and making exciting discoveries about Mars’ habitability. While scientists are eager to study the red planet’s soils for signs of life, researchers must ponder a considerable new challenge: Acidic fluids – which once flowed on the Martian surface – may have destroyed biological evidence hidden within Mars’ iron-rich clays, according to researchers at Cornell University and at Spain’s Centro de Astrobiología. LOS ALAMOS, N.M., September 3, 2020—The dark, hard coating found on rocks and cliff faces in the desert Southwest could tell us something about life on Mars, explains a new episode of the Mars Technica podcast. This desert varnish, which… When NASA’s Perseverance rover lands on Mars in February after its seven-month-long journey, the mission will only just be beginning. Today, Mars is an arid, dusty, and frigid landscape with an average temperature of minus 80 degrees Fahrenheit—inhospitable to life as we know it. But it wasn’t always that way. To have dependable power to explore the the frigid surface of Mars, NASA’s Perseverance rover is equipped with a type of power system called a radioisotope thermoelectric generator (RTG)—which is what the latest episode of Mars Technica will tell listeners all about. NASA’s new Perseverance rover, which just started its seven-month journey to Mars, carries on board what is likely the most versatile instrument ever created to understand the planet’s past habitability: SuperCam—and a new podcast will tell listeners all about it. Could Jezero Crater hold the keys to unlocking an ancient and hidden past when life might have existed on the Martian surface? By: Bill Wellock \| Published: July 27, 2020 \| 2:27 pm \| SHARE: This summer, NASA’s Perseverance rover mission will begin its exploration of Mars, gathering valuable data that will help scientists understand our neighboring planet.Once on Mars, the rover will search for signs of ancient microscopic life and collect data about the planet’s geology and climate. When NASA’s Perseverance rover launches from Florida on its way to Mars, it will carry aboard what is likely the most versatile instrument ever made to better understand the Red Planet’s past habitability. NASA is planning to launch its latest rover destined for Mars on July 30, with an anticipated arrival date on the red planet in February 2021. The rover, named Perseverance, will look for evidence of ancient life and collect soil… Silver, bug-eyed extraterrestrials zooming across the cosmos in bullet-speed spaceships. Green, oval-faced creatures hiding out in a secret fortress at Nevada’s Area 51 base. Cartoonish, throaty-voiced relatives of Marvin the Martian who don armor and Spartan-style helmets. We humans are fascinated with the possibility of life on the Red Planet. This paper — from the group that previously examined Martian dust storms — shifts focus to the electrochemical processes resulting from dust storms that may power the movement of chlorine, which is ongoing on Mars today. The research was published May 28 in the Journal of Geophysical Research: Planets. Science aboard an Alabama Space Grant Consortium (ASGC) student-led cube satellite mission called AEGIS could be valuable to developing future human outposts on the moon and in space travel to Mars if NASA gives the go-ahead for a 2022 flight. When the Mars 2020 rover is officially named on February 18, Buffalo State College’s Kevin Williams will have played a role in choosing its moniker. Williams, director of Buffalo State’s Whitworth Ferguson Planetarium and associate professor of earth sciences and science education, was one of… Scientists at Berkeley Lab have developed a diamond anvil sensor that could lead to a new generation of smart, designer materials, as well as the synthesis of new chemical compounds, atomically fine-tuned by pressure. Northern Arizona University professor Christopher Edwards and postdoc Jennifer Buz are co-authors of a study published this week in Geophysical Research Letters that mapped several locations on Mars at high and mid-latitudes where water ice exists at a depth as little as an inch below the planet’s surface.
A cylinder is a three-dimensional object that looks like a rod with circular ends. The radius of a cylinder is the distance from the center of one of the circular faces to its edge. If you know the volume and the height of a cylinder, you can find its radius by using the formula for the volume of a cylinder. Know the Formula for the Volume of a Cylinder The formula for the volume of a cylinder contains three elements: the radius of the cylinder (r), the height (h) of the cylinder, and the ratio of the circumference of a circle to its diameter pi. To find the volume of a cylinder, you multiply pi by the cylinder's height and the square of its radius. Here is the formula in mathematical terms: V = pi x h x r^2 Solve for the Radius (r) Since you want to find the radius of the cylinder, you need to rearrange the formula to solve for the term r, which is the radius. First, divide both sides by pi and h. These terms will cancel on the right side of the equation, leaving only r^2. Now take the square root of both sides to get rid of the square on the radius. This leaves us with the following: r = square root of (V / (pi x h)) Plug in the Values for Height (h) and Volume (V) and Calculate Now just plug your numbers into the equation and compute the radius. For example, if your cylinder has a height of 10 centimeters and a volume of 30 cubic centimeters, the calculation would look like the following: r = square root of (30 cm^3 / (3.14 x 10 cm)) = 0.98 cm Remember: pi is always equal to approximately 3.14. Always remember to include your units in your calculations and especially in your answer.
Task 19: Motion Vectors, Angles & Rotation It's time to start moving images around! In a few of the previous tasks you have typed in or loaded code that moves objects around on the screen. It's time to explore the different ways motion can be achieved using code. All objects when placed on the screen have one thing in common, coordinates. There is typically at a minimum an X and Y coordinate associated with an object that correlates to a particular point on the screen. The CIRCLE statement requires a single set of coordinates while the LINE statement requires a pair of them. Another command we'll investigate later in this task is _MAPTRIANGLE which requires three coordinate pairs. By changing an object's coordinates you can effectively make an object move on the screen. The direction in which an object moves is known as its vector. Let's start with a very simple bouncing ball demo. Load the code named BouncingBall.BAS located in your .\tutorial\task19\ directory. Figure 1 - Simple Object Movement To move an object around on the computer screen you need to know at the very minimum the following: The horizontal and vertical vectors create a slope for the object to follow. The slope defines the direction and steepness of the object's path. For instance if BallXvector! and BallYvector! are both set to a value of 1 the ball would move to the right one pixel and down one pixel with each passing frame. The ball's slope would be 1 setting its travel direction to 135 degrees. By varying the value in the vector variables between -1 and 1 and then multiplying those vector variables by the balls speed the ball can be made to go in any direction at any speed. Note: Remember that the computer screen's (0, 0) coordinate is located in the upper left corner. Slopes are effectively flipped vertically from what you learned in school where (0, 0) was located in the bottom left hand corner. With (0, 0) being in the lower left corner a slope of 1 would point in a 45 degree direction. The next example allows the speed to be adjusted through the use of the right and left arrow keys. In lines 15 and 16 of the previous example the speed was incorporated into the vector values right away. In the following example the speed is not applied until later in the main loop. This example is included as BouncingBall2.BAS in your .\tutorial\task19\ directory. Figure 2 - Object Movement With Speed Control The previous example also converted all of the motion associated variables into a single TYPE definition. Vary rarely are you going to have a game with just one moving object. By utilizing a TYPE statement it's trivial to add more objects through the use of an array. More on that later. In the next example the vertical and horizontal vectors can be manually changed to see the effect on the direction of the ball. The vectors are used to draw a slope line from the center of the object indicating speed and direction of object travel to help visualize how vectors work together to create 360 degree movement. Use of the right and left arrow keys allow the horizontal (X) vector to be varied between -1 and 1 and the up and down arrow keys allow the vertical (Y) vector to be varied between -1 and 1. This code is included as BouncingBall3.BAS in your .\tutorial\task19\ directory. Figure 3 - Controlling Both Vector Values X and Y vectors can be used to put an object into any 360 degree motion. The best way to do this is to convert an angle from 0 to 359 into the corresponding X and Y vector values for that heading. Another valuable tool to have at your disposal is the ability to calculate an angle between two objects. Once the angle from one object to another has been established that angle can be used to set the corresponding X and Y vector values. The following example program includes two functions that do this. The Angle2Vector() function returns the X and Y vector values for an angle passed to it. The P2PAngle() function returns the angle between two X,Y coordinate pairs. This angle can be fed into Angle2Vector() to effectively point an object in the direction of another. Use the mouse to move the red circle around on the screen. The green circle will always follow the red circle. This program is saved as BallChaser.BAS in your .\tutorial\task19\ directory. Figure 4 - An Object Following Another Both functions Angle2Vector() and P2PAngle() return values based on 0 degrees being North (up), 90 degrees being East (right), 180 degrees being South (down), and 270 degrees being West (left). Note that in the Angle2Vector() function the constant PIDIV180 has been used. That could just as easily have been the actual value of 0.0174532 there. Through the use of these two functions you can set any object, such as a sprite, in any direction on the screen or toward another object. The P2PAngle() function can also be used to convert vector values to angles, the opposite of Angle2Vector(). Simply take the X,Y location of an object and the X,Y location values plus the vector values as the second point like so: Angle! = P2PAngle(x!, y!, x! + xvector!, y! + yvector!) Rotation of a sprite can be done with help from the _MAPTRIANGLE statement. The _MAPTRIANGLE statement can be used to convert a rectangle into two separate triangular areas. The four corners of the rectangle can then be rotated to any angle around a center point. The new corner coordinate locations are then used by _MAPTRIANGLE to map the triangular areas of the sprite to the new coordinates. The following is an example that uses _MAPTRIANGLE to rotate a series of sprites that create an animation that rotates in relation to mouse movement. Use the mouse to move the brains around on the screen and the zombie will chase it. This example has been saved as ZombieRotate.BAS in your .\tutorial\task19\ directory. Figure 5 - They're Coming to Get You Barbara! Figure 6 below is a graphical representation of how the sprite is rotated with the help of _MAPTRIANGLE. Figure 6 - Rotating a Sprite The RotateImage() subroutine is where all the rotation happens. RotateImage() requires three parameters: RotateImage Angle!, InImage&, OutImage& Angle! is the new direction of the sprite in degrees from 0 to 359.99. InImage& is the sprite image you wish to rotate and OutImage& will contain the resulting image from the rotation. Line 131 through 138 identifies the coordinates of the four corners of the incoming sprite image. The coordinates are purposely shifted left and up half the width and height to create an image center coordinate of (0,0). Lines 139 and 140 calculate the amount of rotation needed based on the Angle! passed in. Lines 146 through 156 takes each corner coordinate pair one at a time and calculates new locations for them. The smallest and largest X and Y values are saved so the new width and height of the rotated image can be calculated in lines 157 and 158. Lines 159 and 160 are used to move the rotated image right and down half the width and height to compensate for creating the (0,0) point in the center that was done in lines 131 through 138. Lines 161 through 168 then adds these offsets back in. Line 169 creates a new image holder for the rotated image with the computed width and height from lines 157 and 158. Finally lines 187 and 189 use _MAPTRIANGLE to grab the triangular areas from the original incoming sprite image and map them to the new rotated coordinates contained within the new rotated image. The RotateImage() subroutine is my goto routine for rotating sprites of any size on the screen. Don't let the _MAPTRIANGLE statement intimidate you. Play around with it to get familiar with how it works. It's a very powerful graphics tool at your disposal. It can also be used to map images onto irregular polygon surfaces such as walls going into the distance.
Nuclear magnetic resonance spectroscopy This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. (November 2016) (Learn how and when to remove this template message) Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy or magnetic resonance spectroscopy (MRS), is a spectroscopic technique to observe local magnetic fields around atomic nuclei. The sample is placed in a magnetic field and the NMR signal is produced by excitation of the nuclei sample with radio waves into nuclear magnetic resonance, which is detected with sensitive radio receivers. The intramolecular magnetic field around an atom in a molecule changes the resonance frequency, thus giving access to details of the electronic structure of a molecule and its individual functional groups. As the fields are unique or highly characteristic to individual compounds, in modern organic chemistry practice, NMR spectroscopy is the definitive method to identify monomolecular organic compounds. Similarly, biochemists use NMR to identify proteins and other complex molecules. Besides identification, NMR spectroscopy provides detailed information about the structure, dynamics, reaction state, and chemical environment of molecules. The most common types of NMR are proton and carbon-13 NMR spectroscopy, but it is applicable to any kind of sample that contains nuclei possessing spin. NMR spectra are unique, well-resolved, analytically tractable and often highly predictable for small molecules. Different functional groups are obviously distinguishable, and identical functional groups with differing neighboring substituents still give distinguishable signals. NMR has largely replaced traditional wet chemistry tests such as color reagents or typical chromatography for identification. A disadvantage is that a relatively large amount, 2–50 mg, of a purified substance is required, although it may be recovered through a workup. Preferably, the sample should be dissolved in a solvent, because NMR analysis of solids requires a dedicated magic angle spinning machine and may not give equally well-resolved spectra. The timescale of NMR is relatively long, and thus it is not suitable for observing fast phenomena, producing only an averaged spectrum. Although large amounts of impurities do show on an NMR spectrum, better methods exist for detecting impurities, as NMR is inherently not very sensitive - though at higher frequencies, sensitivity is higher. Correlation spectroscopy is a development of ordinary NMR. In two-dimensional NMR, the emission is centered around a single frequency, and correlated resonances are observed. This allows identifying the neighboring substituents of the observed functional group, allowing unambiguous identification of the resonances. There are also more complex 3D and 4D methods and a variety of methods designed to suppress or amplify particular types of resonances. In nuclear Overhauser effect (NOE) spectroscopy, the relaxation of the resonances is observed. As NOE depends on the proximity of the nuclei, quantifying the NOE for each nucleus allows for construction of a three-dimensional model of the molecule. NMR spectrometers are relatively expensive; universities usually have them, but they are less common in private companies. Modern NMR spectrometers have a very strong, large and expensive liquid helium-cooled superconducting magnet, because resolution directly depends on magnetic field strength. Less expensive machines using permanent magnets and lower resolution are also available, which still give sufficient performance for certain application such as reaction monitoring and quick checking of samples. There are even benchtop nuclear magnetic resonance spectrometers. NMR can be observed in magnetic fields less than a millitesla. Low-resolution NMR produces broader peaks which can easily overlap one another causing issues in resolving complex structures. The use of higher strength magnetic fields result in clear resolution of the peaks and is the standard in industry. - 1 History - 2 Basic NMR techniques - 3 Correlation spectroscopy - 4 Solid-state nuclear magnetic resonance - 5 Biomolecular NMR spectroscopy - 6 See also - 7 References - 8 Further reading - 9 External links The Purcell group at Harvard University and the Bloch group at Stanford University independently developed NMR spectroscopy in the late 1940s and early 1950s. Edward Mills Purcell and Felix Bloch shared the 1952 Nobel Prize in Physics for their discoveries. Basic NMR techniques When placed in a magnetic field, NMR active nuclei (such as 1H or 13C) absorb electromagnetic radiation at a frequency characteristic of the isotope. The resonant frequency, energy of the radiation absorbed, and the intensity of the signal are proportional to the strength of the magnetic field. For example, in a 21 Tesla magnetic field, hydrogen atoms (commonly referred to as protons) resonate at 900 MHz. It is common to refer to a 21 T magnet as a 900 MHz magnet since hydrogen is the most common nucleus detected, however different nuclei will resonate at different frequencies at this field strength in proportion to their nuclear magnetic moments. An NMR spectrometer typically consists of a spinning sample-holder inside a very strong magnet, a radio-frequency emitter and a receiver with a probe (an antenna assembly) that goes inside the magnet to surround the sample, optionally gradient coils for diffusion measurements, and electronics to control the system. Spinning the sample is usually necessary to average out diffusional motion, however some experiments call for a stationary sample when solution movement is an important variable. For instance, measurements of diffusion constants (diffusion ordered spectroscopy or DOSY) are done using a stationary sample with spinning off, and flow cells can be used for online analysis of process flows. The vast majority of molecules in a solution are solvent molecules, and most regular solvents are hydrocarbons and so contain NMR-active protons. In order to avoid detecting only signals from solvent hydrogen atoms, deuterated solvents are used where 99+% of the protons are replaced with deuterium (hydrogen-2). The most widely used deuterated solvent is deuterochloroform (CDCl3), although other solvents may be used depending on the solubility of a sample. Deuterium oxide (D2O) and deuterated DMSO (DMSO-d6) are often used when CDCl3 doesn't work, and other deuterated solvents can be used as needed. The chemical shifts of a molecule will change slightly between solvents, and the solvent used will almost always be reported with chemical shifts. NMR spectra are often calibrated against the known solvent residual proton peak instead of added tetramethylsilane. Shim and lock To detect the very small frequency shifts due to nuclear magnetic resonance, the applied magnetic field must be constant throughout the sample volume. High resolution NMR spectrometers use shims to adjust the homogeneity of the magnetic field to parts per billion (ppb) in a volume of a few cubic centimeters. In order to detect and compensate for inhomogeneity and drift in the magnetic field, the spectrometer maintains a "lock" on the solvent deuterium frequency with a separate lock unit. In modern NMR spectrometers shimming is adjusted automatically, though in some cases the operator has to optimize the shim parameters manually to obtain the best possible resolution. Acquisition of spectra Upon excitation of the sample with a radio frequency (60–1000 MHz) pulse, a nuclear magnetic resonance response - a free induction decay (FID) - is obtained. It is a very weak signal, and requires sensitive radio receivers to pick up. A Fourier transform is carried out to extract the frequency-domain spectrum from the raw time-domain FID. A spectrum from a single FID has a low signal-to-noise ratio, but it improves readily with averaging of repeated acquisitions. Good 1H NMR spectra can be acquired with 16 repeats, which takes only minutes. However, for elements heavier than hydrogen, the relaxation time is rather long, e.g. around 8 seconds for 13C. Thus, acquisition of quantitative heavy-element spectra can be time-consuming, taking tens of minutes to hours. Following the pulse, the nuclei are, on average, excited to a certain angle vs. the spectrometer magnetic field. The extent of excitation can be controlled with the pulse width, typically ca. 3-8 µs for the optimal 90° pulse. The pulse width can be determined by plotting the (signed) intensity as a function of pulse width. It follows a sine curve, and accordingly, changes sign at pulse widths corresponding to 180° and 360° pulses. Decay times of the excitation, typically measured in seconds, depend on the effectiveness of relaxation, which is faster for lighter nuclei and in solids, and slower for heavier nuclei and in solutions, and they can be very long in gases. If the second excitation pulse is sent prematurely before the relaxation is complete, the average magnetization vector has not decayed to ground state, which affects the strength of the signal in an unpredictable manner. In practice, the peak areas are then not proportional to the stoichiometry; only the presence, but not the amount of functional groups is possible to discern. An inversion recovery experiment can be done to determine the relaxation time and thus the required delay between pulses. A 180° pulse, an adjustable delay, and a 90° pulse is transmitted. When the 90° pulse exactly cancels out the signal, the delay corresponds to the time needed for 90° of relaxation. Inversion recovery is worthwhile for quantitive 13C, 2D and other time-consuming experiments. A spinning charge generates a magnetic field that results in a magnetic moment proportional to the spin. In the presence of an external magnetic field, two spin states exist (for a spin 1/2 nucleus): one spin up and one spin down, where one aligns with the magnetic field and the other opposes it. The difference in energy (ΔE) between the two spin states increases as the strength of the field increases, but this difference is usually very small, leading to the requirement for strong NMR magnets (1-20 T for modern NMR instruments). Irradiation of the sample with energy corresponding to the exact spin state separation of a specific set of nuclei will cause excitation of those set of nuclei in the lower energy state to the higher energy state. For spin 1/2 nuclei, the energy difference between the two spin states at a given magnetic field strength is proportional to their magnetic moment. However, even if all protons have the same magnetic moments, they do not give resonant signals at the same frequency values. This difference arises from the differing electronic environments of the nucleus of interest. Upon application of an external magnetic field, these electrons move in response to the field and generate local magnetic fields that oppose the much stronger applied field. This local field thus "shields" the proton from the applied magnetic field, which must therefore be increased in order to achieve resonance (absorption of rf energy). Such increments are very small, usually in parts per million (ppm). For instance, the proton peak from an aldehyde is shifted ca. 10 ppm compared to a hydrocarbon peak, since as an electron-withdrawing group, the carbonyl deshields the proton by reducing the local electron density. The difference between 2.3487 T and 2.3488 T is therefore about 42 ppm. However a frequency scale is commonly used to designate the NMR signals, even though the spectrometer may operate by sweeping the magnetic field, and thus the 42 ppm is 4200 Hz for a 100 MHz reference frequency (rf). However, given that the location of different NMR signals is dependent on the external magnetic field strength and the reference frequency, the signals are usually reported relative to a reference signal, usually that of TMS (tetramethylsilane). Additionally, since the distribution of NMR signals is field dependent, these frequencies are divided by the spectrometer frequency. However, since we are dividing Hz by MHz, the resulting number would be too small, and thus it is multiplied by a million. This operation therefore gives a locator number called the "chemical shift" with units of parts per million. In general, chemical shifts for protons are highly predictable since the shifts are primarily determined by simpler shielding effects (electron density), but the chemical shifts for many heavier nuclei are more strongly influenced by other factors including excited states ("paramagnetic" contribution to shielding tensor). The chemical shift provides information about the structure of the molecule. The conversion of the raw data to this information is called assigning the spectrum. For example, for the 1H-NMR spectrum for ethanol (CH3CH2OH), one would expect signals at each of three specific chemical shifts: one for the CH3 group, one for the CH2 group and one for the OH group. A typical CH3 group has a shift around 1 ppm, a CH2 attached to an OH has a shift of around 4 ppm and an OH has a shift anywhere from 2–6 ppm depending on the solvent used and the amount of hydrogen bonding. While the O atom does draw electron density away from the attached H through their mutual sigma bond, the electron lone pairs on the O bathe the H in their shielding effect. In paramagnetic NMR spectroscopy, measurements are conducted on paramagnetic samples. The paramagnetism gives rise to very diverse chemical shifts. In 1H NMR spectroscopy, the chemical shift range can span 500 ppm. Because of molecular motion at room temperature, the three methyl protons average out during the NMR experiment (which typically requires a few ms). These protons become degenerate and form a peak at the same chemical shift. The shape and area of peaks are indicators of chemical structure too. In the example above—the proton spectrum of ethanol—the CH3 peak has three times the area of the OH peak. Similarly the CH2 peak would be twice the area of the OH peak but only 2/3 the area of the CH3 peak. Software allows analysis of signal intensity of peaks, which under conditions of optimal relaxation, correlate with the number of protons of that type. Analysis of signal intensity is done by integration—the mathematical process that calculates the area under a curve. The analyst must integrate the peak and not measure its height because the peaks also have width—and thus its size is dependent on its area not its height. However, it should be mentioned that the number of protons, or any other observed nucleus, is only proportional to the intensity, or the integral, of the NMR signal in the very simplest one-dimensional NMR experiments. In more elaborate experiments, for instance, experiments typically used to obtain carbon-13 NMR spectra, the integral of the signals depends on the relaxation rate of the nucleus, and its scalar and dipolar coupling constants. Very often these factors are poorly known - therefore, the integral of the NMR signal is very difficult to interpret in more complicated NMR experiments. Some of the most useful information for structure determination in a one-dimensional NMR spectrum comes from J-coupling or scalar coupling (a special case of spin-spin coupling) between NMR active nuclei. This coupling arises from the interaction of different spin states through the chemical bonds of a molecule and results in the splitting of NMR signals. For a proton, the local magnetic field is slightly different depending on whether an adjacent nucleus points towards or against the spectrometer magnetic field, which gives rise to two signals per proton instead of one. These splitting patterns can be complex or simple and, likewise, can be straightforwardly interpretable or deceptive. This coupling provides detailed insight into the connectivity of atoms in a molecule. Coupling to n equivalent (spin ½) nuclei splits the signal into a n+1 multiplet with intensity ratios following Pascal's triangle as described on the right. Coupling to additional spins will lead to further splittings of each component of the multiplet e.g. coupling to two different spin ½ nuclei with significantly different coupling constants will lead to a doublet of doublets (abbreviation: dd). Note that coupling between nuclei that are chemically equivalent (that is, have the same chemical shift) has no effect on the NMR spectra and couplings between nuclei that are distant (usually more than 3 bonds apart for protons in flexible molecules) are usually too small to cause observable splittings. Long-range couplings over more than three bonds can often be observed in cyclic and aromatic compounds, leading to more complex splitting patterns. For example, in the proton spectrum for ethanol described above, the CH3 group is split into a triplet with an intensity ratio of 1:2:1 by the two neighboring CH2 protons. Similarly, the CH2 is split into a quartet with an intensity ratio of 1:3:3:1 by the three neighboring CH3 protons. In principle, the two CH2 protons would also be split again into a doublet to form a doublet of quartets by the hydroxyl proton, but intermolecular exchange of the acidic hydroxyl proton often results in a loss of coupling information. Coupling to any spin ½ nuclei such as phosphorus-31 or fluorine-19 works in this fashion (although the magnitudes of the coupling constants may be very different). But the splitting patterns differ from those described above for nuclei with spin greater than ½ because the spin quantum number has more than two possible values. For instance, coupling to deuterium (a spin 1 nucleus) splits the signal into a 1:1:1 triplet because the spin 1 has three spin states. Similarly, a spin 3/2 nucleus splits a signal into a 1:1:1:1 quartet and so on. Coupling combined with the chemical shift (and the integration for protons) tells us not only about the chemical environment of the nuclei, but also the number of neighboring NMR active nuclei within the molecule. In more complex spectra with multiple peaks at similar chemical shifts or in spectra of nuclei other than hydrogen, coupling is often the only way to distinguish different nuclei. Second-order (or strong) coupling The above description assumes that the coupling constant is small in comparison with the difference in NMR frequencies between the inequivalent spins. If the shift separation decreases (or the coupling strength increases), the multiplet intensity patterns are first distorted, and then become more complex and less easily analyzed (especially if more than two spins are involved). Intensification of some peaks in a multiplet is achieved at the expense of the remainder, which sometimes almost disappear in the background noise, although the integrated area under the peaks remains constant. In most high-field NMR, however, the distortions are usually modest and the characteristic distortions (roofing) can in fact help to identify related peaks. Second-order effects decrease as the frequency difference between multiplets increases, so that high-field (i.e. high-frequency) NMR spectra display less distortion than lower frequency spectra. Early spectra at 60 MHz were more prone to distortion than spectra from later machines typically operating at frequencies at 200 MHz or above. More subtle effects can occur if chemically equivalent spins (i.e., nuclei related by symmetry and so having the same NMR frequency) have different coupling relationships to external spins. Spins that are chemically equivalent but are not indistinguishable (based on their coupling relationships) are termed magnetically inequivalent. For example, the 4 H sites of 1,2-dichlorobenzene divide into two chemically equivalent pairs by symmetry, but an individual member of one of the pairs has different couplings to the spins making up the other pair. Magnetic inequivalence can lead to highly complex spectra which can only be analyzed by computational modeling. Such effects are more common in NMR spectra of aromatic and other non-flexible systems, while conformational averaging about C-C bonds in flexible molecules tends to equalize the couplings between protons on adjacent carbons, reducing problems with magnetic inequivalence. Correlation spectroscopy is one of several types of two-dimensional nuclear magnetic resonance (NMR) spectroscopy or 2D-NMR. This type of NMR experiment is best known by its acronym, COSY. Other types of two-dimensional NMR include J-spectroscopy, exchange spectroscopy (EXSY), Nuclear Overhauser effect spectroscopy (NOESY), total correlation spectroscopy (TOCSY) and heteronuclear correlation experiments, such as HSQC, HMQC, and HMBC. In correlation spectroscopy, emission is centered on the peak of an individual nucleus; if its magnetic field is correlated with another nucleus by through-bond (COSY, HSQC, etc.) or through-space (NOE) coupling, a response can also be detected on the frequency of the correlated nucleus. Two-dimensional NMR spectra provide more information about a molecule than one-dimensional NMR spectra and are especially useful in determining the structure of a molecule, particularly for molecules that are too complicated to work with using one-dimensional NMR. The first two-dimensional experiment, COSY, was proposed by Jean Jeener, a professor at Université Libre de Bruxelles, in 1971. This experiment was later implemented by Walter P. Aue, Enrico Bartholdi and Richard R. Ernst, who published their work in 1976. Solid-state nuclear magnetic resonance A variety of physical circumstances do not allow molecules to be studied in solution, and at the same time not by other spectroscopic techniques to an atomic level, either. In solid-phase media, such as crystals, microcrystalline powders, gels, anisotropic solutions, etc., it is in particular the dipolar coupling and chemical shift anisotropy that become dominant to the behaviour of the nuclear spin systems. In conventional solution-state NMR spectroscopy, these additional interactions would lead to a significant broadening of spectral lines. A variety of techniques allows establishing high-resolution conditions, that can, at least for 13C spectra, be comparable to solution-state NMR spectra. Two important concepts for high-resolution solid-state NMR spectroscopy are the limitation of possible molecular orientation by sample orientation, and the reduction of anisotropic nuclear magnetic interactions by sample spinning. Of the latter approach, fast spinning around the magic angle is a very prominent method, when the system comprises spin 1/2 nuclei. Spinning rates of ca. 20 kHz are used, which demands special equipment. A number of intermediate techniques, with samples of partial alignment or reduced mobility, is currently being used in NMR spectroscopy. Applications in which solid-state NMR effects occur are often related to structure investigations on membrane proteins, protein fibrils or all kinds of polymers, and chemical analysis in inorganic chemistry, but also include "exotic" applications like the plant leaves and fuel cells. For example, Rahmani et al. studied the effect of pressure and temperature on the bicellar structures' self-assembly using deuterium NMR spectroscopy. Biomolecular NMR spectroscopy Much of the innovation within NMR spectroscopy has been within the field of protein NMR spectroscopy, an important technique in structural biology. A common goal of these investigations is to obtain high resolution 3-dimensional structures of the protein, similar to what can be achieved by X-ray crystallography. In contrast to X-ray crystallography, NMR spectroscopy is usually limited to proteins smaller than 35 kDa, although larger structures have been solved. NMR spectroscopy is often the only way to obtain high resolution information on partially or wholly intrinsically unstructured proteins. It is now a common tool for the determination of Conformation Activity Relationships where the structure before and after interaction with, for example, a drug candidate is compared to its known biochemical activity. Proteins are orders of magnitude larger than the small organic molecules discussed earlier in this article, but the basic NMR techniques and some NMR theory also applies. Because of the much higher number of atoms present in a protein molecule in comparison with a small organic compound, the basic 1D spectra become crowded with overlapping signals to an extent where direct spectral analysis becomes untenable. Therefore, multidimensional (2, 3 or 4D) experiments have been devised to deal with this problem. To facilitate these experiments, it is desirable to isotopically label the protein with 13C and 15N because the predominant naturally occurring isotope 12C is not NMR-active and the nuclear quadrupole moment of the predominant naturally occurring 14N isotope prevents high resolution information from being obtained from this nitrogen isotope. The most important method used for structure determination of proteins utilizes NOE experiments to measure distances between atoms within the molecule. Subsequently, the distances obtained are used to generate a 3D structure of the molecule by solving a distance geometry problem. NMR can also be used to obtain information on the dynamics and conformational flexibility of different regions of a protein. "Nucleic acid NMR" is the use of NMR spectroscopy to obtain information about the structure and dynamics of polynucleic acids, such as DNA or RNA. As of 2003[update], nearly half of all known RNA structures had been determined by NMR spectroscopy. Nucleic acid and protein NMR spectroscopy are similar but differences exist. Nucleic acids have a smaller percentage of hydrogen atoms, which are the atoms usually observed in NMR spectroscopy, and because nucleic acid double helices are stiff and roughly linear, they do not fold back on themselves to give "long-range" correlations. The types of NMR usually done with nucleic acids are 1H or proton NMR, 13C NMR, 15N NMR, and 31P NMR. Two-dimensional NMR methods are almost always used, such as correlation spectroscopy (COSY) and total coherence transfer spectroscopy (TOCSY) to detect through-bond nuclear couplings, and nuclear Overhauser effect spectroscopy (NOESY) to detect couplings between nuclei that are close to each other in space. Parameters taken from the spectrum, mainly NOESY cross-peaks and coupling constants, can be used to determine local structural features such as glycosidic bond angles, dihedral angles (using the Karplus equation), and sugar pucker conformations. For large-scale structure, these local parameters must be supplemented with other structural assumptions or models, because errors add up as the double helix is traversed, and unlike with proteins, the double helix does not have a compact interior and does not fold back upon itself. NMR is also useful for investigating nonstandard geometries such as bent helices, non-Watson–Crick basepairing, and coaxial stacking. It has been especially useful in probing the structure of natural RNA oligonucleotides, which tend to adopt complex conformations such as stem-loops and pseudoknots. NMR is also useful for probing the binding of nucleic acid molecules to other molecules, such as proteins or drugs, by seeing which resonances are shifted upon binding of the other molecule. Carbohydrate NMR spectroscopy addresses questions on the structure and conformation of carbohydrates. The analysis of carbohydrates by 1H NMR is challenging due to the limited variation in functional groups, which leads to 1H resonances concentrated in narrow bands of the NMR spectrum. In other words, there is poor spectral dispersion. The anomeric proton resonances are segregated from the others due to fact that the anomeric carbons bear two oxygen atoms. For smaller carbohydrates, the dispersion of the anomeric proton resonances facilitates the use of 1D TOCSY experiments to investigate the entire spin systems of individual carbohydrate residues. - Distance geometry - Earth's field NMR - In vivo magnetic resonance spectroscopy - Functional magnetic resonance spectroscopy of the brain - Low field NMR - Magnetic Resonance Imaging - NMR crystallography - NMR spectra database - NMR tube - includes a section on sample preparation - NMR spectroscopy of stereoisomers - Nuclear magnetic resonance spectroscopy of proteins - Nuclear quadrupole resonance - Pulsed field magnet - Proton-enhanced nuclear induction spectroscopy - Relaxation (NMR) - Triple-resonance nuclear magnetic resonance spectroscopy - Zero field NMR - Structural biology : practical NMR applications (PDF) (2nd ed.). Springer. p. 67. ISBN 978-1-4614-3964-6. Retrieved 7 December 2018. - Paudler, William (1974). Nuclear Magnetic Resonance. 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ISBN 978-0470034590. - Martin, G.E; Zekter, A.S., Two-Dimensional NMR Methods for Establishing Molecular Connectivity; VCH Publishers, Inc: New York, 1988 (p.59) - "National Ultrahigh-Field NMR Facility for Solids". Retrieved 2014-09-22. - A. Rahmani, C. Knight, and M. R. Morrow. Response to hydrostatic pressure of bicellar dispersions containing anionic lipid: Pressure-induced interdigitation. 2013, 29 (44), pp 13481–13490, doi:10.1021/la4035694 - Fürtig, Boris; Richter, Christian; Wöhnert, Jens; Schwalbe, Harald (2003). "NMR Spectroscopy of RNA". ChemBioChem. 4 (10): 936–62. doi:10.1002/cbic.200300700. PMID 14523911. - Addess, Kenneth J.; Feigon, Juli (1996). "Introduction to 1H NMR Spectroscopy of DNA". In Hecht, Sidney M. Bioorganic Chemistry: Nucleic Acids. New York: Oxford University Press. ISBN 978-0-19-508467-2. - Wemmer, David (2000). "Chapter 5: Structure and Dynamics by NMR". In Bloomfield, Victor A.; Crothers, Donald M.; Tinoco, Ignacio. Nucleic acids: Structures, Properties, and Functions. Sausalito, California: University Science Books. ISBN 978-0-935702-49-1. - John D. Roberts (1959). Nuclear Magnetic Resonance : applications to organic chemistry. McGraw-Hill Book Company. ISBN 9781258811662. - J.A.Pople; W.G.Schneider; H.J.Bernstein (1959). High-resolution Nuclear Magnetic Resonance. McGraw-Hill Book Company. - A. Abragam (1961). The Principles of Nuclear Magnetism. Clarendon Press. ISBN 9780198520146. - Charles P. Slichter (1963). Principles of magnetic resonance: with examples from solid state physics. Harper & Row. ISBN 9783540084761. - John Emsley; James Feeney; Leslie Howard Sutcliffe (1965). High Resolution Nuclear Magnetic Resonance Spectroscopy. Pergamon. ISBN 9781483184081. \|Wikimedia Commons has media related to Nuclear magnetic resonance spectroscopy.\| - James Keeler. "Understanding NMR Spectroscopy" (reprinted at University of Cambridge). University of California, Irvine. Retrieved 2007-05-11. - The Basics of NMR - A non-technical overview of NMR theory, equipment, and techniques by Dr. Joseph Hornak, Professor of Chemistry at RIT - GAMMA and PyGAMMA Libraries - GAMMA is an open source C++ library written for the simulation of Nuclear Magnetic Resonance Spectroscopy experiments. PyGAMMA is a Python wrapper around GAMMA. - relax Software for the analysis of NMR dynamics - Vespa - VeSPA (Versatile Simulation, Pulses and Analysis) is a free software suite composed of three Python applications. These GUI based tools are for magnetic resonance (MR) spectral simulation, RF pulse design, and spectral processing and analysis of MR data.
Download Physcis Notes Of Thermal Properties Of Matter For Class 11 In PDF The branch dealing with measurement of temperature is called thremometry and the devices used to measure temperature are called thermometers. Heat is a form of energy called thermal energy which flows from a higher temperature body to a lower temperature body when they are placed in contact. Heat or thermal energy of a body is the sum of kinetic energies of all its constituent particles, on account of translational, vibrational and rotational motion. The SI unit of heat energy is joule (J). The practical unit of heat energy is calorie. 1 cal = 4.18 J 1 calorie is the quantity of heat required to raise the temperature of 1 g of water by 1°C. Mechanical energy or work (W) can be converted into heat (Q) by 1 W = JQ where J = Joule’s mechanical equivalent of heat. J is a conversion factor (not a physical quantity) and its value is 4.186 J/cal. Temperature of a body is the degree of hotness or coldness of the body. A device which is used to measure the temperature, is called a thermometer. Highest possible temperature achieved in laboratory is about 108 while lowest possible temperature attained is 10-8 K. Branch of Physics dealing with production and measurement temperature close to 0 K is known as cryagenics, while that deaf with the measurement of very high temperature is called pyromet Temperature of the core of the sun is 107 K while that of its surface 6000 K. NTP or STP implies 273.15 K (0°C = 32°F). 1. Celsius Scale In this scale of temperature, the melting point ice is taken as 0°C and the boiling point of water as 100°C and space between these two points is divided into 100 2. Fahrenheit Scale In this scale of temperature, the melt point of ice is taken as 32°F and the boiling point of water as 211 and the space between these two points is divided into 180 equal parts. 3. Kelvin Scale In this scale of temperature, the melting pouxl ice is taken as 273 K and the boiling point of water as 373 K the space between these two points is divided into 100 equal pss The property of an object which changes with temperature, is call thermometric property. Different thermometric properties thermometers have been given below where p, p100. and pt, are pressure of a gas at constant volume 0°C, 100°C and t°C. A constant volume gas thermometer can measure tempera from – 200°C to 500°C. Rt = R0(1 + αt + βt2) where α and β are constants for a metal. As β is too small therefore we can take Rt = R0(1 + αt) where, α = temperature coefficient of resistance and R0 and Rt, are electrical resistances at 0°C and t°C. where R1 and R2 are electrical resistances at temperatures t1 and t2. where R100 is the resistance at 100°C. Platinum resistance thermometer can measure temperature from —200°C to 1200°C. (iii) Length of Mercury Column in a Capillary Tube lt= l0(1 + αt) where α = coefficient of linear expansion and l0, lt are lengths of mercury column at 0°C and t°C. Thermo Electro Motive Force When two junctions of a thermocouple are kept at different temperatures, then a thermo-emf is produced between the junctions, which changes with temperature difference between the junctions. E = at + bt2 where a and b are constants for the pair of metals. Unknown temperature of hot junction when cold junction is at 0°C. Where E100 is the thermo-emf when hot junction is at 100°C. A thermo-couple thermometer can measure temperature from —200°C to 1600°C. When there is no transfer of heat between two bodies in contact, the the bodies are called in thermal equilibrium. If two bodies A and B are separately in thermal equilibrium with thirtli body C, then bodies A and B will be in thermal equilibrium with each other. The values of pressure and temperature at which water coexists inequilibrium in all three states of matter, i.e., ice, water and vapour called triple point of water. Triple point of water is 273 K temperature and 0.46 cm of mere pressure. The amount of heat required to raise the temperature of unit mass the substance through 1°C is called its specific heat. It is denoted by c or s. Its SI unit is joule/kilogram-°C'(J/kg-°C). Its dimensions is [L2T-2θ-1]. The specific heat of water is 4200 J kg-1°C-1 or 1 cal g-1 C-1, which high compared with most other substances. Gases have two types of specific heat 1. The specific heat capacity at constant volume (Cv ). 2. The specific heat capacity at constant pressure (Cr). Specific heat at constant pressure (Cp) is greater than specific heat constant volume (CV), i.e., Cp > CV . For molar specific heats Cp – CV = R where R = gas constant and this relation is called Mayer’s formula. The ratio of two principal sepecific heats of a gas is represented by γ. The value of y depends on atomicity of the gas. Amount of heat energy required to change the temperature of any substance is given by Q = mcΔt • where, m = mass of the substance, • c = specific heat of the substance and • Δt = change in temperature. Heat capacity of any body is equal to the amount of heat energy required to increase its temperature through 1°C. Heat capacity = me where c = specific heat of the substance of the body and m = mass of the body. Its SI unit is joule/kelvin (J/K). It is the quantity of water whose thermal capacity is same as the heat capacity of the body. It is denoted by W. W = ms = heat capacity of the body. The heat energy absorbed or released at constant temperature per unit mass for change of state is called latent heat. Heat energy absorbed or released during change of state is given by Q = mL where m = mass of the substance and L = latent heat. Its unit is cal/g or J/kg and its dimension is [L2T-2 ]. For water at its normal boiling point or condensation temperature (100°C), the latent heat of vaporisation is L = 540 cal/g = 40.8 kJ/ mol = 2260 kJ/kg For water at its normal freezing temperature or melting point (0°C), the latent heat of fusion is L = 80 cal/ g = 60 kJ/mol = 336 kJ/kg It is more painful to get burnt by steam rather than by boiling was 100°C gets converted to water at 100°C, then it gives out 536 heat. So, it is clear that steam at 100°C has more heat than wat 100°C (i.e., boiling of water). After snow falls, the temperature of the atmosphere becomes very This is because the snow absorbs the heat from the atmosphere to down. So, in the mountains, when snow falls, one does not feel too but when ice melts, he feels too cold. There is more shivering effect of ice cream on teeth as compare that of water (obtained from ice). This is because when ice cream down, it absorbs large amount of heat from teeth. Conversion of solid into liquid state at constant temperature is melting. Conversion of liquid into vapour at all temperatures (even below boiling point) is called cevaporation. Boiling When a liquid is heated gradually, at a particular temperature saturated vapour pressure of the liquid becomes equal to atmospheric pressure, now bubbles of vapour rise to the surface d liquid. This process is called boiling of the liquid. The temperature at which a liquid boils, is called boiling point The boiling point of water increases with increase in pre sure decreases with decrease in pressure. The conversion of a solid into vapour state is called sublimation. The conversion of vapours into solid state is called hoar fr.. This is the branch of heat transfer that deals with the measorette heat. The heat is usually measured in calories or kilo calories. When a hot body is mixed with a cold body, then heat lost by ha is equal to the heat gained by cold body Heat lost = Heat gain Increase in size on heating is called thermal expansion. There are three types of thermal expansion. 1. Expansion of solids 2. Expansion of liquids 3. Expansion of gases Three types of expansion -takes place in solid. Linear Expansion Expansion in length on heating is called linear expansion. l2 = l1(1 + α Δt) where, ll and l2 are initial and final lengths,Δt = change in temperature and α = coefficient of linear expansion. α = (Δl/l * Δt) where 1= real length and Δl = change in length and Δt= change in temperature. Superficial Expansion Expansion in area on heating is called superficial expansion. Increase in area A2 = A1(1 + β Δt) where, A1 and A2 are initial and final areas and β is a coefficient of superficial expansion. β = (ΔA/A * Δt) where. A = area, AA = change in area and At = change in temperature. Cubical Expansion Expansion in volume on heating is called cubical expansion. Increase in volume V2 = V1(1 + γΔt) where V1 and V2 are initial and final volumes and γ is a coefficient of cubical expansion. where V = real volume, AV =change in volume and Δt = change in temperature. Relation between coefficients of linear, superficial and cubical expansions β = 2α and γ = 3α Or α:β:γ = 1:2:3 In liquids only expansion in volume takes place on heating. (i) Apparent Expansion of Liquids When expansion of th container containing liquid, on heating is not taken into accoun then observed expansion is called apparent expansion of liquids. Coefficient of apparent expansion of a liquid (ii) Real Expansion of Liquids When expansion of the container, containing liquid, on heating is also taken into account, then observed expansion is called real expansion of liquids. Coefficient of real expansion of a liquid Both, yr, and ya are measured in °C-1. We can show that yr = ya+ yg where, yr, and ya are coefficient of real and apparent expansion of liquids and yg is coefficient of cubical expansion of the container. Anamalous Expansion of Water When temperature of water is increased from 0°C, then its vol decreases upto 4°C, becomes minimum at 4°C and then increases. behaviour of water around 4°C is called, anamalous expansion water. 3. Expansion of Gases There are two types of coefficient of expansion in gases (i) Volume Coefficient (γv) At constant pressure, the change in volume per unit volume per degree celsius is called volume coefficient. where V0, V1, and V2 are volumes of the gas at 0°C, t1°C and t2°C. (ii) Pressure Coefficient (γp) At constant volume, the change in pressure per unit pressure pe degree celsius is called pressure coefficient. where p0, p1 and p2 are pressure of the gas at 0°C, t1° C and t2° C. 1. When rails are laid down on the ground, space is left between the end of two rails. 2. The transmission cables are not tightly fixed to the poles. 3. The iron rim to be put on a cart wheel is always of slightly smaller diameter than that of wheel. 4. A glass stopper jammed in the neck of a glass bottle can be taken out by warming the neck of the bottles. • Due to increment in its time period a pendulum clock becomes slow in summer and will • Loss of time in a time period ΔT =(1/2)α ΔθT ∴ Loss of time in any given time interval t can be given by ΔT =(1/2)α Δθt • At some higher temperature a scale will expand and scale reading will be lesser than true values, so that true value = scale reading (1 + α Δt) Here, Δt is the temperature difference. • However, at lower temperature scale reading will be more or true value will be less. Please send your queries to firstname.lastname@example.org you can aslo visit our facebook page to get quick help. Link of our facebook page is given in sidebar Copyright @ ncerthelp.com A free educational website for CBSE, ICSE and UP board.
The Arctic Circle is the parallel of latitude that runs 66° 33' 39," or roughly 66.5°, north of the Equator. Approximately 15,000 kilometers (9,300 miles) to the south is the Antarctic Circle, of equal diameter to and parallel to the Arctic Circle as well as equally distant from the Equator. Together with the Equator and the tropics of Cancer and Capricorn, these five unseen circular lines comprise the major circles of latitude that mark maps of the Earth. All five are determined by the Earth's rotation on its axis and the Earth's tilt toward and away from the Sun in its orbit. The circle, though invisible and, in fact, moving, is a product of the same phenomenon that provides the world with four seasons and this largely austere part of the globe with an odd formula of light and darkness shared only by its polar opposite. The Geometry of the Circle The Arctic Circle marks the southern extremity of the polar day of the summer solstice in June and the polar night of the winter solstice in December. Within the whole area of the Arctic Circle, the Sun is above the horizon for at least 24 continuous hours once per year, in conjunction with the Arctic's summer solstice, which is often referred to as the "midnight sun." Likewise, in conjunction with the Arctic's winter solstice, the Arctic sun will be below the horizon in the entire area for at least 24 continuous hours, which could just as easily be called the "noontime night." The darkness is often alleviated, though, by the awesome beauty of the Aurora Borealis, or "Northern Lights," which result from the interplay of the Earth's magnetic field and the solar wind. Points within the circle experience longer periods of continuous light and darkness depending on their proximity to the North Pole, where six months of sunlight alternate with a half-year of darkness. (In fact, because of refraction and because the sun appears as a disk and not a point, part of the midnight sun may be seen at the night of the summer solstice up to about 90 km (56 miles) south of the Arctic Circle; similarly, at the day of the winter solstice part of the sun may be seen up to about 90 km north of the circle. This is true at sea level; these limits increase with elevation above sea level, but in mountainous regions there is often no direct view of the horizon.) Because of a slow wobble that the Earth has in its rotation over a period of more than 40,000 years, the Arctic Circle also moves slowly about, to the point that it is problematic to say exactly where it lies even one day to the next. Over a period of nearly 20 years, the Earth's tilt oscillates about 280 meters (924 feet), which causes the circle at present to be moving north at the rate of about 14 meters (46 feet) per year. The Circle's Name The Arctic Ocean lies wholly within the Arctic Circle. The ocean, the circle, and the region take their names from the Greek word arctus, meaning "bear," a reference to the Big and Little Bear constellations that can always be seen overhead on clear nights in the polar region. Everything north of the Arctic Circle is properly known as the Arctic while the zone just to the south of the circle is the Northern Temperate Zone. The North Pole lies about 2,600 kilometers (1,600 miles) from the Arctic Circle. Because of the moderating influence of open water—even warm water escaping from under polar pack ice— the North Pole is often less cold than points on the circle. Countries on the Circle There are seven countries that have significant territory within the Arctic Circle. They are, in order from the International Date Line heading east: The nation of Iceland barely grazes the Arctic Circle, with less than one km² of its territory lying north of it. The line crosses or passes south of just a few tiny islets. Greenland is the only one of these countries with most of its area within the circle, though the vast majority of its population resides south of it. Circumpolar Population, Transport Lines, and Economy In contrast to the area south of the Antarctic Circle, where there are virtually no permanent residents, the population of the total area north of the Arctic Circle is in the vicinity of two million. The majority (more than 60 percent) are in Russia, followed in order by Norway and Finland. The Arctic population of North America, including Greenland, comprises less than three percent of all people living within the circle. Murmansk in northwestern Russia is the circumpolar region's largest city. The ethnic links among the indigenous people of the Arctic are not at all certain though they share some elements of their daily lifestyle, such as clothing, shelter, and weaponry. Linguistic connections haven't been found, and the different communities have historically been isolated from one another. The Inuit people (once called Eskimos) of Greenland, Canada, and Alaska have tenuous but slowly growing links with the native people of northern Siberia, such as the Nenet and Yakut. The three Nordic nations have each built a railroad line extending north of the circle but connecting with their national capitals well to the south. In Norway's and Finland's case, the railways stretch a relatively short distance, but in Sweden's the track nearly reaches the nation's northern limits. In Russia there are two lines, one to Murmansk and the other farther east, yet west of the Ural Mountains. No rail lines have been built into the Arctic in North America. A proposed rail tunnel under the Bering Strait to Siberia would lie just south of the Arctic Circle. The Nordic countries all have highway systems extending well into their Arctic territory, as does Russia in the Murmansk region. Canada's Dempster Highway, also referred to as Yukon Highway 5 and Northwest Territories Highway 8, is a highway that connects the Klondike Highway in Yukon, Canada to Inuvik, Northwest Territories on the Mackenzie River delta. During the winter months, the highway extends to Tuktoyaktuk, on the northern coast of Canada, using frozen portions of the Mackenzie River delta as an ice road also known as the Tuktoyaktuk Winter Road. The highway crosses the Peel River and the Mackenzie Rivers using a combination of seasonal ferry service and ice bridges. Canada has no such links into the Arctic sections of its Nunavut territories. The James Dalton Highway in Alaska reaches from Fairbanks, Alaska to the Arctic Ocean at the town of Deadhorse, Alaska along the North Slope. The town consists of facilities for the workers and companies that operate at the nearby Prudhoe Bay oil fields. Though there is a growing interest in travel north of the Arctic Circle focusing particularly on the area's relatively non-endangered wildlife and endangered wildlife such as polar bears, tourism remains on a fairly low scale. Quick visits by adventurers to the North Pole are somewhat popular among those who seek to be able to claim they have been there. Farming is difficult in the Arctic since much of the ground is tundra, though there are certain crops in prepared soil, such as cabbage, that grow large quickly in the continuous light of the midnight sun. Fishing and the land bound industries related to it are the dominant source of livelihood, along with hunting. The herding and care of reindeer are an enduring activity in the Lapland (or Sami) sections of Finland, Sweden, and Norway. There are major, but not generally well known, rivers flowing north past the Arctic Circle into the Arctic Ocean. The Mackenzie River runs through the Northwest Territories and empties into the ocean a few hundred kilometers east of Alaska's northeast corner. The Ob, Yenisey, and Lena rivers of Siberia drain immense areas of northern Asia even as far south as Kazakhstan and Mongolia and meet the ocean in extensive estuaries and deltas that are frozen in winter. Many islands and small archipelagoes are strewn about the Arctic. Besides Greenland, Earth's largest island, there are several others that are also among the world's biggest. They have such names as Canada's Baffin, Victoria, and Ellesmere islands; Norway's Spitsbergen; and Russia's Novaya Zemlya and Wrangel Island. All links retrieved April 12, 2016. 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Presentation on theme: "KS3 Mathematics S3 3-D shapes"— Presentation transcript: 1KS3 Mathematics S3 3-D shapes The aim of this unit is to teach pupils to:Use 2-D representations, including plans and elevations, to visualise 3-D shapes and deduce some of their propertiesMaterial in this unit is linked to the Key Stage 3 Framework supplement of examples ppS3 3-D shapes 2S3 3-D shapes Contents A S3.1 Solid shapes A S3.2 2-D representations of 3-D shapesAS3.3 NetsAS3.4 Plans and elevationsAS3.5 Cross-sections 33-D shapes 3-D stands for three-dimensional. 3-D shapes have length, width and height.For example, a cube has equal length, width and height.How many faces does a cube have?6How many edges does a cube have?FaceExplain that two faces meet at an edge and two or more edges meet at a vertex.12How many vertices does a cube have?8EdgeVertex 4Three-dimensional shapes Some examples of three-dimensional shapes include:A cubeA square-based pyramidA cylinderExplain that just as a square can be described as a special type of rectangle, a cube can be described as a special type of cuboid.For each solid shape ask pupils to tell you how many faces, edges and vertices it has. Ask pupils to tell you the shape of each face (ask if this is possible for a sphere). For the cylinder, ask pupils to imagine that the curved face is ‘unrolled’ and laid flat.Explain that if all the faces of a solid shape are polygons, the shape is called a polyhedron (plural polyhedra). Ask pupils which of the solid shapes shown on the board are polyhedra.If all the faces are regular polygons, the solid is a regular polyhedron. Ask pupils which solid shapes shown on the board are regular polyhedra.There are only five regular polyhedra, of which the cube, with six square faces, and the tetrahedron, with four equilateral triangular faces, are two. The other three are the octahedron (eight triangular faces), the dodecahedron (twelve pentagonal faces) and the icosahedron (20 triangular faces).Tell pupils that a prism is a shape with a constant cross-section. The triangular prism is one example, ask pupils to identify the other two (the cube and the cylinder).Nets of each of these solids (except the sphere) can be found in S2.3 Nets.A triangular prismA sphereA tetrahedron 5Describing 3-D shapes made from cubes For this activity you will need a set of interconnecting cubes. Ask a volunteer to stand with their back to the board while you construct a 3-D shape using the virtual cubes on the board.Members of the class must describe the shape shown on the board to the volunteer who must create the shape using real multilink cubes. 6Equivalent shape match For each shape, challenge pupils to find the same shape shown in a different orientation. 7S3.2 2-D representations of 3-D shapes ContentsS3 3-D shapesAS3.1 Solid shapesAS3.2 2-D representations of 3-D shapesAS3.3 NetsAS3.4 Plans and elevationsAS3.5 Cross-sections 82-D representations of 3-D shapes When we draw a 3-D shape on a 2-D surface such as a page in a book or on a board or screen, it is called a 2-D representation of a 3-D shape.Imagine a shape made from four interlocking cubes joined in an L-shape.On a square grid we can draw the shape as follows:We start by drawing the L-shape. From each vertex we draw a 45 º sloping line (point out that a line that slopes one square along for one square up slopes at an angle of 45° to the horizontal).We then complete the drawing by joining the end-points of the sloping lines.Notice that there are three sets of parallel lines: horizontal lines, vertical lines, and 45º sloping lines.We can use shading to differentiate between the faces that are facing forwards, the faces that are facing to the side and the faces that are facing upwards.The disadvantage of using a square grid to draw shapes made from cubes is that it is not possible to make the edges the same length (the 45º sloping edge is shorter).This view is sometimes called an oblique view. 9Drawing 3-D shapes on an isometric grid The dots in an isometric grid form equilateral triangles when joined together.When drawing an 2-D representation of a 3-D shape make sure that the grid is turned the right way round.The dots should form clear vertical lines. 10Drawing 3-D shapes on an isometric grid We can use an isometric grid to draw the four cubes joined in an L-shape as follows:Again the diagram has three sets of parallel lines: one set is vertical, and two sets are 30º from the horizontal in opposite directions.The advantage of drawing shapes made from cubes on isometric paper is that all the edges are the same length. 112-D representations of 3-D objects There are several different ways of drawing the same shape.Are these all of the possibilities?You may wish to have a model of this shape made of interconnecting cubes in class. You can invite pupils to think logically about all of the different possible orientations there are and use the model to demonstrate these.Challenge pupils to draw these on isometric paper.Can you draw the shape in a different way that is not shown here?How many different ways are there? 12Drawing 3-D shapes on an isometric grid Use this activity to practice and to demonstrate isometric drawings of 3-dimensional shapes made from cubes.Use the pen tool, set to draw straight lines, to draw the required shape on the grid.As a more challenging exercise ask pupils to draw the given shape in different orientations of with extra cubes added in given positions. 13Making shapes with four cubes How many different solids can you make with four interlocking cubes?Challenge pupils to find all of the solids that can be made from four cubes. The solution is shown on the next slide. Pupils may use real cubes if they need to, but should record their results as drawings on isometric paper.Point out that when we say ‘different’ shapes, we do not include rotations and reflections of the same shape.Suggest to pupils that if they work systematically, they can be more certain of finding all the shapes. For example, there are only two different shapes that can be made from three cubes. Pupils could start with one of their two shapes and make shapes from four cubes by moving a single cube to different positions. They should draw each one ignoring reflections and rotations of the same shape.These shapes are called tetracubes.Make as many shapes as you can from four cubes and draw each of them on isometric paper. 14Making shapes with four cubes You should have seven shapes altogether, as follows:Pupils can compare their answers with these pictures. They should be able to match shapes that they have drawn in a different orientation. 15Making shapes from five cubes Investigate the number of different solids you can make with five interlocking cubes.Extend the activity to five cubes.Pupils could start by finding all of the shapes that are made up of a single layer. There are 12 of these, called pentominos.Pupils can then move on to using more layers to make pentacubes. There are 11 shapes made from more than one layer, not including rotations and reflections.If reflections are allowed, there are 29 possible shapes altogether (not including reflections there are 23).Make as many as you can and draw each of them on isometric paper. 16Opposite faces Here are three views of the same cube. Each face is painted a different colour.This problem shows different isometric views of the same cube.Establish that the yellow and blue faces are opposite each other, as are the green and the pink faces, and the orange and the purple faces.Ask pupils to justify their reasoning.What colours are opposite each other? 17S3 3-D shapes Contents A S3.1 Solid shapes A S3.2 2-D representations of 3-D shapesAS3.3 NetsAS3.4 Plans and elevationsAS3.5 Cross-sections 18Can you tell which 3-D shape it would make? NetsHere is an example of a net:This means that if you cut this shape out and folded it along the dotted lines, you could stick the edges together to make a 3-D shape.This net is of a square-based pyramid.Ask pupils to describe or sketch other possible nets for the same shape.Challenge pupils to construct the net of a square-based pyramid of base length 3 cm, and sloping edge of length 4 cm, using a ruler and a pair of compasses.Links:S6 Construction and loci – constructing nets.S8 Perimeter, area and volume – surface area.Can you tell which 3-D shape it would make? 19NetsThis animation shows how the net can be folded up to make to make a pyramid. 20What 3-D shape would this net make? NetsWhat 3-D shape would this net make?Ask pupils to describe or sketch other possible nets for the same shape.Challenge pupils to construct the net of a cuboid of length 5 cm, width 3 cm and height 2 cm, using a ruler and a protractor, a set square or a pair of compasses.Links:S6 Construction and loci – constructing nets.S8 Perimeter, area and volume – surface area of a cuboid.A cuboid 21What 3-D shape would this net make? NetsWhat 3-D shape would this net make?Ask pupils to describe or sketch other possible nets for the same shape.Stress that the slanting edge of the triangular face must be the same length as the edge of the rectangle that will join onto it.Challenge pupils to construct the net of a triangular prism with a length of 5 cm and a triangular cross section whose base is 2 cm and whose slanting edge is 3 cm. They should use a ruler and a pair of compasses.Link:S6 Construction and loci – constructing nets.A triangular prism 22What 3-D shape would this net make? NetsWhat 3-D shape would this net make?Ask pupils to describe or sketch other possible nets for the same shape.Stress that each triangle is an equilateral triangle.Challenge pupils to construct the net of a tetrahedron with edge length 4 cm, using a ruler and a pair of compasses.Link:S6 Construction and loci – constructing nets.S8 Perimeter, area and volume – surface area.A tetrahedron 23What 3-D shape would this net make? NetsWhat 3-D shape would this net make?Ask pupils to describe or sketch other possible nets for the same shape.Stress that the height of each rectangle must be the same lengths as edges of the pentagon.Challenge pupils to construct this net using a ruler and a protractor. The length of the completed prism should be 5 cm with the edges of the pentagonal faces of length 2 cm.Link:S6 Construction and loci – constructing nets.S8 Perimeter, area and volume – surface area.A pentagonal prism 24Nets of cubes Here is a net of a cube. MNABCDEFGHIJKLWhen the net is folded up which sides will touch?A andBC andND andME andLPupils could make this net and fold it into a cube to verify which sides touch.F andIG andHJ andK 25Nets of cubesSix different squares joined together are shown each time this activity is reset. Pupils must decide whether or not they represent the net of a cube. 26Nets of diceUse the fact that the opposite sides of a die add up to seven to drag the missing faces into place. 27S3 3-D shapes Contents A S3.1 Solid shapes A S3.2 2-D representations of 3-D shapesAS2.3 NetsAS3.4 Plans and elevationsAS3.5 Cross-sections 28Shape sorterA solid is made from cubes. By turning the shape it can be posted through each of these three holes:Can you describe what this shape will look like?Provide pupils with interlocking cubes and ask them to make a shape that could be rotated to fit through all three holes. Is there more than one possibility?Can you build this shape using interlocking cubes? 29Shape sorterA solid is made from cubes. By turning the shape it can posted through each of these three holes:Here is a picture of the shape that will fit:Here is one possibility; a few variations are possible (by moving the cube at bottom left). 30Plans and elevations A solid can be drawn from various view points: 2 cm7 cmPlan view2 cm3 cm2 cmSide elevation3 cm3 cm7 cmFront elevation7 cmDefine the plan view as the view of a solid from directly above. In this example the plan view is a 2 cm by 7 cm rectangle.Define the front elevation as the view of the solid from directly in front. In this example the front elevation is a 3 cm by 7 cm rectangle.Define the side elevation as the view of the solid from the side. In this example the side elevation is a 3 cm by 2 cm rectangle. 31Choose the shape Front elevation: Side elevation: Plan view: A: A: B: Ask pupils to choose the shape that corresponds to the three views given. 32Choose the shape Front elevation: Side elevation: Plan view: A: B: C: Ask pupils to choose the shape that corresponds to the three views given. 33Choose the shape Front elevation: Side elevation: Plan view: A: A: B: Ask pupils to choose the shape that corresponds to the three views given. 34Choose the shape Front elevation: Side elevation: Plan view: A: B: B: Ask pupils to choose the shape that corresponds to the three views given. 35PlansSometimes the plan of a solid made from cubes has numbers on each square to tell us the number of cubes on that base.For example, this plan:21represents this solid: 36Drawing shapes from plans Ask a volunteer to draw the solid shown in the plan on the isometric grid. Use the pen tool, set to draw straight lines.Pupils may wish to build the shape first using interlocking cubes. 37Shadows What solid shape could produce this shadow? The obvious answer is a cuboid, although any prism could be orientated to produce this shadow. We could also have a pyramid with a rectangular base. 38Shadows What solid shape could produce this shadow? Possible answers include a tetrahedron, any pyramid (including a cone) or a triangular prism. 39Shadows What solid shape could produce this shadow? Possible answers include a sphere, a cylinder or a cone. 40Shadows What solid shape could produce this shadow? Possible answers include a cube, a cuboid with a square cross-section, a square-based pyramid or any prism whose length is equal to its height.
The word network protocol designates a set of rules or conventions to carry out a particular task. In data transmission, the network protocol is used in a less broad sense to indicate the set of rules or specifications that are used to implement one or more levels of the OSI model. A network protocol defines that it communicates, how it communicates, and when it communicates. The critical elements of a network protocol are its syntax, its semantics and its timing. Syntax: It refers to the structure of the data format, that is, the order in which they presented. For example, a simple network protocol could expect the first eight bits of data to be the sender’s address, the next eight bits, the receiver’s address and the rest of the flow to be the message itself. Semantics: It refers to the meaning of each bit section. How do you interpret a specific pattern and action is taken based on that representation. For example, does an address identify the route to be taken or the final destination of the message? Timing: It defines two characteristics: When the data should send and how quickly it should send. For example, if a sender produces data at a speed of 100Mbps, but the receiver can process data only at 1 Mbps, the transmission overload the receiver, and a large amount of data loss. We’ll be covering the following topics in this tutorial: Not all network protocols perform all functions, as it would imply a significant duplication of effort. There are several examples of the same type of functions present in network protocols of different levels. The functions of the network protocols can group into the following categories: Segmentation and assembly: It is when an entity (anything capable of sending or receiving information) of the application sends data in messages or a continuous sequence, lower level network protocols may need to divide the data into smaller blocks and all of it. For convenience, it is called a protocol data unit (PDU) to a block of data exchanging between two entities through a network protocol. Encapsulated: Each PDU consists not only of data but also of control information. Instead, some PDUs contain only control information, no data. Control information classified into three categories: • Address: you can indicate the address of the sender and the receiver. • Error address code: sometimes some frame check sequence is included for error detection. • Protocol control: additional information is included to implement the network protocol functions listed in the rest of this section. Connection Control: An entity can transmit data to another entity so that each PDU is treated independently of the previous PDUs. It is known as the transfer of non-connection oriented data; An example is the use of datagrams. Although this mode is useful, an equally important technique is the transfer of connection-oriented data, of which the virtual circuit is an example. If the stations provide for an extended exchange of data and some details of their network protocol change dynamically, it is preferable (even necessary) for the transfer of connection-oriented data. A logical association, or connection, is established between entities. • Connection establishment • Data transfer • Connection release Shipping ordered: If two communicated entities are at different stations in a network, there is a danger that the PDUs will not be received in the same order in which they send because they follow different paths through the network. In connection-oriented protocols, it is generally necessary that the order of the PDUs be maintained. For example, if you transfer a file between two systems, we would like to be sure that the records of the received file are in the same order as those of the transmitted file, and not mixed. If each PDU has a unique number, and the numbers are assigned sequentially, the reordering of the PDUs received based on the sequence numbers is a simple logical task for the receiving entity. The only problem with this scheme is that the sequence numbers repeated due to the use of a finite field of sequence numbers (module some maximum number). Flow control: Flow control is a function performed by the receiving entity to limit the amount or rate of data sent by the issuing entity. The purest form of flow control is a stop-and-wait procedure, in which each PDU must confirm before the next one sent. The use of more efficient network protocols implies the use of some form of credit offered by the issuer, which is the amount of data that can send without confirmation. Error control: The use of techniques to manage the loss or errors of data and control information is necessary. Most of the techniques include error detection, based on the use of a frame check sequence, and PDU re-transmission. Addressing: The concept of addressing in a communications architecture is complex and encompasses a large number of concepts such as the level of addressing, scope of the address, connection identifiers and mode of address. Multiplexing: Multiplexing is related to the concept of addressing. In a single system, a form of multiplexing supported through multiple connections. For example, with X.25, there can be multiple virtual circuits that end in the same final system; It can say that these virtual circuits multiplexed on the physical interface between the final system and the network. Transmission services: A network protocol can offer a wide variety of additional services to entities that make use of it. Three common examples are the priority, degree of service and safety. The most common network protocols The network protocol determines the mode and organization of the information (both data and controls) for transmission through the physical medium with the low-level protocol. The most common network protocols are: IPX / SPX (Internetwork Packet Exchange / Sequenced Packet Exchange) is a set of network protocols developed by Novell to used in your Netware network operating system. IPX / SPX groups fewer protocols than TCP / IP, so it does not require the same general load that TCP / IP needs. IPX / SPX can be used in both small and large networks and allows data routing. NetBEUI (NetBIOS Extended User Interface) is a fast and straightforward network protocol that was designed to use in conjunction with the NetBios protocol (Net-Ware Basic Input Output System) developed by Microsoft and IBM for small networks. NetBEUI operates in the Transport layers of the OSI Model. Since NetBEUI only provides the services that required in the OSI transport and network layers, it needs to work with NetBios that operates in the OSI model layer and is responsible for establishing the communication session between the 2 computers connected to the net. Microsoft networks also include two other components: the redirector and the Server Message Block. The re-director operates at the application layer and makes a client computer perceive all network resources as if they were local. The server message block (Server Message Block or SMB) for its part, provides same-level communication between the re-directors included in the client machines and network server. The server message block operates in the presentation layer of the OSI model. Although it is an excellent low-cost transport protocol, NetBEUI is not a protocol that can route through routers, so it cannot use in-network interconnections. Therefore, while NetBEUI is a network protocol option for small and simple networks, it is not valid for more extensive networks that require the use of routers. TCP / IP Often referred to as the “low bid protocol” TCP / IP has become the de facto standard for corporate network connection. TCP / IP networks are widely scalable, so TCP / IP can be used for both small and large networks. TCP / IP is a set of routing protocols that can run on different software platforms (Windows, Unix, etc.) and almost all network operating systems support it as the default network protocol. TCP / IP consists of a series of member protocols that make up the TCP / IP stack. And since the set of TCP / IP protocols developed before the OSI reference model completed, the protocols that comprise it do not correspond correctly with the different layers of the model. This protocol is included in the Apple Macintosh computer operating system since its inception and allows computers and peripherals to be interconnected with great simplicity for the user, since it does not require any configuration, on the other hand, the operating system takes care of everything. Although many network administrators do not consider AppleTalk a corporate or interconnect network protocol, AppleTalk allows data routing through routers. AppleTalk can support Ethernet, Token Ring, and FDI network architectures.
Helicobacter pylori, previously known as Campylobacter pylori, is a Gram-negative, microaerophilic bacterium usually found in the stomach. It was identified in 1982 by Australian scientists Barry Marshall and Robin Warren, who found that it was present in a person with chronic gastritis and gastric ulcers, conditions not previously believed to have a microbial cause. It is also linked to the development of duodenal ulcers and stomach cancer. However, over 80% of individuals infected with the bacterium are asymptomatic, and it may play an important role in the natural stomach ecology. More than 50% of the world’s population has H. pylori in their upper gastrointestinal tracts. Infection is more common in developing countries than Western countries. H. pylori’s helical shape (from which the genus name derives) is thought to have evolved to penetrate the mucoid lining of the stomach. Signs and symptoms Up to 85% of people infected with H. pylori never experience symptoms or complications. Acute infection may appear as an acute gastritis with abdominal pain (stomach ache) or nausea. Where this develops into chronic gastritis, the symptoms, if present, are often those of nonulcer dyspepsia: stomach pains, nausea, bloating, belching, and sometimes vomiting or black stool. Individuals infected with H. pylori have a 10 to 20% lifetime risk of developing peptic ulcers and a 1 to 2% risk of acquiring stomach cancer. Inflammation of the pyloric antrum is more likely to lead to duodenal ulcers, while inflammation of the corpus (body of the stomach) is more likely to lead to gastric ulcers and gastric carcinoma. However, H. pylori possibly plays a role only in the first stage that leads to common chronic inflammation, but not in further stages leading to carcinogenesis. A meta-analysis conducted in 2009 concluded the eradication of H. pylori reduces gastric cancer risk in previously infected individuals, suggesting the continued presence of H. pylori constitutes a relative risk factor of 65% for gastric cancers; in terms of absolute risk, the increase was from 1.1% to 1.7%. Helicobacter pylori has been associated with colorectal polyps and colorectal cancer. It may also be associated with eye disease. Pain typically occurs when the stomach is empty, between meals, and in the early morning hours, but it can also occur at other times. Less common ulcer symptoms include nausea, vomiting, and loss of appetite. Bleeding can also occur; prolonged bleeding may cause anemia leading to weakness and fatigue. If bleeding is heavy, hematemesis, hematochezia, or melena may occur. Colonization with H. pylori is not a disease in and of itself, but a condition associated with a number of disorders of the upper gastrointestinal tract. Testing for H. pylori is not routinely recommended. Testing is recommended if peptic ulcer disease or low-grade gastric MALT lymphoma is present, after endoscopic resection of early gastric cancer, for first-degree relatives with gastric cancer, and in certain cases of dyspepsia. Several methods of testing exist, including invasive and noninvasive testing methods. Noninvasive tests for H. pylori infection may be suitable and include blood antibody tests, stool antigen tests, or the carbon urea breath test (in which the patient drinks 14C—or 13C-labelled urea, which the bacterium metabolizes, producing labelled carbon dioxide that can be detected in the breath). It is not known which non-invasive test is more accurate for diagnosing a H. pylori infection, and the clinical significance of the levels obtained with these tests are not clear. Some drugs can affect H. pylori urease activity and give false negatives with the urea-based tests. An endoscopic biopsy is an invasive means to test for H. pylori infection. Low-level infections can be missed by biopsy, so multiple samples are recommended. The most accurate method for detecting H. pylori infection is with a histological examination from two sites after endoscopic biopsy, combined with either a rapid urease test or microbial culture. Helicobacter pylori is a major cause of certain diseases of the upper gastrointestinal tract. Rising antibiotic resistance increases the need to search for new therapeutic strategies; this might include prevention in the form of vaccination. Much work has been done on developing viable vaccines aimed at providing an alternative strategy to control H. pylori infection and related diseases, including stomach cancer. Researchers are studying different adjuvants, antigens, and routes of immunization to ascertain the most appropriate system of immune protection; however, most of the research only recently moved from animal to human trials. An economic evaluation of the use of a potential H. pylori vaccine in babies found its introduction could, at least in the Netherlands, prove cost-effective for the prevention of peptic ulcer and stomach cancer. A similar approach has also been studied for the United States. The presence of bacteria in the stomach may be beneficial, reducing the prevalence of asthma, rhinitis, dermatitis, inflammatory bowel disease, gastroesophageal reflux disease, and esophageal cancer by influencing systemic immune responses. Recent evidence suggests that nonpathogenic strains of H. pylori may be beneficial, e.g., by normalizing stomach acid secretion, and may play a role in regulating appetite, since its presence in the stomach results in a persistent but reversible reduction in the level of ghrelin. Further information: Helicobacter pylori eradication protocols Once H. pylori is detected in a person with a peptic ulcer, the normal procedure is to eradicate it and allow the ulcer to heal. The standard first-line therapy is a one-week “triple therapy” consisting of proton pump inhibitors such as omeprazole and the antibiotics clarithromycin and amoxicillin. Variations of the triple therapy have been developed over the years, such as using a different proton pump inhibitor, as with pantoprazole or rabeprazole, or replacing amoxicillin with metronidazole for people who are allergic to penicillin. In areas with higher rates of clarithromycin resistance, other options are recommended. Such a therapy has revolutionized the treatment of peptic ulcers and has made a cure to the disease possible. Previously, the only option was symptom control using antacids, H2-antagonists or proton pump inhibitors alone. An increasing number of infected individuals are found to harbor antibiotic-resistant bacteria. This results in initial treatment failure and requires additional rounds of antibiotic therapy or alternative strategies, such as a quadruple therapy, which adds a bismuth colloid, such as bismuth subsalicylate. For the treatment of clarithromycin-resistant strains of H. pylori, the use of levofloxacin as part of the therapy has been suggested. Ingesting lactic acid bacteria exerts a suppressive effect on H. pylori infection in both animals and humans, and supplementing with Lactobacillus- and Bifidobacterium-containing yogurt improved the rates of eradication of H. pylori in humans. Symbiotic butyrate-producing bacteria which are normally present in the intestine are sometimes used as probiotics to help suppress H. pylori infections as an adjunct to antibiotic therapy. Butyrate itself is an antimicrobial which destroys the cell envelope of H. pylori by inducing regulatory T cell expression (specifically, FOXP3) and synthesis of an antimicrobial peptide called LL-37, which arises through its action as a histone deacetylase inhibitor. The substance sulforaphane, which occurs in broccoli and cauliflower, has been proposed as a treatment. Periodontal therapy or scaling and root planing has also been suggested as an additional treatment. Helicobacter pylori colonizes the stomach and induces chronic gastritis, a long-lasting inflammation of the stomach. The bacterium persists in the stomach for decades in most people. Most individuals infected by H. pylori never experience clinical symptoms, despite having chronic gastritis. About 10–20% of those colonized by H. pylori ultimately develop gastric and duodenal ulcers. H. pylori infection is also associated with a 1–2% lifetime risk of stomach cancer and a less than 1% risk of gastric MALT lymphoma. In the absence of treatment, H. pylori infection—once established in its gastric niche—is widely believed to persist for life. In the elderly, however, infection likely can disappear as the stomach’s mucosa becomes increasingly atrophic and inhospitable to colonization. The proportion of acute infections that persist is not known, but several studies that followed the natural history in populations have reported apparent spontaneous elimination. Mounting evidence suggests H. pylori has an important role in protection from some diseases. The incidence of acid reflux disease, Barrett’s esophagus, and esophageal cancer have been rising dramatically at the same time as H. pylori’s presence decreases. In 1996, Martin J. Blaser advanced the hypothesis that H. pylori has a beneficial effect by regulating the acidity of the stomach contents. The hypothesis is not universally accepted as several randomized controlled trials failed to demonstrate worsening of acid reflux disease symptoms following eradication of H. pylori. Nevertheless, Blaser has reasserted his view that H. pylori is a member of the normal flora of the stomach. He postulates that the changes in gastric physiology caused by the loss of H. pylori account for the recent increase in incidence of several diseases, including type 2 diabetes, obesity, and asthma. His group has recently shown that H. pylori colonization is associated with a lower incidence of childhood asthma. At least half the world’s population is infected by the bacterium, making it the most widespread infection in the world. Actual infection rates vary from nation to nation; the developing world has much higher infection rates than the West (Western Europe, North America, Australasia), where rates are estimated to be around 25%. The age when someone acquires this bacterium seems to influence the pathologic outcome of the infection. People infected at an early age are likely to develop more intense inflammation that may be followed by atrophic gastritis with a higher subsequent risk of gastric ulcer, gastric cancer, or both. Acquisition at an older age brings different gastric changes more likely to lead to duodenal ulcer. Infections are usually acquired in early childhood in all countries. However, the infection rate of children in developing nations is higher than in industrialized nations, probably due to poor sanitary conditions, perhaps combined with lower antibiotics usage for unrelated pathologies. In developed nations, it is currently uncommon to find infected children, but the percentage of infected people increases with age, with about 50% infected for those over the age of 60 compared with around 10% between 18 and 30 years. The higher prevalence among the elderly reflects higher infection rates in the past when the individuals were children rather than more recent infection at a later age of the individual. In the United States, prevalence appears higher in African-American and Hispanic populations, most likely due to socioeconomic factors. The lower rate of infection in the West is largely attributed to higher hygiene standards and widespread use of antibiotics. Despite high rates of infection in certain areas of the world, the overall frequency of H. pylori infection is declining. However, antibiotic resistance is appearing in H. pylori; many metronidazole- and clarithromycin-resistant strains are found in most parts of the world. Helicobacter pylori is contagious, although the exact route of transmission is not known. Person-to-person transmission by either the oral–oral or fecal–oral route is most likely. Consistent with these transmission routes, the bacteria have been isolated from feces, saliva, and dental plaque of some infected people. Findings suggest H. pylori is more easily transmitted by gastric mucus than saliva. Transmission occurs mainly within families in developed nations, yet can also be acquired from the community in developing countries. H. pylori may also be transmitted orally by means of fecal matter through the ingestion of waste-tainted water, so a hygienic environment could help decrease the risk of H. pylori infection. Helicobacter pylori migrated out of Africa along with its human host circa 60,000 years ago. Recent research states that genetic diversity in H. pylori, like that of its host, decreases with geographic distance from East Africa. Using the genetic diversity data, researchers have created simulations that indicate the bacteria seem to have spread from East Africa around 58,000 years ago. Their results indicate modern humans were already infected by H. pylori before their migrations out of Africa, and it has remained associated with human hosts since that time. H. pylori was first discovered in the stomachs of patients with gastritis and ulcers in 1982 by Drs. Barry Marshall and Robin Warren of Perth, Western Australia. At the time, the conventional thinking was that no bacterium could live in the acid environment of the human stomach. In recognition of their discovery, Marshall and Warren were awarded the 2005 Nobel Prize in Physiology or Medicine. Before the research of Marshall and Warren, German scientists found spiral-shaped bacteria in the lining of the human stomach in 1875, but they were unable to culture them, and the results were eventually forgotten. The Italian researcher Giulio Bizzozero described similarly shaped bacteria living in the acidic environment of the stomach of dogs in 1893. Professor Walery Jaworski of the Jagiellonian University in Kraków investigated sediments of gastric washings obtained by lavage from humans in 1899. Among some rod-like bacteria, he also found bacteria with a characteristic spiral shape, which he called Vibrio rugula. He was the first to suggest a possible role of this organism in the pathogenesis of gastric diseases. His work was included in the Handbook of Gastric Diseases, but it had little impact, as it was written in Polish. Several small studies conducted in the early 20th century demonstrated the presence of curved rods in the stomachs of many people with peptic ulcers and stomach cancers. Interest in the bacteria waned, however, when an American study published in 1954 failed to observe the bacteria in 1180 stomach biopsies. Interest in understanding the role of bacteria in stomach diseases was rekindled in the 1970s, with the visualization of bacteria in the stomachs of people with gastric ulcers. The bacteria had also been observed in 1979, by Robin Warren, who researched it further with Barry Marshall from 1981. After unsuccessful attempts at culturing the bacteria from the stomach, they finally succeeded in visualizing colonies in 1982, when they unintentionally left their Petri dishes incubating for five days over the Easter weekend. In their original paper, Warren and Marshall contended that most stomach ulcers and gastritis were caused by bacterial infection and not by stress or spicy food, as had been assumed before. Some skepticism was expressed initially, but within a few years multiple research groups had verified the association of H. pylori with gastritis and, to a lesser extent, ulcers. To demonstrate H. pylori caused gastritis and was not merely a bystander, Marshall drank a beaker of H. pylori culture. He became ill with nausea and vomiting several days later. An endoscopy 10 days after inoculation revealed signs of gastritis and the presence of H. pylori. These results suggested H. pylori was the causative agent. Marshall and Warren went on to demonstrate antibiotics are effective in the treatment of many cases of gastritis. In 1987, the Sydney gastroenterologist Thomas Borody invented the first triple therapy for the treatment of duodenal ulcers. In 1994, the National Institutes of Health stated most recurrent duodenal and gastric ulcers were caused by H. pylori, and recommended antibiotics be included in the treatment regimen. The bacterium was initially named Campylobacter pyloridis, then renamed C. pylori in 1987 (pylori being the genitive of pylorus, the circular opening leading from the stomach into the duodenum, from the Ancient Greek word πυλωρός, which means gatekeeper). When 16S ribosomal RNA gene sequencing and other research showed in 1989 that the bacterium did not belong in the genus Campylobacter, it was placed in its own genus, Helicobacter from the ancient Greek hělix/έλιξ “spiral” or “coil”. In October 1987, a group of experts met in Copenhagen to found the European Helicobacter Study Group (EHSG), an international multidisciplinary research group and the only institution focused on H. pylori. The Group is involved with the Annual International Workshop on Helicobacter and Related Bacteria, the Maastricht Consensus Reports (European Consensus on the management of H. pylori), and other educational and research projects, including two international long-term projects: European Registry on H. pylori Management (Hp-EuReg) – a database systematically registering the routine clinical practice of European gastroenterologists. Optimal H. pylori management in primary care (OptiCare) – a long-term educational project aiming to disseminate the evidence based recommendations of the Maastricht IV Consensus to primary care physicians in Europe, funded by an educational grant from United European Gastroenterology.
* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project Applications of Normal Distribution Reasoning based on normal distributions is an important skill that goes throughout the rest of the course. In this lecture, we will look at a few problems that illustrate what you can do with normal distributions. One of the variables that we know do follow normal distributions is the height of people. For all these problems, we’re going to assume that women’s heights are normally distributed with a mean of 65 inches and a standard deviation of 3 inches. In the textbook’s notation, we can also state X ~ N (65,3) . Finding Probabilities from Given Values of Random Variable 1) What is the probability that a woman is between 64 inches and 69 inches tall (5’4” to 5’9”)? Put another way, what fraction of women’s heights are in this range? Using the notation of random variables, we would write this as P(64 < X < 69). First, draw a horizontal axis and label it x, write the units (inches) below it, and draw a normal pdf centered over the mean of 65 inches. Then mark and label 65 on the axis, mark and label 64 to the left of it and 69 to the right of it, draw vertical lines from the 64 and the 69 to the curve and shade the part between them, above the x-axis, and under the curve: If you are using GeoGebra, then you will immediately see that the software tells you P(64 < X <69) =0.5393. If you are using the calculator, then you need to find the normalcdf (not normalpdf) function. Enter the number on the left where the shading begins, the number on the right where it ends, the mean of the distribution, and its standard deviation, all separated by commas, normalcdf (64, 69, 65, 3), and you will get 0.539347. Round this to the nearest ten-thousandth (four places after the decimal point), or equivalently to the nearest hundredth of a percent, and you come up with the correct answer: 0.5393, or 53.93%. In the last lecture, we mentioned that in the old days, everyone has to learn how to look up a Z-table, the table the shows the relationship between area and Z-score for the standard normal. Then how does GeoGebra and normalcdf do it? Well, it’s no magic. The software simply converts any normal distribution to a standard normal, using the familiar relationship of Z-score: Z x So our example above will be converted to: P(64 X 69) P( 64 65 69 65 Z ) P(0.33 Z 1.33) , which gives you exactly the 3 3 same area, just under a different scale: It’s not necessary that you always convert all normal distributions to Z, but it’s useful to recognize how it is handled by the software, since we will be doing the same later in inferential statistics. 2) What is the probability that a woman is taller than 5 feet, 10 inches, or 70 inches? Put another way, what fraction of women are taller than 70 inches? This would be written as P(X > 70). Start the same way as in Problem 1, but you have to mark and label only one number besides the mean, the 70. Then shade to the right of the 70, because that’s where the taller heights are: GeoGebra is fairly self-explanatory here. With the calculator, the only complication using normalcdf is that there is no number on the right where the shading ends, so put in a big one, and if you’re not sure if it’s big enough put in a bigger one and see if it changes your answer, at least to the nearest tenthousandth. normalcdf ( 70, 1000, 65, 3)=0.04779, so the rounded answer is 0.0478, or 4.78%. Find Cut-Off Values of the Random Variable from Probability In the problems above, we found the probability that the random variable falls within a certain range. Now we’re going to reverse the process. We’ll start with the probability of a certain range, and then we’ll have to find the values of the random variable that determine that range. I’ll call these values cutoffs. Sometimes they are also called “inverse probability” problems. In these three problems, we’ll use the same situation as above: Women’s heights are normally distributed with a mean of 65 inches and a standard deviation of 3 inches. 1) How short does a woman have to be to be in the shortest 10% of women? If we call this cut-off c, this could be written as finding c such that P(X < c) = 0.10. We’ll do the same kind of diagram as before, but this time we’ll label the known probability, 10%, and we do this above the shaded area, definitely not on the x-axis, because it’s an area, not a height. The hardest part of the diagram is deciding which side of the mean to put the c on and which side of the c to shade. You really have to think about it. In this case, since by definition 50% of women are shorter than the mean, the cut-off for 10% has to be less than the mean. The picture here shows that how GeoGebra can be used to find the cut-off values: instead of entering the cut-off values, you can enter 0.10 as the probability, and GeoGebra will solve for the cut-off value (61.1553). Using the calculator, you will need to resort to the invNorm function, followed by the percent of data under the normal curve to the left of (always to the left of, no matter which side of c the shading is on) the cut-off, then the mean and standard deviation, separated by commas. So in our example, we will do invNorm (0.10, 65, 3), or, to the nearest inch, like the mean and standard deviation, 61 inches. So about 10% of women are shorter than 61 inches. You can check this using normalcdf, and you might as well use more of the cut-off than we rounded to, for greater assurance that your check shows you got the right answer. You get normalcdf (0, 61.1553, 65, 3), which come to 0.0999997, or 10%. 2) How tall does a woman have to be to be in the tallest fourth of women? (What is the cut-off for the tallest 25% of women?) If we call this height c, we want to find the value of c such that P(X > c) = 0.25. Here’s the diagram: In GeoGebra it’s quite simple: you will just have to switch the left to the right tail. In the calculator, when we use invNorm we must put in 0.75, because the calculator finds cut-offs for areas to the left only: invNorm (0.75, 65, 3). Here 0.75 comes from the fact that the total area must be equal to 1. When we subtract the area to the right, we are getting the area to the left of the cut-off. Again, either GeoGebra or invNorm rely on the standard normal Z table to compute these values. To see how this is done, you will first need to first the cut-off value for the 25% area to the right: $P(Z > 0.67) = 0.25$ Then using the relationship between the Z score and X, we can solve for x as the unknown: Z x 0.67 x 65 3 Using the algebra you have learned, you will find x = 3*0.67 + 65 = 67.0, which is how the software arrived at the answer. You won’t have to do it this way every time, but it’s helpful to keep in mind, since this relation is used later on in finding the margin of error for confidence intervals. 3) What if we’re interested in finding cut-offs for a middle group of women’s heights, say the middle 40%? Obviously, we’re looking for two numbers here, one on either side of the mean, with the same distance to the mean. Call them c1 and c2 . Then we are looking for these values so that P(c1 X c2 ) 0.40 You probably noticed that the normal calculator in GeoGebra can’t really find two cut-offs at once – in fact, the figure above was drawn using a different tool. But c1 and c2 are not two independent values, since they are equally far from 65, the mean. To use the normal calculator, we must find out how much area is under the curve to the left of c1 . Well, if 100% of area is under the entire curve, then what’s left over after taking away the middle 40% is 1-0.40=0.60, and since that 60% is split evenly between the two tails (the parts at the sides), that gives 30% for each tail. So c1 is the number such that P( X c1 ) 0.30 . So c1 , the cut-off value on the left, is 63.4 inches. How much area is there under the curve to the left of c2 ? Either subtract the 30% to the right from 100%, or add up the 30% in the left tail and the 40% in the middle, and you’ll get 70% either way. So c2 is the number such that P( X c2 ) 0.70 , and you will find that c2 66.6 inches. So to the first decimal, the middle 40% of heights go from 63.4 to 66.6 inches. If you use invNorm on a calculator, the process will be similar. Summary Here are a few tips that may help you solve problems related to the normal distribution: 1) 2) 3) 4) 5) First identify the distribution: is it continuous? Is it Normal? Draw a graph of the normal PDF with the mean and standard deviation Examine the question to see whether you are looking for a probability, or cut-off values. Shade the approximate areas under the normal PDF. Use the software/calculator to solve the unknown, and compare the output with your graph. Remember that if you have found a probability to be more than 1, then you probably misunderstood the question!
Rami Qahwaji, Professor of Visual Computing, University of Bradford The sun is the most important source of energy for sustaining life on Earth, but it gives us a lot more than just light and heat. It also gives us solar storms. Disturbances on the sun, such as coronal mass ejections produced by solar flares that emanate from active sunspot regions, can cause solar storms. Solar flares and coronal mass ejections emit vast quantities of radiation and charged particles into space. Many people still remember the collapse of Canada's Quebec electrical grid on resulting in power outages and reduced system functionality. Satellites, space stations and astronauts, aviation, GPS, power grids and more can be affected. As our civilization becomes more advanced, we become more vulnerable to the effects of solar storms. Now, as the sun's activity is on the increase, we need to get better at predicting solar weather. Many people still remember the collapse of Canada’s Quebec electrical grid on 13 March 1989, which lasted for nine hours and affected six million people. It caused hundreds of millions of dollars in damages and lost revenues. This blackout was caused by solar storms. These days, we're much more reliant on technology, which is in turn increasingly vulnerable to the effects of space and its unique natural disasters.dge technology in 1859 was limited to electrical telegraphs, and most of those failed all over Europe and North America, in some cases giving their operators electric shocks. These days, we’re much more reliant on technology, which is in turn increasingly vulnerable to the effects of space and its unique natural disasters. Space is vast, cold, dark and awash with radiation. Radiation in space comes mainly from galactic cosmic radiation — high energy particles thrown out from other galaxies — and solar particle events — high energy particles from our own sun. In space radiation, atoms are accelerated in interstellar space to speeds close to the speed of light. Eventually, the electrons are stripped out and only the positively charged nucleus remains. Humans have been observing and counting sunspots for more than 400 years, making this the longest running experiment (opens in new tab) in the world. The sun has an 11-year sunspot cycle, and at the moment, we are in the middle of that cycle. Now it's approaching "solar maximum," where the greatest solar activity occurs. The next solar maximum is expected to begin in 2025. People are familiar with the northern lights, which is one visible effect of solar radiation. Earth’s magnetic field, which protects us from most of the dangers of space radiation, directs the charged particles to the poles, where they enter our atmosphere and cause beautiful light displays. But the radiation can also impact technology and people. During strong solar radiation storms, energetic protons can damage electronic circuits inside satellites and the biological DNA of astronauts. Passengers and crew flying over the north pole would be exposed to increased radiation. These radiation storms can create errors that make navigation operations extremely difficult. Energetic protons can also ionize the atoms and molecules in the atmosphere, creating a layer of free electrons. This layer can absorb high-frequency radio waves, causing a blackout of high-frequency communications, also known as shortwave radio. With our increasing reliance on technology, predicting the weather in space is crucial. However, accurately predicting space weather has long been a challenging problem for experts. Predicting space weather Understanding the complexity of sunspots will help us predict whether significant solar flares may happen. My colleagues and I developed a real-time automated computer system which uses image processing and artificial intelligence technologies to monitor and analyse solar satellite data. This helps predict the likelihood of solar flares in the coming 24 hours. We pioneered new techniques for automatic processing, detection and feature extraction of solar features — like active regions and sunspots — captured by NASA's solar dynamics observatory satellite. We also introduced the first automated and real-time system to classify sunspots. Before this, the classification of sunspots was a manual process painstakingly carried out by experts. Space missions and astronauts are much more likely to be affected by radiation, because they aren’t protected by Earth's magnetic field. The effects on humans could include radiation sickness, increased risk for cancer, degenerative diseases and central nervous system effects. Despite these risks, human and robotic activities are increasing in space and NASA is working to land humans on Mars by the 2030s. There are two rovers — Curiosity and Perseverance — and one lander currently operational on Mars, with another rover planned for launch in 2022. Our space weather prediction system is publicly available, and is now used as one of the decision-making tools for NASA's robotic missions and to manage radiation effects on NASA's Chandra X-ray Observatory orbit. As we continue venturing further into space, we’ll need to strengthen our current space weather prediction capabilities to build a greater picture of solar activity and mitigate its effects around the solar system. This task is incredibly challenging, as most solar observations are taken for Earth’s field of view. Better modelling and investigation of the evolution of solar features is necessary to accommodate for the drastically different celestial orbits around the Sun. Follow all of the Expert Voices issues and debates — and become part of the discussion — on Facebook and Twitter. The views expressed are those of the author and do not necessarily reflect the views of the publisher.
A research team of astronomers from the University of Tokyo and the National Astronomical Society of Japan (NAOJ) has identified the location of red star-forming galaxies around a galaxy cluster situated four billion light years distant from Earth. A panoramic observation with the Subaru Telescope yielded the result. Scientists surmise that such "red-burning galaxies" are in a transitional phase from a young generation of galaxies to older one; they may demonstrate the dramatic evolution of galaxies in the environment surrounding the cluster. The key areas for understanding how environment shaped galaxy evolution in the past universe may be where red-burning galaxies are most numerous, in small groups on the outskirts of the rich cluster rather than within it. The birth of galaxies occurred more than ten billion years ago in the ancient Universe. Assembled under their own gravity, early galaxies formed into big clusters or small groups. During the process of assemblage, their properties changed in relation to their surrounding environments, just as human traits change in the contexts of their lives. For example, galaxies grouped in high-density environments such as clusters tend to be elliptical or lenticular while solitary ones tend to be spiral galaxies. How galaxies form and evolve is one of the biggest mysteries in recent extragalactic astronomy. When and how did patterns of galactic formation become established and evolve? To address this question, many astronomers are investigating distant clusters of galaxies where assemblage of galaxies occurred in the early universe. A research team led by Dr. Yusei Koyama used the Subaru Prime Focus Camera (Suprime-Cam) to carry out a panoramic observation targeting a relatively well-known rich cluster, CL0939+4713, located four billion light years away from Earth (see Fig. 1). The team used a special filter that can detect the hydrogen-alpha (Hα) line emitted by ionized hydrogen four billion years ago . Koyama's team members carefully compared the images taken with and without the special filter and then identified more than 400 galaxies showing an excess of Hα in the special filter images (see Fig. 2). Such narrow-band "excess" galaxies are likely to be star-forming galaxies. Surprisingly, Koyama's team found that an unexpectedly large number of star-forming galaxies had red colors. Even more interesting was the location of these red-burning galaxies; they reside primarily in the group-scale environments located far away from the main body of the cluster . These findings raise some intriguing questions. What is the physical origin of these red-burning galaxies? Why are they concentrated in groups and not in clusters? No one, including the research team members, knows the answer yet. At a minimum, the strong Hα emissions clearly show that the red-burning galaxies are actively forming new stars. Therefore, their red colors are likely to be produced by dust rather than by old stellar populations. The researchers expect that the strong gravity of the main cluster will cause the groups where the red-burning galaxies are most numerous to merge with it. The most significant result of this research is that the properties of galaxies are indeed changing in relatively sparse environments before they are finally absorbed into a very rich cluster. The research team noticed that the number of old galaxies, without active star-formation, appeared to be increasing in the group environments, exactly where the red-burning galaxies are most numerous. This suggests that the red-burning galaxies are related to the increase in old galaxies, and that they are likely to be in a transitional phase from a younger to an older generation. The finding that such transitional galaxies are located most frequently within group environments shows that galaxy groups are the key environments for understanding how environment shapes the evolution of galaxies. The research team emphasized the important contribution of the unique wide-field capability of the Subaru Telescope for accomplishing this research, because its panoramic imaging revealed the location of the transitional galaxies. The same research team now plans to conduct a new observation to identify the physical origin of the red-burning galaxies discovered in this study. This should be an important and exciting step toward a more complete understanding of the environments shaping the galaxies in the present-day universe. Explore further: Precise ages of largest number of stars hosting planets ever measured More information: "Red Star-Forming Galaxies and Their Environment at z=0.4 Revealed by Panoramic Hα imaging," Koyama, Y. et al., 2011, The Astrophysical Journal, vol. 734, pp. 66-78.
These two ratios are clearly independent of the size of the triangle and depend solely upon the size of the angles of a right angled triangle. By definition the value of equalities shown in equation (2) is called . Using the same analysis two other ratios can be identified. These are In Conclusion, considering the following right angled triangle:- In addition if we put a = 1 . The following diagram can be drawn. The two perpendicular Coordinates are Ox and Oy. The radius OP is of unit length and the angle xOP is measured clockwise from xOP and the coordinates of P are defined as whatever the position of P. The signs are defined as in ordinary Algebraic graphs. From the definitions and from the graph it can be seen that:- In the first quadrant, sin is +ve; cos is +ve; tan is +ve. In the second quadrant, sin is +ve; cos is -ve; tan is -ve. In the third quadrant, sin is -ve; cos is -ve; tan is +ve. In the forth quadrant, sin is -ve; cos is +ve; tan is -ve. There are various methods of remembering the above table. One way is by using the CAST diagram. Each letter stands for the positive ratios. e.g. In the first quadrant all ratios are positive whilst in the third quadrant only tan is positive. Since the magnitude of the projections of the unit radius on the axies depend solely on the acute angle which the radius makes with the x-axis, any ratio of any angle is equal numerically to the same ratio of the acute angle which the radius makes with the x-axis. The sign must be found from the Cast circle. Find the value of sin 210 degrees. As 210 is in the third quadrant the sin is negative and the acute angle which the radius makes with the x-axis is 30 degrees. To simplify expressions such as follow the same logic but for simplicity imagine that to be acute. The formula will apply for all values of but the argument is simplified by supposing that it is acute. In defining the ratios the following graph was used. It can be seen that the value of is given by the y-ordinate. Thus by drawing a circle of unit radius, the value of of the sine of any angle can be found. In this way the following graph was drawn. On the left hand circle is measured from Ox in an anticlockwise direction whilst on the right hand graph is measured along the x axis in the normal way. the values taken by the cosine as the angle increases from 0 to 90 degrees will be the same as those taken by the sine as the angle decreases from 90 degrees to 0. The two graphs are identical in shape and magnitude but displaced by 90 degrees. The tan of the angle will be infinite whenever the cosine is zero. To construct the graph, CX is drawn at unit length. The points are markedoff on the line XY and correspond to the various angles chosen for CP. If a point Q is plotted such that its abscissa on ON is equal to the number of degrees in the chosen angle XCP. This process is repeated for each value of the angle XCP. Last Modified: 1 Jun 10 @ 12:22 Page Rendered: 2022-03-14 15:43:03
The sum of two numbers is 50, and their difference is 30. Find the numbers. A system was introduced to define the numbers present from negative infinity to positive infinity. The system is known as the Number system. Number system is easily represented on a number line and Integers, whole numbers, natural numbers can be all defined on a number line. The number line contains positive numbers, negative numbers, and zero. An equation is a mathematical statement that connects two algebraic expressions of equal values with ‘=’ sign. For example: In equation 3x+2 = 5, 3x+ 2 is the left-hand side expression and 5 is the right-hand side expression connected with the ‘=’ sign. Hey! Looking for some great resources suitable for young ones? You've come to the right place. Check out our self-paced courses designed for students of grades I-XII. Start with topics like Python, HTML, ML, and learn to make some games and apps all with the help of our expertly designed content! So students worry no more, because GeeksforGeeks School is now here! There are mainly 3 types of equations: - Linear Equation - Quadratic Equation - Polynomial Equation Here, we will study the Linear equations. Linear equations in one variable are equations that are written as ax + b = 0, where a and b are two integers and x is a variable, and there is only one solution. 3x+2 = 5, for example, is a linear equation with only one variable. As a result, there is only one solution to this equation, which is x = 3/11. A linear equation in two variables, on the other hand, has two solutions. A one-variable linear equation is one with a maximum of one variable of order one. The formula is ax + b = 0, using x as the variable. There is just one solution to this equation. Here are a few examples: - 4x = 8 - 5x + 10 = -20 - 1 + 6x = 11 Linear equations in one variable are written in standard form as: ax + b = 0 - The numbers ‘a’ and ‘b’ are real. - Neither ‘a’ nor ‘b’ are equal to zero. Solving Linear Equations in One Variable The steps for solving an equation with only one variable are as follows: Step 1: If there are any fractions, use LCM to remove them. Step 2: Both sides of the equation should be simplified. Step 3: Remove the variable from the equation. Step 4: Make sure your response is correct. Problem Statement: The sum of two numbers is 50, and their difference is 30. The task is to find the numbers. Let both numbers be first and second. According to the problem statement: first + second = 50 (Consider this as 1st equation) first – second = 30 (Consider this as 2nd equation) Add both equations: first + second + first – second = 50 + 30 2 * first = 80 first = 80 / 2 first = 40 So from this, we get first = 40, put this value in any equation i.e. first + second = 50 (Put the value of first in this equation) 40 + second = 50 second = 50-40 second = 10 So, the numbers are 40 and 10. If we consider the case i.e. second – first = 30 then the solution will be the same and the first number will become 10 and the second number will become 40. Sample Problem: The sum of three numbers is 50, and the sum of the first two numbers from those three numbers is 30. The task is to find the third number. Let the numbers be first, second, and third. According to the problem statement: first + second + third = 50 (Consider this as 1st equation) first + second = 30 (Consider this as 2nd equation) So, put the value of the 2nd equation in the 1st equation i.e. first + second +third = 50 (Put the value of first+second in this equation) 30 + third = 50 third = 50-30 third = 20 So, the third number is 20.
The world is getting warmer. Whether the cause is human activity or natural variability—and the preponderance of evidence says it’s humans—thermometer readings all around the world have risen steadily since the beginning of the Industrial Revolution. (Click on bullets above to step through the decades.) According to an ongoing temperature analysis conducted by scientists at NASA’s Goddard Institute for Space Studies (GISS), the average global temperature on Earth has increased by about 0.8° Celsius (1.4° Fahrenheit) since 1880. Two-thirds of the warming has occurred since 1975, at a rate of roughly 0.15-0.20°C per decade. But why should we care about one degree of warming? After all, the temperature fluctuates by many degrees every day where we live. The global temperature record represents an average over the entire surface of the planet. The temperatures we experience locally and in short periods can fluctuate significantly due to predictable cyclical events (night and day, summer and winter) and hard-to-predict wind and precipitation patterns. But the global temperature mainly depends on how much energy the planet receives from the Sun and how much it radiates back into space—quantities that change very little. The amount of energy radiated by the Earth depends significantly on the chemical composition of the atmosphere, particularly the amount of heat-trapping greenhouse gases. A one-degree global change is significant because it takes a vast amount of heat to warm all the oceans, atmosphere, and land by that much. In the past, a one- to two-degree drop was all it took to plunge the Earth into the Little Ice Age. A five-degree drop was enough to bury a large part of North America under a towering mass of ice 20,000 years ago. The maps above show temperature anomalies, or changes, not absolute temperature. They depict how much various regions of the world have warmed or cooled when compared with a base period of 1951-1980. (The global mean surface air temperature for that period was estimated to be 14°C (57°F), with an uncertainty of several tenths of a degree.) In other words, the maps show how much warmer or colder a region is compared to the norm for that region from 1951-1980. Global temperature records start around 1880 because observations did not sufficiently cover enough of the planet prior to that time. The period of 1951-1980 was chosen largely because the U.S. National Weather Service uses a three-decade period to define “normal” or average temperature. The GISS temperature analysis effort began around 1980, so the most recent 30 years was 1951-1980. It is also a period when many of today’s adults grew up, so it is a common reference that many people can remember. The line plot below shows yearly temperature anomalies from 1880 to 2014 as recorded by NASA, NOAA, the Japan Meteorological Agency, and the Met Office Hadley Centre (United Kingdom). Though there are minor variations from year to year, all four records show peaks and valleys in sync with each other. All show rapid warming in the past few decades, and all show the last decade as the warmest. To conduct its analysis, GISS uses publicly available data from 6,300 meteorological stations around the world; ship- and buoy-based observations of sea surface temperature; and Antarctic research station measurements. These three data sets are loaded into a computer analysis program—available for public download from the GISS web site—that calculates trends in temperature anomalies relative to the average temperature for the same month during 1951-1980. The objective, according to GISS scientists, is to provide an estimate of temperature change that could be compared with predictions of global climate change in response to atmospheric carbon dioxide, aerosols, and changes in solar activity. As the maps show, global warming doesn’t mean temperatures rose everywhere at every time by one degree. Temperatures in a given year or decade might rise 5 degrees in one region and drop 2 degrees in another. Exceptionally cold winters in one region might be followed by exceptionally warm summers. Or a cold winter in one area might be balanced by an extremely warm winter in another part of the globe. Generally, warming is greater over land than over the oceans because water is slower to absorb and release heat (thermal inertia). Warming may also differ substantially within specific land masses and ocean basins. The graph below shows the long-term temperature trends in relation to El Niño or La Niña events, which can skew temperatures warmer or colder in any one year. Orange bars represent global temperature anomalies in El Niño years, with the red line showing the longer trend. Blue bars depict La Niña years, with a blue line showing the trend. Neutral years are shown in gray, and the black line shows the overall temperature trend since 1950. Since the year 2000, land temperature changes are 50 percent greater in the United States than ocean temperature changes; two to three times greater in Eurasia; and three to four times greater in the Arctic and the Antarctic Peninsula. Warming of the ocean surface has been largest over the Arctic Ocean, second largest over the Indian and Western Pacific Oceans, and third largest over most of the Atlantic Ocean. In the global maps at the top of this page, the years from 1885 to 1945 tend to appear cooler (more blues than reds), growing less cool as we move toward the 1950s. Decades within the base period do not appear particularly warm or cold because they are the standard against which all decades are measured. The leveling off between the 1940s and 1970s may be explained by natural variability and possibly by cooling effects of aerosols generated by the rapid economic growth after World War II. Fossil fuel use also increased in the post-War era (5 percent per year), boosting greenhouse gases. But aerosol cooling is more immediate, while greenhouse gases accumulate slowly and take much longer to leave the atmosphere. The strong warming trend of the past three decades likely reflects a shift from comparable aerosol and greenhouse gas effects to a predominance of greenhouse gases, as aerosols were curbed by pollution controls, according to GISS director Jim Hansen. - Hansen, J., R. Ruedy, M. Sato, and K. Lo (2010). Global surface temperature change. Reviews of Geophysics, 48 (RG4004) - National Academy of Sciences (2010). Advancing the Science of Climate Change. Accessed December 1, 2010. - NASA (2010, January 21). 2009: Second Warmest Year on Record; End of Warmest Decade. Accessed November 30, 2010. - NASA (2010, January 21). NASA Climatologist Gavin Schmidt Discusses the Surface Temperature Record. Accessed November 30, 2010. - NASA Earth Observatory (2010, June 3) Fact Sheet: Global Warming. November 30, 2010. - NASA Goddard Institute for Space Studies (n.d.). GISS Surface Temperature Analysis. Accessed November 30, 2010. - NOAA National Climatic Data Center (n.d.). Global Warming Frequently Asked Questions. Accessed December 1, 2010. - NOAA Paleoclimatology. (n.d.) Climate Timeline Tool: Climate Resources for 1000 Years. Accessed December 1, 2010. By Michael Carlowicz - Snowpack in the Sierra Nevada - Antarctic Sea Ice - Arctic Sea Ice - Growing Deltas in Atchafalaya Bay - Antarctic Ozone Hole - Mountaintop Mining, West Virginia - Shrinking Aral Sea - Development of Orlando, Florida - Water Level in Lake Powell - Recovery at Mt. St. Helens - Global Temperatures - Columbia Glacier, Alaska - Coastline Change - Amazon Deforestation - Fire in Etosha National Park - Green Seasons of Maine - Drought Cycles in Australia - Athabasca Oil Sands - Burn Recovery in Yellowstone - Severe Storms - Seasons of the Indus River - Urbanization of Dubai - Seasons of Lake Tahoe - Solar Activity - Larsen-B Ice Shelf - Mesopotamia Marshes - Yellow River Delta - El Niño, La Niña, and Rainfall - Global Biosphere
A new joint study by the University of Warwick and the British Antarctic Survey used historical data to extend scientists’ previous estimates of the likelihood of space super-storms. These storms may originate with solar flares, seen to erupt explosively on the sun during years of high solar activity. Space super-storms aren’t harmful to humans, because our atmosphere protects us, but they can be hugely disruptive to our modern technologies. They can cause power blackouts, take out satellites, disrupt aviation and cause temporary loss of GPS signals and radio communications, scientists say. The new work shows that what the scientists called “severe” space super-storms occurred 42 years out of the last 150 years. What they called “great” super-storms occurred in 6 years out of 150. The new work also sheds light on what’s called the Carrington event of 1859, the largest super-storm in recorded history. The new work is based on an analysis of magnetic field records at opposite ends of the Earth (U.K. and Australia). It was published January 22, 2020 in Geophysical Research Letters. A statement from the University of Warwick on January 29, 2020, explained: This result was made possible by a new way of analyzing historical data … from the last 14 solar cycles, way before the space age began in 1957, instead of the last five solar cycles currently used. The study doesn’t mean that there is one “great” space super-storm exactly every 25 years. Instead, it tells you the likelihood of a powerful storm occurring any given year. As the new paper’s summary pointed out: We find that on average there is a 4% chance of at least one … severe storm per year, and a 0.7% chance of a Carrington class storm per year … That’s a relatively high estimate, higher than was previously thought. Lead author Sandra Chapman of the University of Warwick commented: These super-storms are rare events but estimating their chance of occurrence is an important part of planning the level of mitigation needed to protect critical national infrastructure. The Carrington storm of 1859 – often called the Carrington event – is the biggest space super-storm we know about. It’s the one everyone talks about when speaking of the potential threat from these storms. It happened 161 years ago and so fell outside the date range of this study; however, the new analysis does estimate what amplitude it would need to have been to be in the same class as the other super-storms that were included the study. For purposes of this study, the Carrington storm is considered a “great” storm. A more recent example of a space super-storm – in this case a “severe” storm as defined by this study – would be the one of March 1989. It caused a nine-hour outage of Hydro-Québec’s electricity transmission system. In 2012, the Earth narrowly avoided trouble when a coronal mass ejection – a powerful eruption near the sun’s surface that often goes hand-in-hand with solar flares – traveled across space from the sun, barely missing the Earth. According to satellite measurements, if it had hit the Earth, it would have caused a super-storm. Richard Horne, who leads Space Weather at the British Antarctic Survey and who was a co-author on this study, commented: Our research shows that a super-storm can happen more often than we thought. Don’t be misled by the stats, it can happen any time, we simply don’t know when and right now we can’t predict when. Here’s more from the scientists’ statement about space super-storms: Space weather is driven by activity from the sun. Smaller scale storms are common, but occasionally larger storms occur that can have a significant impact. One way to monitor this space weather is by observing changes in the magnetic field at the earth’s surface. High quality observations at multiple stations have been available since the beginning of the space age (1957). The sun has an approximately 11-year cycle of activity which varies in intensity and this data, which has been extensively studied, covers only five cycles of solar activity. If we want a better estimate of the chance of occurrence of the largest space storms over many solar cycles, we need to go back further in time. The aa geomagnetic index is derived from two stations at opposite ends of the earth (in U.K. and Australia) to cancel out the Earth’s own background field. This goes back over 14 solar cycles or 150 years, but has poor resolution. Using annual averages of the top few percent of the aa index the researchers found that a ‘severe’ super-storm occurred in 42 years out of 150 (28%), while a ‘great’ super-storm occurred in 6 years out of 150 (4%) or once in every 25 years. Bottom line: Scientists used magnetic field data to extend estimates for the frequency of space super-storms back 150 years. Deborah Byrd created the EarthSky radio series in 1991 and founded EarthSky.org in 1994. Today, she serves as Editor-in-Chief of this website. She has won a galaxy of awards from the broadcasting and science communities, including having an asteroid named 3505 Byrd in her honor. A science communicator and educator since 1976, Byrd believes in science as a force for good in the world and a vital tool for the 21st century. "Being an EarthSky editor is like hosting a big global party for cool nature-lovers," she says.
In describing a histogram, there are three main factors to take into account: the shape, the centre, and the spread. The shape of a histogram can indicate whether there is a tendency for some data values to occur more than others, or not. A graph’s symmetry can be described as being approximately symmetrical, positively skewed, or negatively skewed. Symmetrical distributions can also take in the form of two different peaks. In the case where there are two distinct peaks that are symmetrical about the dip, the distribution is referred to as being bimodal. These graphs usually have the lowest values having the highest frequencies. In this case the mean will be greater than the median. Negatively skewed data values have their highest data values with the highest frequency. Generally, the mean will be less than median in these data sets. There are three measures of centre that can be used to describe a histogram. They are the mean, median and mode, which can be inferred from a labelled histogram. A distribution’s spread can be used to compare two distributions. The spread of the distribution is referred to as the maximum range of the distribution. range = largest value – smallest value The histogram below can be described as having a broad peak, or a wide spread. On the contrary, the histogram above can be described as having a narrow peak. Want to suggest an edit? Have some questions? General comments? Let us know how we can make this resource more useful to you.
About This Chapter SAT Math: Quadratic Equations - Chapter Summary This chapter on quadratic equations is designed to help you review familiar concepts and impart new information as you get ready to take the math section of the SAT examination. Prepare by watching video lessons that demonstrate how to use the area method to factor equations, perform operations with binomials and polynomials, and factor quadratic expressions. The use of the FOIL method is also outlined. Study the lessons in order to: - Calculate non-standard quadratic equations - Solve equations with the quadratic formula - Change an equation to intercept form from standard form by factoring - Work with polynomials with a non-1 leading coefficient - Use the FOIL method to multiply binomials and complete practice problems - Review the rules for multiplying, adding and subtracting polynomials - Use the FOIL in reverse method - Discover how to complete the square All of this chapter's lessons are self paced and easily accessible 24/7 via a mobile device. While you get set to pass the math portion of the SAT examination, watch the informative videos and submit your questions to the knowledgeable instructors. You'll find main video topics under the timeline link. The online lessons include written transcripts that contain bold keywords. You'll also find self-assessment quizzes in this chapter. Print them out for even greater convenience. SAT Math: Quadratic Equations Chapter Objectives There are four content areas on the math section of the SAT examination. Express your knowledge of quadratic equations when you're answering questions on the examination's Passport to Advanced Math section. This chapter's lessons reflect some of the questions and concepts you'll encounter. Overall, there are 58 questions on the SAT Math examination. You'll complete 45 standard multiple-choice questions along with 13 student-produced response questions. 1. How to Solve Quadratics That Are Not in Standard Form It isn't always the case that your equation will be set up nicely for you to solve. In this lesson, learn how to factor or use the quadratic formula to solve quadratic equations, even when they are not in standard form. 2. How to Use the Quadratic Formula to Solve a Quadratic Equation When solving a quadratic equation by factoring doesn't work, the quadratic formula is here to save the day. Learn what it is and how to use it in this lesson. 3. How to Solve a Quadratic Equation by Factoring If your favorite video game, 'Furious Fowls,' gave you the quadratic equation for each shot you made, would you be able to solve the equation to make sure every one hit its target? If not, you will after watching this video! 4. Factoring Quadratic Equations: Polynomial Problems with a Non-1 Leading Coefficient Once you get good at factoring quadratics with 1x squared in the front of the expression, it's time to try ones with numbers other than 1. It will be the same general idea, but there are a few extra steps to learn. Do that here! 5. Multiplying Binomials Using FOIL and the Area Method From the distributive property, to FOIL, to the area model, to happy faces and claws, there are many different ways to learn how to multiply binomials. In this lesson, you'll learn how to use all of them and get to pick which one you like the most. 6. Multiplying Binomials Using FOIL & the Area Method: Practice Problems There are a few mistakes that are easy to make when multiplying binomials with FOIL and also a few ways to complicate problems like this, so why not make sure you're brushed up on your skills? You'll also learn a shortcut and how to use the area method to multiply even bigger polynomials. 7. How to Add, Subtract and Multiply Polynomials Adding, subtracting and multiplying polynomials are, basically, the same as adding, subtracting and multiplying numbers. They only difference is that we have a pesky variable to worry about, but this video will show you that's no problem, so no worries! This method has worked for many of my students, and I think it will work for you, too! 8. How to Factor Quadratic Equations: FOIL in Reverse So, you know how to multiply binomials with the FOIL method, but can you do it backwards? That's exactly what factoring is, and it can be pretty tricky. Check out this lesson to learn a method that will allow you to factor quadratic trinomials with a leading coefficient of 1. 9. How to Complete the Square Completing the square can help you learn where the maximum or minimum of a parabola is. If you're running a business and trying to make some money, it might be a good idea to know how to do this! Find out what I'm talking about here. 10. Completing the Square Practice Problems Completing the square is one of the most confusing things you'll be asked to do in an algebra class. Once you get the general idea, it's best to get in there and actually do a few practice problems to make sure you understand the process. Do that here! Earning College Credit Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level. To learn more, visit our Earning Credit Page Transferring credit to the school of your choice Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you. Other chapters within the SAT Prep: Practice & Study Guide course - SAT: About the Test - SAT Writing: About the Writing Section - SAT Writing: Text & Argument Analysis - SAT Writing: Word Choice & Expression - SAT Writing: Standard English Grammar - SAT Writing: Writing & Language Test Practice - SAT Writing: The Essay Portion - SAT Writing: Planning and Writing Your Essay - SAT Writing: Parts of an Essay - SAT Writing: Sentence Clarity and Structure - SAT Writing: Essay Writing Skills - SAT Writing: How to Write An Argument - SAT Writing: Supporting Your Writing - SAT Writing: Revising Your Writing - SAT Reading: About the Reading Section - SAT Reading: Reading Passages - SAT Reading: Understanding Reading Passages - SAT Reading: Interpreting & Analyzing Text - SAT Reading: Literary Terms - SAT Reading: US Documents & Speeches - SAT Vocabulary Practice - SAT Math: About the Math Section - SAT Math: Numbers and Operations - SAT Math: Exponents - SAT Math: Equations and Expressions - SAT Math: Rational Equations and Expressions - SAT Math: Inequalities - SAT Math: Functions - SAT Math: Ratios, Rates & Proportional Relationships - SAT Math: Unit Rate & Measurement Conversions - SAT Math: Geometry and Measurement - SAT Math: Triangles & Trigonometric Ratios - SAT Math: Data Analysis, Statistics and Probability - SAT Flashcards
An adder is a digital circuit that performs addition of numbers. In many computers and other kinds of processors adders are used in the arithmetic logic units or ALU. They are also used in other parts of the processor, where they are used to calculate addresses, table indices, increment and decrement operators and similar operations. Although adders can be constructed for many number representations, such as binary-coded decimal or excess-3, the most common adders operate on binary numbers. In cases where two's complement or ones' complement is being used to represent negative numbers, it is trivial to modify an adder into an adder–subtractor. Other signed number representations require more logic around the basic adder. The half adder adds two single binary digits A and B. It has two outputs, sum (S) and carry (C). The carry signal represents an overflow into the next digit of a multi-digit addition. The value of the sum is 2C + S. The simplest half-adder design, pictured on the right, incorporates an XOR gate for S and an AND gate for C. The Boolean logic for the sum (in this case S) will be A′B + AB′ whereas for the carry (C) will be AB. With the addition of an OR gate to combine their carry outputs, two half adders can be combined to make a full adder. The half adder adds two input bits and generates a carry and sum, which are the two outputs of a half adder. The input variables of a half adder are called the augend and addend bits. The output variables are the sum and carry. The truth table for the half adder is: Inputs Outputs A B C S 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 A full adder adds binary numbers and accounts for values carried in as well as out. A one-bit full-adder adds three one-bit numbers, often written as A, B, and Cin; A and B are the operands, and Cin is a bit carried in from the previous less-significant stage. The full adder is usually a component in a cascade of adders, which add 8, 16, 32, etc. bit binary numbers. The circuit produces a two-bit output. Output carry and sum typically represented by the signals Cout and S, where the sum equals 2Cout + S. A full adder can be implemented in many different ways such as with a custom transistor-level circuit or composed of other gates. One example implementation is with S = A ⊕ B ⊕ Cin and Cout = (A ⋅ B) + (Cin ⋅ (A ⊕ B)). In this implementation, the final OR gate before the carry-out output may be replaced by an XOR gate without altering the resulting logic. Using only two types of gates is convenient if the circuit is being implemented using simple integrated circuit chips which contain only one gate type per chip. A full adder can also be constructed from two half adders by connecting A and B to the input of one half adder, then taking its sum-output S as one of the inputs to the second half adder and Cin as its other input, and finally the carry outputs from the two half-adders are connected to an OR gate. The sum-output from the second half adder is the final sum output (S) of the full adder and the output from the OR gate is the final carry output (Cout). The critical path of a full adder runs through both XOR gates and ends at the sum bit s. Assumed that an XOR gate takes 1 delays to complete, the delay imposed by the critical path of a full adder is equal to The critical path of a carry runs through one XOR gate in adder and through 2 gates (AND and OR) in carry-block and therefore, if AND or OR gates take 1 delay to complete, has a delay of The truth table for the full adder is: Inputs Outputs A B Cin Cout S 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 Adders supporting multiple bitsEdit It is possible to create a logical circuit using multiple full adders to add N-bit numbers. Each full adder inputs a Cin, which is the Cout of the previous adder. This kind of adder is called a ripple-carry adder (RCA), since each carry bit "ripples" to the next full adder. Note that the first (and only the first) full adder may be replaced by a half adder (under the assumption that Cin = 0). The layout of a ripple-carry adder is simple, which allows fast design time; however, the ripple-carry adder is relatively slow, since each full adder must wait for the carry bit to be calculated from the previous full adder. The gate delay can easily be calculated by inspection of the full adder circuit. Each full adder requires three levels of logic. In a 32-bit ripple-carry adder, there are 32 full adders, so the critical path (worst case) delay is 3 (from input to carry in first adder) + 31 × 2 (for carry propagation in latter adders) = 65 gate delays. The general equation for the worst-case delay for a n-bit carry-ripple adder, accounting for both the sum and carry bits, is To reduce the computation time, engineers devised faster ways to add two binary numbers by using carry-lookahead adders (CLA). They work by creating two signals (P and G) for each bit position, based on whether a carry is propagated through from a less significant bit position (at least one input is a 1), generated in that bit position (both inputs are 1), or killed in that bit position (both inputs are 0). In most cases, P is simply the sum output of a half adder and G is the carry output of the same adder. After P and G are generated, the carries for every bit position are created. Some advanced carry-lookahead architectures are the Manchester carry chain, Brent–Kung adder (BKA), and the Kogge–Stone adder (KSA). Some other multi-bit adder architectures break the adder into blocks. It is possible to vary the length of these blocks based on the propagation delay of the circuits to optimize computation time. These block based adders include the carry-skip (or carry-bypass) adder which will determine P and G values for each block rather than each bit, and the carry-select adder which pre-generates the sum and carry values for either possible carry input (0 or 1) to the block, using multiplexers to select the appropriate result when the carry bit is known. By combining multiple carry-lookahead adders, even larger adders can be created. This can be used at multiple levels to make even larger adders. For example, the following adder is a 64-bit adder that uses four 16-bit CLAs with two levels of lookahead carry units. If an adding circuit is to compute the sum of three or more numbers, it can be advantageous to not propagate the carry result. Instead, three-input adders are used, generating two results: a sum and a carry. The sum and the carry may be fed into two inputs of the subsequent 3-number adder without having to wait for propagation of a carry signal. After all stages of addition, however, a conventional adder (such as the ripple-carry or the lookahead) must be used to combine the final sum and carry results. A full adder can be viewed as a 3:2 lossy compressor: it sums three one-bit inputs and returns the result as a single two-bit number; that is, it maps 8 input values to 4 output values. Thus, for example, a binary input of 101 results in an output of 1 + 0 + 1 = 10 (decimal number 2). The carry-out represents bit one of the result, while the sum represents bit zero. Likewise, a half adder can be used as a 2:2 lossy compressor, compressing four possible inputs into three possible outputs. Such compressors can be used to speed up the summation of three or more addends. If the addends are exactly three, the layout is known as the carry-save adder. If the addends are four or more, more than one layer of compressors is necessary, and there are various possible designs for the circuit: the most common are Dadda and Wallace trees. This kind of circuit is most notably used in multipliers, which is why these circuits are also known as Dadda and Wallace multipliers. - Lancaster, Geoffrey A. (2004). Excel HSC Software Design and Development. Pascal Press. p. 180. ISBN 978-1-74125175-3. - Mano, M. Morris (1979). Digital Logic and Computer Design. Prentice-Hall. pp. 119–123. ISBN 978-0-13-214510-7. - Satpathy, Pinaki (2016). Design and Implementation of Carry Select Adder Using T-Spice. Anchor Academic Publishing. p. 22. ISBN 978-3-96067058-2. - Burgess, Neil (2011). Fast Ripple-Carry Adders in Standard-Cell CMOS VLSI. 20th IEEE Symposium on Computer Arithmetic. pp. 103–111. - Brent, Richard Peirce; Kung, Hsiang Te (March 1982). "A Regular Layout for Parallel Adders". IEEE Transactions on Computers. C-31 (3): 260–264. doi:10.1109/TC.1982.1675982. ISSN 0018-9340. S2CID 17348212. - Kogge, Peter Michael; Stone, Harold S. (August 1973). "A Parallel Algorithm for the Efficient Solution of a General Class of Recurrence Equations". IEEE Transactions on Computers. C-22 (8): 786–793. doi:10.1109/TC.1973.5009159. S2CID 206619926. - Reynders, Nele; Dehaene, Wim (2015). Ultra-Low-Voltage Design of Energy-Efficient Digital Circuits. Analog Circuits and Signal Processing Series. Analog Circuits And Signal Processing (ACSP) (1 ed.). Cham, Switzerland: Springer International Publishing AG Switzerland. doi:10.1007/978-3-319-16136-5. ISBN 978-3-319-16135-8. ISSN 1872-082X. LCCN 2015935431. - Liu, Tso-Kai; Hohulin, Keith R.; Shiau, Lih-Er; Muroga, Saburo (January 1974). "Optimal One-Bit Full-Adders with Different Types of Gates". IEEE Transactions on Computers. Bell Laboratories: IEEE. C-23 (1): 63–70. doi:10.1109/T-C.1974.223778. ISSN 0018-9340. S2CID 7746693. - Lai, Hung Chi; Muroga, Saburo (September 1979). "Minimum Binary Parallel Adders with NOR (NAND) Gates". IEEE Transactions on Computers. IEEE. C-28 (9): 648–659. doi:10.1109/TC.1979.1675433. S2CID 23026844. - Mead, Carver; Conway, Lynn (1980) [December 1979]. Introduction to VLSI Systems (1 ed.). Reading, MA, USA: Addison-Wesley. Bibcode:1980aw...book.....M. ISBN 978-0-20104358-7. Retrieved 2018-05-12. - Davio, Marc; Dechamps, Jean-Pierre; Thayse, André (1983). Digital Systems, with algorithm implementation (1 ed.). Philips Research Laboratory, Brussels, Belgium: John Wiley & Sons, a Wiley-Interscience Publication. ISBN 978-0-471-10413-1. LCCN 82-2710. - Hardware algorithms for arithmetic modules, includes description of several adder layouts with figures. - Interactive Full Adder Simulation (requires Java), Interactive Full Adder circuit constructed with Teahlab's online circuit simulator. - Interactive Half Adder Simulation (requires Java), Half Adder circuit built with Teahlab's circuit simulator. - 4-bit Full Adder Simulation built in Verilog, and the accompanying Ripple Carry Full Adder Video Tutorial - Shirriff, Ken (November 2020). "Reverse-engineering the carry-lookahead circuit in the Intel 8008 processor".
Presentation on theme: " Objective: To look for relationships between two quantitative variables."— Presentation transcript: Objective: To look for relationships between two quantitative variables Scatterplots may be the most common and most effective display for data. o In a scatterplot, you can see patterns, trends, relationships, and even the occasional extraordinary value sitting apart from the others. Scatterplots are the best way to start observing the relationship and the ideal way to picture associations between two quantitative variables. When looking at scatterplots, we will look for direction, form, strength, and unusual features. Direction: o A pattern that runs from the upper left to the lower right is said to have a negative direction (just like the graph of a line with a negative slope). o A trend running the other way has a positive direction (just like the graph of a line with a positive slope). Direction (cont.) Can the NOAA predict where a hurricane will go? The figure shows a negative direction and a negative association between the year since 1970 and the and the prediction errors made by NOAA. As the years have passed, the predictions have improved (errors have decreased). Form: o If the relationship isn’t straight, but curves gently, while still increasing or decreasing steadily, we can often find ways to make it more nearly straight. Strength: o At one extreme, the points appear to follow a single stream (whether straight, curved, or bending all over the place). Strength (cont.): o At the other extreme, the points appear as a vague cloud with no discernible trend or pattern: o Note: we will quantify the amount of scatter soon. It is important to determine which of the two quantitative variables goes on the x-axis and which on the y-axis. This determination is made based on the roles played by the variables. When the roles are clear, the explanatory or predictor variable goes on the x-axis, and the response variable (variable of interest) goes on the y-axis. What do you expect the scatterplot to look like? Remember direction, form, strength, and unusual features. 1. Drug dosage and degree of pain relief 2. Calories consumed and weight loss Data collected from students in Statistics classes included their heights (in inches) and weights (in pounds): Here we see positive association and a fairly straight form, there seems to a high outlier. Outlier How strong is the association between weight and height of Statistics students? If we had to put a number on the strength, we would not want it to depend on the units we used. A scatterplot of heights (in centimeters) and weights (in kilograms) doesn’t change the shape of the pattern: Note that the underlying linear pattern seems steeper in the standardized plot than in the original scatterplot. That’s because we made the scales of the axes the same. Equal scaling gives a neutral way of drawing the scatterplot and a fairer impression of the strength of the association The points in the upper right and lower left (those in green) strengthen the impression of a positive association between height and weight. The points in the upper left and lower right where z x and z y have opposite signs (those in red) tend to weaken the positive association. Points with z-scores of zero (those in blue) don’t vote either way, because their product is zero. correlation coefficient (r) The correlation coefficient (r) gives us a numerical measurement of the strength of the linear relationship between the explanatory and response variables. Calculating this by hand can be time consuming and redundant. Below are the steps to calculating it with the use of a calculator: o Make sure your diagnostics are ON (2 nd Catalog, scroll to Diagnostics ON Enter) o Store your values into L1 and L2 (x and y respectively) o Stat Calc 8: LinReg(a+bx) o Before pressing Enter, define the lists: L1, L2 Enter Correlation Correlation measures the strength of the linear association between two quantitative variables. Before you use correlation, you must check several conditions: o Quantitative Variables Condition o Straight Enough Condition o Outlier Condition Quantitative Variables Condition: o Correlation applies only to quantitative variables. o Don’t apply correlation to categorical data camouflaged as quantitative (zip codes, ID #s, area codes, etc.). o Check that you know the variables’ units and what they measure. Straight Enough Condition: o You can calculate a correlation coefficient for any pair of variables. o But correlation measures the strength only of the linear association, and will be misleading if the relationship is not linear. Outlier Condition: o Outliers can distort the correlation dramatically. o An outlier can make an otherwise small correlation look big or hide a large correlation. o It can even give an otherwise positive association a negative correlation coefficient (and vice versa). o When you see an outlier, it’s often a good idea to report the correlations with and without the point. The sign of a correlation coefficient gives the direction of the association. Correlation is always between –1 and +1. o Correlation can be exactly equal to –1 or +1, but these values are unusual in real data because they mean that all the data points fall exactly on a single straight line. o A correlation near zero corresponds to a weak linear association. Correlation treats x and y symmetrically: o The correlation of x with y is the same as the correlation of y with x. Correlation has no units. Correlation is not affected by changes in the center or scale of either variable. o Correlation depends only on the z-scores, and they are unaffected by changes in center or scale. Correlation measures the strength of the linear association between the two variables. o Variables can have a strong association but still have a small correlation if the association isn’t linear. Correlation is sensitive to outliers. A single outlying value can make a small correlation large or make a large one small. caused Whenever we have a strong correlation, it is tempting to explain it by imagining that the predictor variable has caused the response to help. never Scatterplots and correlation coefficients never prove causation. lurking variable A hidden variable that stands behind a relationship and determines it by simultaneously affecting the other two variables is called a lurking variable. It is common in some fields to compute the correlations between each pair of variables in a collection of variables and arrange these correlations in a table. Sketch a scatterplot of the following information. Discuss the direction, form, and strength of the association. If the data meet the appropriate conditions, find the correlation coefficient (r).
Presentation on theme: "KS3 Mathematics D4 Probability"— Presentation transcript: 1 KS3 Mathematics D4 Probability The aim of this unit is to teach pupils to:Use the vocabulary of probabilityUse the probability scale; find and justify theoretical probabilitiesCollect and record experimental data, and estimate probabilities based on the dataCompare experimental and theoretical probabilitiesMaterial in this unit is linked the Framework’s supplement of examples pp276 –285.D4 Probability 2 D4.1 The language of probability ContentsD4 ProbabilityD4.1 The language of probabilityD4.2 The probability scaleD4.3 Calculating probabilityD4.4 Probability diagramsD4.5 Experimental probability1 of 20 3 The language of probability Probability is a measurement of the chance or likelihood of an event happening.Words that we might use to describe probabilities include:50-50 chancelikelyunlikelypoor chancecertainvery likelypossibleAsk pupils to give examples of sentences for each phrase.impossibleeven chanceprobable 4 Fair games A game is played with marbles in a bag. One of the following bags is chosen for the game. The teacher then pulls a marble at random from the chosen bag:bag abag bbag cDiscuss the following questions:a) From which bag are the girls most likely to win a point? Why?b) From which bag are the boys least likely to win a point? Why?c) From which bag is impossible for the girls to win a point?d) From which bag are the boys certain to win a point?e) From which bag is it equally likely for the boys or the girls to win a point?f) Are any of the bags unfair? Why?If a red marble is pulled out of the bag, the girls get a point.If a blue marble is pulled out of the bag, the boys get a point.Which would be the fair bag to use? 5 A game is fair if all the players have an equal chance of winning. Fair gamesA game is fair if all the players have an equal chance of winning.Which of the following games are fair?A dice is thrown. If it lands on a prime number team A get a point, if it doesn’t team B get a point.There are three prime numbers (2, 3 and 5) and three non-prime numbers (1, 4 and 6).Remind pupils that 1 is not a prime number because it does have two factors.Yes, this game is fair. 6 Fair gamesNine cards numbered 1 to 9 are used and a card is drawn at random.If a multiple of 3 is drawn team A get a point.If a square number is drawn team B get a point.If any other number is drawn team C get a point.There are three multiples of 3 (3, 6 and 9).There are three square numbers (1, 4 and 9).Ask pupils to explain whether or not they think this game is fair.Although there are three cards that would give either team A or team B a point, there are four cards that would give team C a point.If appropriate, stress that the outcome of drawing a multiple of 3 and the outcome of drawing a square number are not mutually exclusive. It is possible to draw a card that is both a multiple of 3 and a square number, that is the card with a 9 on it.Therefore, P(A score a point) + P(B score a point) + P(C score a point) does not equal 1.Only the sum of all mutually exclusive outcomes equals 1.There are four numbers that are neither square nor multiples of 3 (2, 5, 7 and 8).No, this game is not fair. Team C is more likely to win. 7 Fair games A spinner has five equal sectors numbered 1 to 5. The spinner is spun many times.If the spinner stops on an evennumber team A gets 3 points.If the spinner stops on an oddnumber team B gets 2 points.12345Suppose the spinner is spun 50 times.We would expect the spinner to stop on an even number 20 times and on an odd number 30 times.The game is fair because, although the spinner is less likely to stop on an even number, team A gets proportionally more points when it does.The probability of the spinner stopping on an even number is 0.4. The probability of the spinner stopping on an odd number is 0.6. So, the spinner is 50% more likely to stop on an odd number. The game is fair because team A get 50% more points when the spinner stops on an even number.We can show that the game is fair by considering a theoretical game where the spinner is spun 50 times.Team A would score 20 × 3 points = 60 pointsTeam B would score 30 × 2 points = 60 pointsYes, this game is fair. 8 Scratch cards Scratch off a £ sign and win £10! £ £ £ £ nowinnowinnowinnowinDiscuss which card is most likely to win.The yellow card and the blue card both have the same number of £ signs. However the blue card has more no win boxes. Conclude that it has a smaller proportion of £ signs and is less likely to win.The red scratch card has five £ signs and so some pupils may believe that this card has a greater probability of winning. Stress that the red card has a smaller proportion of winning squares than the yellow card (5/16 is less than 3/9). The yellow card is therefore more likely to win a prize.By comparing the proportions of winning squares conclude that the yellow card is most likely to win, followed by the red card. The blue card is least likely to win.You are only allowed to scratch off one square and you can’t see what is behind any of the squares.Which of the scratch cards is most likely to win a prize? 9 Bags of counters Choose a blue counter and win a prize! bag cbag abag bbag cDiscuss which bag is most likely to win.Stress that is the bag with the largest proportion of blue counters that is the most likely to win.Bag a has 4/12 blue counters, bag b has 3/10 blue counters and in bag c there are 2/5 blue counters. Converting these to decimals we have blue in bag a, 0.3 blue in bag b and 0.4 blue in bag c.Bag c is therefore the most likely to win the prize and then bag a. Bag b is the least likely to win.We can also look at the ratio of blue counters to yellow counters.In bag a there are two yellow counters for each blue counter.In bag b there are 21/3 yellow counters for each blue counter.In bag c there is 11/2 yellow counters for each blue counter.Bag c is the most likely to win because there are fewer yellow counters for each blue counter.Stress the difference between ratio and proportion.Proportion compares the parts to the whole and ratio compares the parts to each other.You are only allowed to choose one counter at random from one of the bags.Which of the bags is most likely to win a prize? 10 Probability statements Statements involving probability are often incorrect or misleading. Discuss the following statements:The number 18 is has been drawn the most often in the national lottery so I’m more likely to win if I choose it.I’ve just thrown four heads in a row so I’m much less likely to get a head on my next throw.Discuss each statement in detail.Many misconceptions arise in probability due to a failure to appreciate the random nature of independent events.For example, for the second statement, if we assume that the coin is unbiased then the next throw is just as likely to come up heads than any other throw- the probability is ½- because the coin has no memory and the results are random.It is true that it is very unlikely that five heads in a row would be thrown, however, we are not talking about the probability of getting five heads in a row, we are talking about the probability of the next throw being heads.We could also argue that since it is unlikely that four heads would be thrown in a row the coin must be biased in some way. Based on the coins past history it could therefore be argued that the coin is actually more likely to land heads up.For the last statement, this is only true if the meal served is random and that both curry and pizza are equally likely. If there is a choice involved then the only way to estimate the probability of the next person choosing curry is to carry out a survey to find out which meal people prefer. If 74 out of 100 people surveyed preferred pizza, for example, then we could estimate that the probability of the next person choosing pizza is 0.74 or 74%.There are two choices for lunch, pizza or curry. That means that there is a 50% chance that the next person will choose pizza.I’m so unlucky. If I roll this dice I’ll never get a six. 11 D4.2 The probability scale ContentsD4 ProbabilityD4.1 The language of probabilityD4.2 The probability scaleD4.3 Calculating probabilityD4.4 Probability diagramsD4.5 Experimental probability 12 The probability scaleThe chance of an event happening can be shown on a probability scale.Meeting with King Henry VIIIA day of the week starting with a TThe next baby born being a boyGetting homework this lessonA square having four right anglesimpossibleDiscuss the probability scale. The more likely an event is to occur, the further to the right of the line it is placed. The less likely an event is to occur, the further to the left.unlikelyeven chancelikelycertainLess likelyMore likely 13 The probability scale We measure probability on a scale from 0 to 1. If an event is impossible or has no probability of occurring then it has a probability of 0.If an event is certain it has a probability of 1.This can be shown on the probability scale as:1impossibleeven chancecertainProbabilities are written as fractions, decimal and, less often, as percentages between 0 and 1. 14 The probability scaleAsk pupils to drag the pointer to the correct position on the scale. 15 D4.3 Calculating probability ContentsD4 ProbabilityD4.1 The language of probabilityD4.2 The probability scaleD4.3 Calculating probabilityD4.4 Probability diagramsD4.5 Experimental probability 16 Higher or lowerStart by revealing the first card and asking the class to predict whether the next card will be higher or lower? How often can pupils correctly predict whether the next card will be higher or lower? When can they be completely sure of their answer?Discuss strategies. Strategies may improve as you play more than once; for example, are pupils taking into account all the cards already turned over, or just the last one turned? 17 Listing possible outcomes When you roll a fair dice you are equally likely to get one of six possible outcomes:161616161616Explain that the word ‘fair’ or ‘unbiased’ means that each outcome is equally likely. Some dice are ‘weighted’. That means that the weight of the dice is unevenly distributed and some numbers are more likely to appear than others.The probability of getting any number is 1 (certain) so the probability of getting each different number is 1 ÷ 6 or 1/6.Since each number on the dice is equally likely the probability of getting any one of the numbers is 1 divided by 6 or16 18 Calculating probability What is the probability of the following events?1) A coin landing tails up?3) Drawing a seven of heartsfrom a pack of 52 cards?12P(tails) =152P(7 of ) =2) This spinner stopping onthe red section?4) A baby being born on aFriday?For each example ask pupils to tell you the number of equally likely outcomes before revealing the probability.Introduce the notation of P(n) for the probability of an event n.1417P(red) =P(Friday) = 19 Calculating probability If the outcomes of an event are equally likely then we can calculate the probability using the formula:Probability of an event =Number of successful outcomesTotal number of possible outcomesFor example, a bag contains 1 yellow, 3 green, 4 blue and 2 red marbles.Point out that calculated probabilities are usually given as fractions but that they can also be given as decimals and (less often) as percentages.Ask pupils to give you the probabilities (as decimals, fractions and percentages) of gettingA blue marbleA red marbleA yellow marbleA purple marbleA blue or a green marble etc.What is the probability of pulling a green marble from the bag without looking?310P(green) =or 0.3or 30% 20 Calculating probability This spinner has 8 equal divisions:What is the probability of the spinner landing ona red sector?a blue sector?a green sector?28=14a) P(red) =18b) P(blue) =48=12c) P(green) = 21 Calculating probability A fair dice is thrown. What is the probability of gettinga 2?a multiple of 3?an odd number?a prime number?a number bigger than 6?an integer?16a) P(2) =26=13b) P(a multiple of 3) =36=12c) P(an odd number) = 22 Calculating probability A fair dice is thrown. What is the probability of gettinga 2?a multiple of 3?an odd number?a prime number?a number bigger than 6?an integer?36=12d) P(a prime number) =Don’t write6e) P(a number bigger than 6) =6f) P(an integer) == 1 23 Calculating probability The children in a class were asked how many siblings (brothers and sisters) they had. The results are shown in this frequency table:Number of siblingsNumber of pupils418293567What is the probability that a pupil chosen at random from the class will have two siblings?There are 30 pupils in the class and 9 of them have two siblings.930=310So, P(two siblings) = 24 Calculating probability A bag contains 12 blue balls and some red balls.The probability of drawing a blue ball at random from thebag isHow many red balls are there in the bag?3712 balls represent of the total.37So, 4 balls represent of the total17Reason that if the probability of drawing a blue ball at random is 3/7, then 3/7 of the balls must be blue.To find the total number of balls we must divide the number of blue balls by 3 and multiply by 7 to get 28. The number of red balls is then found by subtracting 12 from 28 to get 16.Discuss alternative methods to calculate this using proportional reasoning or algebra.and, 28 balls represent of the total.7The number of red balls = 28 – 12 =16 25 The probability of an event not occurring The following spinner is spun once:What is the probability of it landing on the yellow sector?14P(yellow) =What is the probability of it not landing on the yellow sector?Two probabilities that add up to one are sometimes called complementary probabilities (compare with number complements).34P(not yellow) =If the probability of an event occurring is p then the probability of it not occurring is 1 – p. 26 The probability of an event not occurring The probability of a factory component being faulty is What is the probability of a randomly chosen component not being faulty?P(not faulty) = 1 – 0.03 =0.97The probability of pulling a picture card out of a full deck ofcards isWhat is the probability not pulling out a picture card?313P(not a picture card) = 1 – =3131013 27 The probability of an event not occurring The following table shows the probabilities of 4 events. For each one work out the probability of the event not occurring.EventProbability of the event occurringProbability of the event not occurring3525AB0.770.23C9201120D8%92% 28 The probability of an event not occurring There are 60 sweets in a bag.10 are cola bottles,14are fried eggs,20 are hearts,the rest are teddies.What is the probability that a sweet chosen at random from the bag is:We can work out the number of sweets that are not teddies by finding the sum of 10, 20 and a ¼ of 60 to get 45.Modify the numbers to make this problem more challenging.56a) Not a cola bottleP(not a cola bottle) =4560=34b) Not a teddyP(not a teddy) = 29 Mutually exclusive outcomes Outcomes are mutually exclusive if they cannot happen at the same time.For example, when you toss a single coin either it will land on heads or it will land on tails. There are two mutually exclusive outcomes.Outcome A: HeadOutcome B: TailWhen you roll a dice either it will land on an odd number or it will land on an even number. There are two mutually exclusive outcomes.Outcomes are mutually exclusive if we can either have one or the other but not both. Stress that if we can use either … or … when describing two or more outcomes then they are probably mutually exclusive.Outcome A: An odd numberOutcome B: An even number 30 Mutually exclusive outcomes A pupil is chosen at random from the class. Which of the following pairs of outcomes are mutually exclusive?Outcome A: the pupil has brown eyes.Outcome B: the pupil has blue eyes.These outcomes are mutually exclusive because a pupil can either have brown eyes, blue eyes or another colour of eyes.Outcome C: the pupil has black hair.Outcome D: the pupil has wears glasses.These outcomes are not mutually exclusive because a pupil could have both black hair and wear glasses. 31 Adding mutually exclusive outcomes If two outcomes are mutually exclusive then their probabilities can be added together to find their combined probability.For example, a game is played with the following cards:What is the probability that a card is a moon or a sun?1313P(moon) =andP(sun) =Ask pupils to tell you the probability of getting a crescent card or a star card.Reveal the solution on the board.Stress that only events that are mutually exclusive can be added in this way. For example, If we are drawing a card at random from a pack P(King) = 2/52, P(Club) = 13/52, but P(King or club) 2/ /52 because a card could be both a king and a club.Drawing a moon and drawing a sun are mutually exclusive outcomes so,13+=23P(moon or sun) = P(moon) + P(sun) = 32 Adding mutually exclusive outcomes If two outcomes are mutually exclusive then their probabilities can be added together to find their combined probability.For example, a game is played with the following cards:What is the probability that a card is yellow or a star?1313P(yellow card) =andP(star) =Ask pupils to tell you the probability of getting a yellow card or a star card. Stress that this cannot be found by adding.The probability is 5/9 because one of the cards is both yellow and a star.Drawing a yellow card and drawing a star are not mutually exclusive outcomes because a card could be yellow and a star.P (yellow card or star) cannot be found by adding. 33 The sum of all mutually exclusive outcomes The sum of all mutually exclusive outcomes is 1.For example, a bag contains red counters, blue counters, yellow counters and green counters.P(blue) = 0.15P(yellow) = 0.4P(green) = 0.35What is the probability of drawing a red counter from the bag?Explain that when we draw a counter from the bag it is either red, blue, yellow or green. These outcomes are therefore mutually exclusive, there are no other possible outcomes and so their combined probabilities must equal 1.Mutually exclusive outcomes can be added together.The decimals on this slide can be changed to make the problem more challenging.P(blue, yellow or green) = =0.9P(red) = 1 – 0.9 =0.1 34 The sum of all mutually exclusive outcomes A box contains bags of crisps. The probability of drawing out the following flavours at random are:2513P(salt and vinegar) =P(ready salted) =The box also contains cheese and onion crisps.What is the probability of drawing a bag of cheese and onion crisps at random from the box?Pupils may need to revise the addition of fractions with different denominators to complete this question. See N6.1 Adding and subtracting fractions.Explain that when we draw a packet of crisps from the box it is either salt and vinegar, cheese and onion or ready salted. These outcomes are therefore mutually exclusive. There are no other possible outcomes and so their combined probabilities must equal 1.25+13=6 + 515=1115P(salt and vinegar or ready salted) =P(cheese and onion) = 1 –1115=415 35 The sum of all mutually exclusive outcomes A box contains bags of crisps. The probability of drawing out the following flavours at random are:2513P(salt and vinegar) =P(ready salted) =The box also contains cheese and onion crisps.There are 30 bags in the box. How many are there of each flavour?25of 30 =Number of salt and vinegar =Pupils may need to revise finding fractions of amounts to complete this question. See N6.2 Finding a fraction of an amount.Explain that the probability relates to the proportion of each flavour. If we know the probability of getting each flavour and the number of bags altogether, then we can use this information to work out the number of each flavour.12 packets13of 30 =Number of ready salted =10 packets415of 30 =Number of cheese and onion =8 packets 36 D4.4 Probability diagrams ContentsD4 ProbabilityD4.1 The language of probabilityD4.2 The probability scaleD4.3 Calculating probabilityD4.4 Probability diagramsD4.5 Experimental probability 37 Finding all possible outcomes of two events Two coins are thrown. What is the probability of getting two heads?Before we can work out the probability of getting two heads we need to work out the total number of equally likely outcomes.There are three ways to do this:1) We can list them systematically.Using H for heads and T for tails, the possible outcomes are:Stress that when there is more than one event it is important to list all the possible outcomes systematically.Listing the outcomes systematically means listing them in a logical order to make sure that none are left out.Explain that TH means, ‘a tail on the first coin and a head on the second’ and that HT means, ‘a head on the first coin and a tail on the second’. These are therefore two separate events.TH and HT are separate equally likely outcomes.TT,TH,HT,HH. 38 Finding all possible outcomes of two events 2) We can use a two-way table.Second coinHTFirstcoinHHHTTHTTFrom the table we see that there are four possible outcomes one of which is two heads so,14P(HH) = 39 Finding all possible outcomes of two events 3) We can use a probability tree diagram.OutcomesSecond coinHHHFirst coinHTHTTHTHTTTAgain we see that there are four possible outcomes so,14P(HH) = 40 Finding the sample space A red dice and a blue dice are thrown and their scores are added together.What is the probability of getting a total of 8 from both dice?There are several ways to get a total of 8 by adding the scores from two dice.We could get a 2 and a 6,a 3 and a 5,a 4 and a 4,Stress that the sample space is the set of all possible outcomes.a 5 and a 3,and a 6 and a 2.To find the set of all possible outcomes, the sample space, we can use a two-way table. 41 Finding the sample space +From the sample space we can see that there are 36 possible outcomes when two dice are thrown.2345678345678845678985678910Five of these have a total of 8.As the two-way table is completed ask pupils what patterns they notice.Use the completed table to justify that the probability of the total score on the two dice being 8 is 5/35.Ask pupils to use the table to give the probabilities of other scores such as:P(3)P(a score less than 7)P(an even score)P(a score that is prime)P(a score that is square)Ask pupils to cancel down any fractions if possible.867891011536P(8) =8789101112 42 Scissors, paper, stoneIn the game scissors, paper, stone two players have to show either scissors, paper, or stone using their hands as follows:scissorspaperstoneThe rules of the game are that:Scissors beats paper (it cuts).Paper beats stone (it wraps).Stone beats scissors (it blunts).If both players show the same hands it is a draw. 43 Scissors, paper, stoneWhat is the probability that both players will show the same hands in a game of scissors, paper, stone?We can list all the possible outcomes in a two-way table using S for Scissors, P for Paper and T for sTone.ScissorsPaperStoneFirst playerSecond playerSSSSSPSTPSPPPPPTTSTPTTTT39=13P(same hands) = 44 Scissors, paper, stoneWhat is the probability that the first player will win a game of scissors, paper, stone?Using the two-way table we can identify all the ways that the first player can win.ScissorsPaperStoneFirst playerSecond playerSSSPSTPSPPPTTSTPTTSPPTRemember the rules of the game:Scissors beats paper; paper beats stone; stone beats scissors.TS39=13P(first player wins) = 45 Scissors, paper, stoneWhat is the probability that the second player will win a game of scissors, paper, stone?Using the two-way table we can identify all the ways that the second player can win.ScissorsPaperStoneFirst playerSecond playerSSSPSTPSPPPTTSTPTTSTPSRemember the rules of the game:Scissors beats paper; paper beats stone; stone beats scissors.TP39=13P(second player wins) = 46 Scissors, paper, stone Is scissors, paper, stone a fair game? 1 P(first player wins) =13P(second player wins) =13P(a draw) =13Both player are equally likely to win so, yes, it is a fair game.Review what is meant by a fair game. In a fair game all players are equally likely to win.Allow pupils to play the game in pairs and to record their results.Discuss the fact that in 30 games we would expect to get 10 wins for the first player, 10 wins for the second player and 10 draws. Discuss why this does not happen in reality.Play scissors paper stone 30 times with a partner.Record the number of wins for each player and the number of draws. Are the results as you expected? 47 D4.5 Experimental probability ContentsD4 ProbabilityD4.1 The language of probabilityD4.2 The probability scaleD4.3 Calculating probabilityD4.4 Probability diagramsD4.5 Experimental probability 48 Estimating probabilities based on data What is the probability a person chosen at random being left-handed?Although there are two possible outcomes, right-handed and left-handed, the probability of someone being left-handed is not ½, why?The two outcomes, being left-handed and being right-handed, are not equally likely. There are more right-handed people than left-handed.To work out the probability of being left-handed we could carry out a survey on a large group of people. 49 Estimating probabilities based on data Suppose 1000 people were ask whether they were left- or right-handed.Of the 1000 people asked 87 said that they were left-handed.From this we can estimate the probability of someone beingleft-handed as or871000If we repeated the survey with a different sample the results would probably be slightly different.The more people we asked, however, the more accurate our estimate of the probability would be. 50 Relative frequencyThe probability of an event based on data from an experiment or survey is called the relative frequency.Relative frequency is calculated using the formula:Relative frequency =Number of successful trialsTotal number of trialsFor example, Ben wants to estimate the probability that a piece of toast will land butter-side-down.He drops a piece of toast 100 times and observes that it lands butter-side-down 65 times.Relative frequency =65100=1320 51 Relative frequencySita wants to know if her dice is fair. She throws it 200 times and records her results in a table:NumberFrequencyRelative frequency13122733843054263231200= 0.15527200= 0.14538200= 0.19030200= 0.150If the dice were fair we would expect to get each outcome an equal number of times.Stress that in an experiment the results are random and unpredictable. If we repeated this experiment we would get a different set of results.Conclude that this dice seems to be fair because the relative frequencies are all close to 1/6 or42200= 0.21032200= 0.160Is the dice fair? 52 Expected frequencyThe theoretical probability of an event is its calculated probability based on equally likely outcomes.If the theoretical probability of an event can be calculated, then when we do an experiment we can work out the expected frequency.Expected frequency = theoretical probability × number of trialsFor example, if you rolled a dice 300 times, how many times would you expect to get a 5?The theoretical probability of getting a 5 is .16So, expected frequency = × 300 =1650 53 Expected frequencyIf you tossed a coin 250 times how many times would you expect to get a tail?12Expected frequency = × 250 =125If you rolled a fair dice 150 times how many times would you expect to a number greater than 2?Stress that the greater the number of trials the closer the experimental frequency will be to the expected frequency.23Expected frequency = × 150 =100 54 Spinners experimentUse the spinners experiment to compare the theoretical probability with the relative frequency for each spinner.Notice that the more times the spinner is spun the closer the relative frequency gets to the theoretical probability. 55 Random resultsRemember that when an experiment is carried out the results will be random and unpredictable.Each time the experiment is repeated the results will be different.The more times an experiment is repeated the more accurate the estimated probability will be.Jenny throws a dice 12 times and doesn’t get a six. She concludes that the dice must be biased.Discuss the unpredictability of random processes.Although you would expect to get two sixes in twelve throws it is possible that you won’t. You would have to thrown the dice many more times to find out if it is biased.
The first composite picture of a dark matter bridge has been captured by scientists. The dark matter bridge is a web-like superstructure that connects galaxies together. Astronomers have been predicting it for decades. The image combines several individual images and has confirmed the predictions that galaxies in the universe are tied together through a cosmic web connected by dark matter. This discovery had been unobservable until now. The mysterious substance dark matter comprises around 25 per cent of the universe. It does not absorb or reflect light, nor shines because of which it has traditionally been largely undetectable, except through gravity. “For decades, researchers have been predicting the existence of dark-matter filaments between galaxies that act like a web-like superstructure connecting galaxies together,” said Mike Hudson, a professor of astronomy at the University of Waterloo in Canada. “This image moves us beyond predictions to something we can see and measure,” said Hudson. A technique called weak gravitational lensing was used by Hudson and Seth Epps, researcher at the University of Waterloo. This technique causes the pictures of distant galaxies to warp slightly under the influence of an unseen mass such as a planet, a black hole, or in this case, dark matter. Pictures from a multi-year sky survey at the Canada-France-Hawaii Telescope were used to measure the effect. Lensing images from more than 23,000 galaxy pairs located 4.5 billion light-years away were combined in order to produce a composite image or map, showing the presence of dark matter between the two galaxies. Results show the dark matter filament bridge is strongest between systems less than 40 million light years apart. “By using this technique, we’re not only able to see that these dark matter filaments in the universe exist, we’re able to see the extent to which these filaments connect galaxies together,” said Epps. The research was published in the journal Royal Astronomical Society.
Fermi Finds the Farthest Blazars NASA's Fermi Gamma-ray Space Telescope has discovered the five most distant gamma-ray blazars yet known. The light detected by Fermi left these galaxies by the time the universe was two billion years old. Two of these galaxies harbor billion-solar-mass black holes that challenge current ideas about how quickly such monsters could grow. Watch this video on the NASA Goddard YouTube channel. Complete transcript available. NASA's Fermi Gamma-ray Space Telescope has identified the farthest gamma-ray blazars, a type of galaxy whose intense emissions are powered by supersized black holes. Light from the most distant object began its journey to us when the universe was 1.4 billion years old, or nearly 10 percent of its present age. Despite their youth, these far-flung blazars host some of the most massive black holes known. That they developed so early in cosmic history challenges current ideas of how supermassive black holes form and grow. Blazars constitute roughly half of the gamma-ray sources detected by Fermi's Large Area Telescope (LAT). Astronomers think their high-energy emissions are powered by matter heated and torn apart as it falls from a storage, or accretion, disk toward a supermassive black hole with a million or more times the sun's mass. A small part of this infalling material becomes redirected into a pair of particle jets, which blast outward in opposite directions at nearly the speed of light. Blazars appear bright in all forms of light, including gamma rays, the highest-energy light, when one of the jets happens to point almost directly toward us. Previously, the most distant blazars detected by Fermi emitted their light when the universe was about 2.1 billion years old. Earlier observations showed that the most distant blazars produce most of their light at energies right in between the range detected by the LAT and current X-ray satellites, which made finding them extremely difficult. Then, in 2015, the Fermi team released a full reprocessing of all LAT data, called Pass 8, that ushered in so many improvements astronomers said it was like having a brand new instrument. The LAT's boosted sensitivity at lower energies increased the chances of discovering more far-off blazars. Two of the blazars boast black holes of a billion solar masses or more. All of the objects possess extremely luminous accretion disks that emit more than two trillion times the energy output of our sun. This means matter is continuously falling inward, corralled into a disk and heated before making the final plunge to the black hole. Black-hole-powered galaxies called blazars are the most common sources detected by NASA's Fermi. As matter falls toward the supermassive black hole at the galaxy's center, some of it is accelerated outward at nearly the speed of light along jets pointed in opposite directions. When one of the jets happens to be aimed in the direction of Earth, as illustrated here, the galaxy appears especially bright and is classified as a blazar. Credits: M. Weiss/CfA For More Information Please give credit for this item to: NASA's Goddard Space Flight Center. However, individual items should be credited as indicated above.
Lesson 7 of 22 Objective: Students will be able to find the product of two numbers using the standard algorithm. According to the fifth grade common core standards students should be able to multiply multi-digit numbers using the standard algorithm. There have been other strategies, used to develop student understanding, taught in previous grades such as partial products and lattice but now it is time to move to the more efficient standard algorithm. In today’s lesson, I hope to show students the efficiency of the standard algorithm and introduce the turtlehead method to them. I want them to focus on explaining their thinking as they are completing each problem. To begin this lesson I will invite students to compete against me in completing a multiplication problem. I will have the student use lattice multiplication while I use the standard algorithm. Alright, we’re going to start out today with a little competition. In order to find a worthy opponent I need someone who uses lattice to solve multiplication problems. Is there anyone who feels brave enough to come up to the board and do a multiplication problem racing against me? I get several students to volunteer so I call a few up and give them the problem. 72 x 14. We all write the problem down and get ready to begin. I say start and we’re off! While the students are still completing the drawing of the lattice box I announce that I’m done. In a joking manner I banter with the students. I’ll just wait until you’re done. What took you so long? (Waiting for few puzzled responses.) Did you guys not hear me say start? (Students smiling and lightly laughing.) To the rest of the class: What happened here? I ask the students to return to their seats and I have everyone turn to their neighbor and talk about what happened during the competition. I bring students back to the whole group to discuss. Students quickly make the connection that my method was much quicker because I didn’t have to draw the lattice first. Today I’m going to show you the steps for this type of multiplication called the standard algorithm. Some of you might already be familiar with this type of multiplication but you may not have learned it using the turtlehead method. To introduce the turtlehead method of multiplication I show the students a short video clip using the method. When the video is finished I ask students to summarize the steps in the video. We then do some sample problems together using the document camera. After two problems, I place another on the whiteboard and ask for a volunteer to walk us through the problem using the turtlehead method. For this first student walk through I choose a student that I know will be able to explain the problem very well. I write one more problem on the board and choose a student that I know is probably struggling a bit with the process. I have this student come up to the board and begin the problem. If they struggle, I allow them to call on another student to give them some advice as to what to do next. I cheer the struggling student for hanging in there, and assure them that they are not the only one struggling. We are all just getting started with something new! To offer students some additional practice with the turtlehead method I give them a set of six two-digit multiplication problems to work on with a partner. While students are working with their partner I ask them to focus on explaining the problem step by step to one another. I circulate and listen in. If students are struggling, I judge whether it is productive struggle, or "in the deep end" struggle. If students are moving toward frustration, I'll suggest some resources (in this case, they can watch the video again) that they can turn to. I'm trying to create independent learners, and encouraging students in identifying and using resources lays a foundation for their future success. After allowing students time to work I bring the class back and ask students to share out their thinking of how they solved each problem.
Digital signal processing (DSP) has come a long way in 20 years. As late as the early 1980s, it still needed to be done on mainframe computers. Research work was done by digitizing signals for analysis in complex computer analysis runs that might return a result a day later. Scientists wrote their own programs or used libraries of programs written specifically to do analysis with. In fact, digital signal processing was used as a way to test filter designs for new electronic circuits. At that time, no one expected that computers would get faster and smaller as quickly as they did. If we strip away the DIGITAL from Digital Signal Processing, we are left with something that we’ve been doing in electronics since it was first invented, Signal Processing! Signal processing is all about taking a signal, applying some change to it, and then getting a new signal out. That change might be amplification or filtration or something else, but nearly all electronic circuits can be considered to be signal processors. Looked on in this way, the signal processor as a black box might be composed of discrete components like capacitors and resistors, or it could be a complex integrated circuit with many circuits to accomplish a more complex task, or it could be a digital system which accepts a signal on its input and outputs the changed signal. So long as it accomplishes its defined task, it doesn’t matter how the box works internally. Digital signal processors require several things to work properly: A processor fast enough and with enough precision to support the mathematics it needs to implement. Supporting memory to store programming, samples, intermediate results, and final results. Analog-to-Digital (A/D) and Digital-to-Analog (D/A) Converters to bring real signals into and out of the digital domain. Programming to do the job. Digital signal processors, even single chip DSP systems, are built from these elements. Twenty years ago, anyone using DSP had to be quite a mathematician to be able to implement and use the algorithms. Today, DSP can be incorporated into devices so simple that they can be mass-produced and operated with as little as the press of a button. The internal programming of a DSP chip is far too complex to deal with here. It is generally proprietary as well, but the basics of how DSP works are simple enough to understand. While you won’t be able to implement your own algorithms after reading this, you will know a little more about how DSP works. Digital systems don’t work with continuous waveforms. Much work was done trying to create analog computers to handle calculations on continuous systems, but analog computers proved to be inflexible, slow, and hard to reconfigure to new tasks. In particular, it was hard to implement general algorithms on them. Maybe if digital systems had not developed so fast through the 1950s and 1960s, we might have solved the problems, but by the 1960s, it was already rare to find an analog computer anywhere. Serious work was done on digital computers where complex algorithms could be coded relatively easily. This meant that we had to get our data into digital form. In the 1960s, digitizing data was often a manual task. As late as the 1980s, much data was read into digital computers from paper tape systems. However, increasingly computers were being harnessed directly to circuits that could produce a digital output when given an analog input. It became possible to take a signal such as the one below: And pass it into the computer automatically as a stream of digital data that looked like this: Once in the computer, the process could be reversed by playing it out through a D/A converter to produce a close approximation of the original waveform. Notice the words ‘close approximation’. No digital sampling system can perfectly reproduce the original signal because each sample is a single number representing the signal in some small, but finite interval. Modern techniques make it possible for that digital sample to be so good that you can’t tell the difference on your CD or DVD, but the difference is still there. Digital systems have errors just like any system. Minimizing these errors to make them unnoticeable occupies much of the time of the digital system designer. Once the signal exists inside our digital system as a stream of samples, we can now process them in a variety of ways. This is where the math gets complicated and we have a real need to know about the mathematics. However, if what needs to be done is simple enough so that it can be done with existing DSP chips, we may not need to know any of the complex mathematics ourselves, leaving it to the chip designers to make the math work right. If you’re doing something special though, then even with DSP chips, you’ll need to be skilled enough to know what can be done and what cannot. Consider though how a simple algorithm can work in the digital domain. One of the simplest possible filters is an averaging filter. Using a digital averaging filter on the signal above, which was generated from two pure tones and a random noise generator, we can smooth out the signal and make it less noisy: It doesn’t perfectly get rid of the noise element, but it does smooth the signal and this may be enough for what we want to do. More complex filters can be constructed by weighted averages of samples taken from the digital stream, but now we run into another complex problem, time. Many of us don’t think much about the time it takes to do calculations. We may be frustrated by how slow our word processor is working or how long it takes for our spreadsheet to calculate, but unless you have worked at the microprocessor level, programming at a very low level, microprocessor time cycles have very little meaning. However, when working with DSP, processing time becomes all important. Consider what we would have to do to average the last three digital samples together and output a signal at the same rate as we are sampling: A new sample has to be taken and stored for use. The new sample has to be averaged with the last two. The result has to be output. All of this has to take place before the next sample is taken. This is STREAM processing, processing the signal in real time. If we are sampling at 10,000 samples per second, then we have 1 ten-thousandth of a second to complete the calculation. This is the long time in the life of any real microprocessor, but may not be enough if we want to use more complex algorithms. Block processing collects a large number of samples, say 1024, at a time and processes them while the next 1024 are being collected. Some algorithms, such as the Fast Fourier Transform can only work in this mode, but even this may not be enough time for very complex calculations. Consider again the signal at the beginning of this note. It was made from two pure tones plus a random noise element. With block processing, we can apply a Fast Fourier Transform to the digitized signal to get an output that looks like this: A Fourier Transform is a special mathematical algorithm that transforms the signal into a representation we can think of as the energy in the signal vs frequency. In this case, we can see that most of the energy is concentrated in two single frequencies and the rest is spread out randomly across the spectrum. The noise is that random element. An Inverse Fourier Transform can return the signal back to it original time sampled form, called the time domain. Why might we want to do a Fourier transform? Simply because we can apply algorithms in the frequency domain that we can’t apply in the time domain. Some things, like tones, stand out in the frequency domain. Other things, like noise, appear as a random element below some threshold in the frequency domain. Clearly, if the signal we wanted to process was our simple two tone system, this would be an easy way of isolating the tones and eliminating most of the noise. However, real life is never that simple. Real signals, like SSB or CW Morse signals vary over time. They change in what seem to be dynamic and almost random ways. There are patterns, or we wouldn’t be able to understand them, but the state of DSP has not grown sophisticated enough yet for us to understand them. We may be able to understand the signals, but even the most complicated processing yet devised can’t come close. This runs us right back up against the time wall. Time is very important to the digital designer. Advances in the speed of DSP processors and microprocessors in general open up new things that a digital designer can do, but always we are limited by time and space requirements. Doing the complex algorithms is easy when you have as much space as you want to store data and as much time as you need for the calculations, but when a DSP processor has to do something in real time, there are severe limits on just how much can be done. To do practical work with DSP, we have to accept that the sophistication, while great, is not infinite. Sophisticated understanding of DSP allows us to recognize a signal in noise by its characteristics. We can process out much of the noise, improving the ratio of signal to noise thereby making it more understandable. We can recognize interfering tones and process them out. Even more, we can adapt as the signal and the noise change over time. No algorithm is perfect, but compared to 20 years ago, the level of improvement in noise reduction is phenomenal. SGC’s ADSP2 takes advantage of these advances and makes digital noise reduction a reality for a wide variety of transceivers and receivers, allowing you to concentrate on the communication and not the noise. For further reading about Digital Signal Processing, SGC has a small book available online for download as a PDF file which can be found on our publications page. For those who would like a more sophisticated understanding of DSP, we recommend Digital Signal Processing Technology, Doug Smith, American Radio Relay League, 2001. SGC Inc., Tel: 425-746-6310 Fax: 425-746-6384 Email: email@example.comSGC reserves the right to change specifications, release dates and price without notice.
Secretary of the Treasury Alexander Hamilton, meanwhile, set out to establish firm financial policies for the country. In his famous Reports on the Public Credit, he proposed that the federal government should assume and pay off all state debts, as well as federal debt—a then-staggering sum in the tens of millions of dollars. Furthermore, Hamilton believed that the new government should sell bonds to encourage investment by citizens and foreign interests. Hamilton wanted his measures to establish confidence in the new U.S. government at home and abroad. His proposal stipulated that Congress would have to fund the entire debt at par, which meant that the federal government would pay back all borrowed money with interest. Hamilton believed that funding the debt at par would send a signal that the United States was a responsible new member of the international community and a safe environment for speculators to invest their money. He also believed that a sizeable national debt would prevent states from drifting from the central government and thus bind them together. However, Hamilton’s ideas seemed ludicrous to many. Secretary of State Jefferson, for instance, believed that a large national debt would be a “national curse” that would depress poor farmers and ruin the economy. To the dismay of the Jeffersonians, assumption and funding at par both worked, as foreign investment began to boost the fledgling U.S. economy. To raise money to pay off these debts, Hamilton suggested that Congress levy an excise tax on liquor. However, because farmers often converted their grain harvests into liquor before shipping (since liquor was cheaper to ship than grain), many congressmen from southern and western agrarian states believed that the excise tax was a scheme to make northern investors richer. A compromise was finally reached in 1790: Congress would assume all federal and state debts and levy an excise tax to raise revenue. In exchange, the nation’s capital would be moved from New York City to the new federal District of Columbia in the South. Hamilton then set out to create a national Bank of the United States, which would serve as a storehouse for federal money but also be funded by private investments. This proposal infuriated Secretary of State Jefferson and sparked even more of a debate than had the Reports on the Public Credit.
So the age old question, "Does size matter?" is the guiding question for this lesson. Of course, the lesson will focus on the size of cells. Your students may misinterpret the title of the lesson, but have fun with it . . . and at least you have their attention. The video clip below will give a short tour that compares the size of common everyday items that we can see with our eyes and then contrast their size with microscopic objects that are relevant to our study of Biology. The video clip was created using the content found on the University of Utah Health Science website. Students will write down the names of each item that they remember discussing throughout this Biology course. Students will also make two observations or reactions to the size comparisons. How size 12 point font compares to a mitochondria or how a coffee bean compares to a transfer RNA. As a follow-up, the class will discuss the size comparison of the items that are viewed on the video clip in a whole-group conversation that focuses on the importance of size differentials. Students will get out a sheet of paper and title it, "Lecture Notes: Cell Growth". These notes will focus on the cell size and examine cell growth. The notes will also encourage students to consider the ratio of volume to surface area as it relates to cell size and function. The objective of this lesson is for students to conceptualize that once cells grow beyond their optimal volume:surface area ration then they are not as efficient in completing cellular functions. By regular cell division, the cells constantly create new, healthy cells and remain at the optimal size to complete their cellular function. As a follow-up, the class will participate in a whole-group discussion using these prompts: These questions will be written on the front board for students to quickly write a response on their paper. Once all students have finished, the class will discuss the responses as a segue to the introduction of Mitosis. The last question will be referred to again at the conclusion of the lesson to introduce the process of mitosis in preparation of the next lesson on Modeling Mitosis. As follow-up to the lecture notes in the previous section, students will create models using provided Cubes Templates. Students will use scissors and tape to construct the three different size models by following the instructions: The students will have created three different sized cubes: 1 cm3, 3 cm3, and a 5cm3. These cubes will serve as models to demonstrate the relationship between surface area and volume as it relates to cellular function. Students will use the Modeling Limits To Cell Size -Student Handout to guide their hands-on experience. This activity will have students calculate the surface area and volume of each cube and record in the data tables of their handout. Students are then asked to calculate the ratio of surface area to volume for each of the three different sized cells. As an analysis of the activity, students are asked to complete the questions from the handout that contain questions such as: The objective of this activity is for students to realize that the smallest cube (cell model) has the highest surface area to volume ratio (6:1). The smallest cell has the greatest surface area of 6cm2 to the lowest volume of 1cm3. This model demonstrates that the smaller the cube the more efficient the surface area to volume ratio which enables the cell to function at a more efficient level for its daily cellular activities. To facilitate the review and discussion of this activity, teachers can utilize the provided Activity Answer Key. As a closing activity for this lesson, students will answer the simple question, "When it comes to cells, does size matter." Hopefully, after modeling cell size and analyzing the surface area to volume ratio, students will conclude that the smaller the cell the more efficient the surface area to volume ratio. In an effort to prepare students for the next lesson on cell division, students will brainstorm as many supporting facts that defend the claim that "cells need to divide so they can remain small and more efficient." Sample Student Response - Cell Size #1 - This student begins his response with vague details, but then realizes that the cell size needs to remain optimal to ensure that nutrients are able to enter and waste is able to leave the cell. Sample Student Response - Cell Size #2 - This student is also able to articulate the need for the cell to divide in order to maintain the optimal ratio of volume:surface area in order to obtain nutrients and expel wastes.
Social justice is a concept of fair and just relations between the individual and society, as measured by the distribution of wealth, opportunities for personal activity, and social privileges. In Western as well as in older Asian cultures, the concept of social justice has often referred to the process of ensuring that individuals fulfill their societal roles and receive what was their due from society. In the current global grassroots movements for social justice, the emphasis has been on the breaking of barriers for social mobility, the creation of safety nets and economic justice. Social justice assigns rights and duties in the institutions of society, which enables people to receive the basic benefits and burdens of cooperation. The relevant institutions often include taxation, social insurance, public health, public school, public services, labor law and regulation of markets, to ensure fair distribution of wealth, and equal opportunity. Interpretations that relate justice to a reciprocal relationship to society are mediated by differences in cultural traditions, some of which emphasize the individual responsibility toward society and others the equilibrium between access to power and its responsible use. Hence, social justice is invoked today while reinterpreting historical figures such as Bartolomé de las Casas, in philosophical debates about differences among human beings, in efforts for gender, ethnic, and social equality, for advocating justice for migrants, prisoners, the environment, and the physically and developmentally disabled. While the concept of social justice can be traced through the theology of Augustine of Hippo and the philosophy of Thomas Paine, the term "social justice" became used explicitly in the 1780s. A Jesuit priest named Luigi Taparelli is typically credited with coining the term, and it spread during the revolutions of 1848 with the work of Antonio Rosmini-Serbati. However, recent research has proved that the use of the expression "social justice" is older (even before the 19th century). For example, in Anglo-America, the term appears in The Federalist Papers, No. 7: "We have observed the disposition to retaliation excited in Connecticut in consequence of the enormities perpetrated by the Legislature of Rhode Island; and we reasonably infer that, in similar cases, under other circumstances, a war, not of parchment, but of the sword, would chastise such atrocious breaches of moral obligation and social justice." In the late industrial revolution, progressive American legal scholars began to use the term more, particularly Louis Brandeis and Roscoe Pound. From the early 20th century it was also embedded in international law and institutions; the preamble to establish the International Labour Organization recalled that "universal and lasting peace can be established only if it is based upon social justice." In the later 20th century, social justice was made central to the philosophy of the social contract, primarily by John Rawls in A Theory of Justice (1971). In 1993, the Vienna Declaration and Programme of Action treats social justice as a purpose of human rights education. Some authors such as Friedrich Hayek criticize the concept of social justice, arguing the lack of objective, accepted moral standard; and that while there is a legal definition of what is just and equitable "there is no test of what is socially unjust", and further that social justice is often used for the reallocation of resources based on an arbitrary standard which may in fact be inequitable or unjust. After the Renaissance and Reformation, the modern concept of social justice, as developing human potential, began to emerge through the work of a series of authors. Baruch Spinoza in On the Improvement of the Understanding (1677) contended that the one true aim of life should be to acquire "a human character much more stable than [one's] own", and to achieve this "pitch of perfection... The chief good is that he should arrive, together with other individuals if possible, at the possession of the aforesaid character." During the enlightenment and responding to the French and American Revolutions, Thomas Paine similarly wrote in The Rights of Man (1792) society should give "genius a fair and universal chance" and so "the construction of government ought to be such as to bring forward... all that extent of capacity which never fails to appear in revolutions." Although there is no certainty about the first use of the term "social justice", early sources can be found in Europe in the 18th century. Some references to the use of the expression are in articles of journals aligned with the spirit of the Enlightenment, in which social justice is described as an obligation of the monarch; also the term is present in books written by Catholic Italian theologians, notably members of the Society of Jesus. Thus, according to this sources and the context, social justice was another term for "the justice of society", the justice that rules the relations among individuals in society, without any mention to socio-economic equity or human dignity. The usage of the term started to become more frequent by Catholic thinkers from the 1840s, including the Jesuit Luigi Taparelli in Civiltà Cattolica, based on the work of St. Thomas Aquinas. He argued that rival capitalist and socialist theories, based on subjective Cartesian thinking, undermined the unity of society present in Thomistic metaphysics as neither were sufficiently concerned with moral philosophy. Writing in 1861, the influential British philosopher and economist, John Stuart Mill stated in Utilitarianism his view that "Society should treat all equally well who have deserved equally well of it, that is, who have deserved equally well absolutely. This is the highest abstract standard of social and distributive justice; towards which all institutions, and the efforts of all virtuous citizens, should be made in the utmost degree to converge." In the later 19th and early 20th century, social justice became an important theme in American political and legal philosophy, particularly in the work of John Dewey, Roscoe Pound and Louis Brandeis. One of the prime concerns was the Lochner era decisions of the US Supreme Court to strike down legislation passed by state governments and the Federal government for social and economic improvement, such as the eight-hour day or the right to join a trade union. After the First World War, the founding document of the International Labour Organization took up the same terminology in its preamble, stating that "peace can be established only if it is based on social justice". From this point, the discussion of social justice entered into mainstream legal and academic discourse. Thus, in 1931, the Pope Pius XI stated the expression for the first time in the Catholic Social Teaching in the encyclical Quadragesimo Anno. Then again in Divini Redepmtoris, the Church pointed out that the realisation of social justice relied on the promotion of the dignity of human person. The same year, and because of the documented influence of Divini Redemptoris in its drafters, the Constitution of Ireland was the first one to establish the term as a principle of the economy in the State, and then other countries around the world did the same throughout the 20th century, even in Socialist regimes such as the Cuban Constitution in 1976. In the late 20th century, a number of liberal and conservative thinkers, notably Friedrich von Hayek rejected the concept by stating that it did not mean anything, or meant too many things. However the concept remained highly influential, particularly with its promotion by philosophers such as John Rawls. Even though the meaning of social justice varies, at least three common elements can be identified in the contemporary theories about it: a duty of the State to distribute certain vital means (such as economic, social, and cultural rights), the protection of human dignity, and affirmative actions to promote equal opportunities for everybody. Hunter Lewis' work promoting natural healthcare and sustainable economies advocates for conservation as a key premise in social justice. His manifesto on sustainability ties the continued thriving of human life to real conditions, the environment supporting that life, and associates injustice with the detrimental effects of unintended consequences of human actions. Quoting classical Greek thinkers like Epicurus on the good of pursuing happiness, Hunter also cites ornithologist, naturalist, and philosopher Alexander Skutch in his book Moral Foundations: The common feature which unites the activities most consistently forbidden by the moral codes of civilized peoples is that by their very nature they cannot be both habitual and enduring, because they tend to destroy the conditions which make them possible. Pope Benedict XVI cites Teilhard de Chardin in a vision of the cosmos as a 'living host' embracing an understanding of ecology that includes humanity's relationship to others, that pollution affects not just the natural world but interpersonal relations as well. Cosmic harmony, justice and peace are closely interrelated: If you want to cultivate peace, protect creation. In The Quest for Cosmic Justice, Thomas Sowell writes that seeking utopia, while admirable, may have disastrous effects if done without strong consideration of the economic underpinnings that support contemporary society. Political philosopher John Rawls draws on the utilitarian insights of Bentham and Mill, the social contract ideas of John Locke, and the categorical imperative ideas of Kant. His first statement of principle was made in A Theory of Justice where he proposed that, "Each person possesses an inviolability founded on justice that even the welfare of society as a whole cannot override. For this reason justice denies that the loss of freedom for some is made right by a greater good shared by others." A deontological proposition that echoes Kant in framing the moral good of justice in absolutist terms. His views are definitively restated in Political Liberalism where society is seen "as a fair system of co-operation over time, from one generation to the next". All societies have a basic structure of social, economic, and political institutions, both formal and informal. In testing how well these elements fit and work together, Rawls based a key test of legitimacy on the theories of social contract. To determine whether any particular system of collectively enforced social arrangements is legitimate, he argued that one must look for agreement by the people who are subject to it, but not necessarily to an objective notion of justice based on coherent ideological grounding. Obviously, not every citizen can be asked to participate in a poll to determine his or her consent to every proposal in which some degree of coercion is involved, so one has to assume that all citizens are reasonable. Rawls constructed an argument for a two-stage process to determine a citizen's hypothetical agreement: This applies to one person who represents a small group (e.g., the organiser of a social event setting a dress code) as equally as it does to national governments, which are ultimate trustees, holding representative powers for the benefit of all citizens within their territorial boundaries. Governments that fail to provide for welfare of their citizens according to the principles of justice are not legitimate. To emphasise the general principle that justice should rise from the people and not be dictated by the law-making powers of governments, Rawls asserted that, "There is ... a general presumption against imposing legal and other restrictions on conduct without sufficient reason. But this presumption creates no special priority for any particular liberty." This is support for an unranked set of liberties that reasonable citizens in all states should respect and uphold — to some extent, the list proposed by Rawls matches the normative human rights that have international recognition and direct enforcement in some nation states where the citizens need encouragement to act in a way that fixes a greater degree of equality of outcome. According to Rawls, the basic liberties that every good society should guarantee are: Thomas Pogge's arguments pertain to a standard of social justice that creates human rights deficits. He assigns responsibility to those who actively cooperate in designing or imposing the social institution, that the order is foreseeable as harming the global poor and is reasonably avoidable. Pogge argues that social institutions have a negative duty to not harm the poor. Pogge speaks of "institutional cosmopolitanism" and assigns responsibility to institutional schemes for deficits of human rights. An example given is slavery and third parties. A third party should not recognize or enforce slavery. The institutional order should be held responsible only for deprivations of human rights that it establishes or authorizes. The current institutional design, he says, systematically harms developing economies by enabling corporate tax evasion, illicit financial flows, corruption, trafficking of people and weapons. Joshua Cohen disputes his claims based on the fact that some poor countries have done well with the current institutional design. Elizabeth Kahn argues that some of these responsibilities[vague] should apply globally. The United Nations calls social justice "an underlying principle for peaceful and prosperous coexistence within and among nations. The United Nations’ 2006 document Social Justice in an Open World: The Role of the United Nations, states that "Social justice may be broadly understood as the fair and compassionate distribution of the fruits of economic growth ...":16 The term "social justice" was seen by the U.N. "as a substitute for the protection of human rights [and] first appeared in United Nations texts during the second half of the 1960s. At the initiative of the Soviet Union, and with the support of developing countries, the term was used in the Declaration on Social Progress and Development, adopted in 1969.":52 The same document reports, "From the comprehensive global perspective shaped by the United Nations Charter and the Universal Declaration of Human Rights, neglect of the pursuit of social justice in all its dimensions translates into de facto acceptance of a future marred by violence, repression and chaos.":6 The report concludes, "Social justice is not possible without strong and coherent redistributive policies conceived and implemented by public agencies.":16 The same UN document offers a concise history: "[T]he notion of social justice is relatively new. None of history’s great philosophers—not Plato or Aristotle, or Confucius or Averroes, or even Rousseau or Kant—saw the need to consider justice or the redress of injustices from a social perspective. The concept first surfaced in Western thought and political language in the wake of the industrial revolution and the parallel development of the socialist doctrine. It emerged as an expression of protest against what was perceived as the capitalist exploitation of labour and as a focal point for the development of measures to improve the human condition. It was born as a revolutionary slogan embodying the ideals of progress and fraternity. Following the revolutions that shook Europe in the mid-1800s, social justice became a rallying cry for progressive thinkers and political activists.... By the mid-twentieth century, the concept of social justice had become central to the ideologies and programmes of virtually all the leftist and centrist political parties around the world ...":11–12 From its founding, Methodism was a Christian social justice movement. Under John Wesley's direction, Methodists became leaders in many social justice issues of the day, including the prison reform and abolition movements. Wesley himself was among the first to preach for slaves rights attracting significant opposition. Today, social justice plays a major role in the United Methodist Church. The Book of Discipline of the United Methodist Church says, "We hold governments responsible for the protection of the rights of the people to free and fair elections and to the freedoms of speech, religion, assembly, communications media, and petition for redress of grievances without fear of reprisal; to the right to privacy; and to the guarantee of the rights to adequate food, clothing, shelter, education, and health care." The United Methodist Church also teaches population control as part of its doctrine. Catholic social teaching consists of those aspects of Roman Catholic doctrine which relate to matters dealing with the respect of the individual human life. A distinctive feature of Catholic social doctrine is its concern for the poorest and most vulnerable members of society. Two of the seven key areas of "Catholic social teaching" are pertinent to social justice: Even before it was propounded in the Catholic social doctrine, social justice appeared regularly in the history of the Catholic Church: The Catechism of the Catholic Church (§§ 1928–1948) contains more detail of the Church's view of social justice. In Muslim history, Islamic governance has often been associated with social justice.[additional citation(s) needed] Establishment of social justice was one of the motivating factors of the Abbasid revolt against the Umayyads. The Shi'a believe that the return of the Mahdi will herald in "the messianic age of justice" and the Mahdi along with the Isa (Jesus) will end plunder, torture, oppression and discrimination. For the Muslim Brotherhood the implementation of social justice would require the rejection of consumerism and communism. The Brotherhood strongly affirmed the right to private property as well as differences in personal wealth due to factors such as hard work. However, the Brotherhood held Muslims had an obligation to assist those Muslims in need. It held that zakat (alms-giving) was not voluntary charity, but rather the poor had the right to assistance from the more fortunate. Most Islamic governments therefore enforce the zakat through taxes. In To Heal a Fractured World: The Ethics of Responsibility, Rabbi Jonathan Sacks states that social justice has a central place in Judaism. One of Judaism's most distinctive and challenging ideas is its ethics of responsibility reflected in the concepts of simcha ("gladness" or "joy"), tzedakah ("the religious obligation to perform charity and philanthropic acts"), chesed ("deeds of kindness"), and tikkun olam ("repairing the world"). The present-day Jāti hierarchy is undergoing changes for a variety of reasons including 'social justice', which is a politically popular stance in democratic India. Institutionalized affirmative action has promoted this. The disparity and wide inequalities in social behaviour of the jātis – exclusive, endogamous communities centred on traditional occupations – has led to various reform movements in Hinduism. While legally outlawed, the caste system remains strong in practice. The Chinese concept of Tian Ming has occasionally been perceived[by whom?] as an expression of social justice. Through it, the deposition of unfair rulers is justified in that civic dissatisfaction and economical disasters is perceived as Heaven withdrawing its favor from the Emperor. A successful rebellion is considered definite proof that the Emperor is unfit to rule. \|Part of a series on\| Social justice is also a concept that is used to describe the movement towards a socially just world, e.g., the Global Justice Movement. In this context, social justice is based on the concepts of human rights and equality, and can be defined as "the way in which human rights are manifested in the everyday lives of people at every level of society". A number of movements are working to achieve social justice in society. These movements are working toward the realization of a world where all members of a society, regardless of background or procedural justice, have basic human rights and equal access to the benefits of their society. Liberation theology is a movement in Christian theology which conveys the teachings of Jesus Christ in terms of a liberation from unjust economic, political, or social conditions. It has been described by proponents as "an interpretation of Christian faith through the poor's suffering, their struggle and hope, and a critique of society and the Catholic faith and Christianity through the eyes of the poor", and by detractors as Christianity perverted by Marxism and Communism. Although liberation theology has grown into an international and inter-denominational movement, it began as a movement within the Catholic Church in Latin America in the 1950s–1960s. It arose principally as a moral reaction to the poverty caused by social injustice in that region. It achieved prominence in the 1970s and 1980s. The term was coined by the Peruvian priest, Gustavo Gutiérrez, who wrote one of the movement's most famous books, A Theology of Liberation (1971). According to Sarah Kleeb, "Marx would surely take issue," she writes, "with the appropriation of his works in a religious context...there is no way to reconcile Marx's views of religion with those of Gutierrez, they are simply incompatible. Despite this, in terms of their understanding of the necessity of a just and righteous world, and the nearly inevitable obstructions along such a path, the two have much in common; and, particularly in the first edition of [A Theology of Liberation], the use of Marxian theory is quite evident." Social justice has more recently made its way into the field of bioethics. Discussion involves topics such as affordable access to health care, especially for low income households and families. The discussion also raises questions such as whether society should bear healthcare costs for low income families, and whether the global marketplace is the best way to distribute healthcare. Ruth Faden of the Johns Hopkins Berman Institute of Bioethics and Madison Powers of Georgetown University focus their analysis of social justice on which inequalities matter the most. They develop a social justice theory that answers some of these questions in concrete settings. Social injustices occur when there is a preventable difference in health states among a population of people. These social injustices take the form of health inequities when negative health states such as malnourishment, and infectious diseases are more prevalent in impoverished nations. These negative health states can often be prevented by providing social and economic structures such as primary healthcare which ensures the general population has equal access to health care services regardless of income level, gender, education or any other stratifying factors. Integrating social justice with health inherently reflects the social determinants of health model without discounting the role of the bio-medical model. The Vienna Declaration and Programme of Action affirm that "Human rights education should include peace, democracy, development and social justice, as set forth in international and regional human rights instruments, in order to achieve common understanding and awareness with a view to strengthening universal commitment to human rights." Social justice principles are embedded in the larger environmental movement. The third principle of The Earth Charter is Social and economic justice, which is described as seeking to 1) Eradicate poverty as an ethical, social, and environmental imperative 2) Ensure that economic activities and institutions at all levels promote human development in an equitable and sustainable manner 3) Affirm gender equality and equity as prerequisites to sustainable development and ensure universal access to education, health care, and economic opportunity, and 4) Uphold the right of all, without discrimination, to a natural and social environment supportive of human dignity, bodily health, and spiritual well-being, with special attention to the rights of indigenous peoples and minorities. The Climate Justice and Environmental Justice movements also incorporate social justice principles, ideas, and practices. Climate justice and environmental justice, as movements within the larger ecological and environmental movement, each incorporate social justice in a particular way. Climate justice includes concern for social justice pertaining to greenhouse gas emissions, climate-induced environmental displacement, as well as climate change mitigation and adaptation. Environmental justice includes concern for social justice pertaining to either environmental benefits or environmental pollution based on their equitable distribution across communities of color, communities of various socio/economic stratification, or any other barriers to justice. Many authors criticize the idea that there exists an objective standard of social justice. Moral relativists deny that there is any kind of objective standard for justice in general. Non-cognitivists, moral skeptics, moral nihilists, and most logical positivists deny the epistemic possibility of objective notions of justice. Political realists believe that any ideal of social justice is ultimately a mere justification for the status quo. Many other people[who?] accept some of the basic principles of social justice, such as the idea that all human beings have a basic level of value, but disagree with the elaborate conclusions that may or may not follow from this. One example is the statement by H. G. Wells that all people are "equally entitled to the respect of their fellowmen." Friedrich Hayek of the Austrian School of economics rejects the very idea of social justice as meaningless, religious, self-contradictory, and ideological, believing that to realize any degree of social justice is unfeasible, and that the attempt to do so must destroy all liberty: There can be no test by which we can discover what is 'socially unjust' because there is no subject by which such an injustice can be committed, and there are no rules of individual conduct the observance of which in the market order would secure to the individuals and groups the position which as such (as distinguished from the procedure by which it is determined) would appear just to us. [Social justice] does not belong to the category of error but to that of nonsense, like the term 'a moral stone'. the notion of "rights" is a mere term of entitlement, indicative of a claim for any possible desirable good, no matter how important or trivial, abstract or tangible, recent or ancient. It is merely an assertion of desire, and a declaration of intention to use the language of rights to acquire said desire. In fact, since the program of social justice inevitably involves claims for government provision of goods, paid for through the efforts of others, the term actually refers to an intention to use force to acquire one's desires. Not to earn desirable goods by rational thought and action, production and voluntary exchange, but to go in there and forcibly take goods from those who can supply them! \|Wikiquote has quotations related to: Social justice\| \|Library resources about \|
The hypotenuse is the side of a right-angled triangle that lies opposite the right angle. It is the largest side of a right-angled triangle. You can calculate it using the Pythagorean theorem or using the formulas of trigonometric functions. The legs are called the sides of a right-angled triangle adjacent to a right angle. In the figure, the legs are designated as AB and BC. Let the lengths of both legs be given. Let's designate them as \| AB \| and \| BC \|. In order to find the length of the hypotenuse \| AC \|, we use the Pythagorean theorem. According to this theorem, the sum of the squares of the legs is equal to the square of the hypotenuse, i.e. in the notation of our figure \| AB \| ^ 2 + \| BC \| ^ 2 = \| AC \| ^ 2. From the formula we obtain that the length of the hypotenuse AC is found as \| AC \| = √ (\| AB \| ^ 2 + \| BC \| ^ 2). Let's look at an example. Let the lengths of the legs \| AB \| = 13, \| BC \| = 21. By the Pythagorean theorem, we obtain that \| AC \| ^ 2 = 13 ^ 2 + 21 ^ 2 = 169 + 441 = 610. In order to obtain the length of the hypotenuse, it is necessary to extract the square root of the sum of the squares of the legs, ie from among 610: \| AC \| = √610. Using the table of squares of integers, we find out that the number 610 is not a complete square of any integer. In order to get the final value of the answer \| AC \| = √610. If the square of the hypotenuse were equal, for example, 675, then √675 = √ (3 * 25 * 9) = 5 * 3 * √3 = 15 * √3. If such a reduction is possible, perform the reverse check - square the result and compare with the original value. Let us know one of the legs and the corner adjacent to it. For definiteness, let it be leg \| AB \| and angle α. Then we can use the formula for the trigonometric function cosine - the cosine of the angle is equal to the ratio of the adjacent leg to the hypotenuse. Those. in our notation cos α = \| AB \| / \| AC \|. From this we obtain the length of the hypotenuse \| AC \| = \| AB \| / cos α. If we know the leg \| BC \| and angle α, then we will use the formula to calculate the sine of the angle - the sine of the angle is equal to the ratio of the opposite leg to the hypotenuse: sin α = \| BC \| / \| AC \|. We get that the length of the hypotenuse is found as \| AC \| = \| BC \| / cos α. For clarity, consider an example. Let the length of the leg \| AB \| = 15. And the angle α = 60 °. We get \| AC \| = 15 / cos 60 ° = 15 / 0.5 = 30. Consider how you can check your result using the Pythagorean theorem. To do this, we need to calculate the length of the second leg \| BC \|. Using the formula for the tangent of the angle tan α = \| BC \| / \| AC \|, we obtain \| BC \| = \| AB \| * tan α = 15 * tan 60 ° = 15 * √3. Then we apply the Pythagorean theorem, we get 15 ^ 2 + (15 * √3) ^ 2 = 30 ^ 2 => 225 + 675 = 900. The check is completed.
Len function in excel is also known as length excel function which is used to identify the length of a given string, this function calculates the number of characters in a given string provided as an input, this is a text function in excel and it is also an inbuilt function which can be accessed by typing =LEN( and providing string as input. LEN in Excel LEN function is a text function in excel that returns the length of a string/ text. LEN Function in Excel can be used to count the number of characters in a text string and able to count letters, numbers, special characters, non-printable characters, and all spaces from an excel cell. In simple words, LENGTH Function is used to calculate the length of a text in an excel cell. LEN Formula in Excel LEN formula in excel has only one compulsory parameter, i.e., text. - text: it is the text for which to calculate the length. How to Use LENGTH Function in Excel? LENGTH function in Excel is very simple and easy to use. Let us understand the working of the LENGTH function in Excel by some examples. LEN function Excel can be used as a worksheet function and as a VBA function. LENGTH function in Excel as a worksheet function. In this LEN example, we are calculating the length of the given string or text in column 1 and apply the LEN function in column 2, and it will calculate the length of the Names provided in column 1, as shown in the below table. We can use the LENGTH function in Excel to calculate the total number of characters in different cells. In this LEN example, we have used LEN Formula in Excel with sum as=SUM(LEN(B17),LEN(C17)) to calculate the total number of characters in different columns, or we can also use =LEN(B17)+LEN(C17) to achieve this. We can use the LEN function Excel to count characters in excelCount Characters In ExcelTo count characters in excel, use the internal formula called “LEN.” This function counts the letters, numbers, characters, and all spaces present in the cell. Since this function counts everything in the cells, this becomes important to know how to exclude some of the alphabets or values., excluding leading and trailing spaces. Here we use the Length formula in excel with TRIM to exclude the leading and trailing spaces. =LEN(TRIM(B31)) and output will be 37. We can use the LEN function to count the number of characters in a cell, excluding all spaces. To achieve this, we can use the substitute and LEN formula combination to achieve this. LEN function can be used as a VBA function. Dim LENcount As Long LENcount = Application.Worksheetfunction.LEN(“Alphabet”) Msgbox(LENcount) // Return the substring “ab” from string “Alphabet” in the message box. The output will be “8” and printed in the message box. Things to Remember - Basically, the Length function used to count how many characters there are in some string. - It can be used on dates and numbers. - Len function does not include formatting length. For example, the length of “100” formatted as “$100.00” is still 3). - If the cell is empty, then the Length function returns 0 as output. - As shown in row three and six, the empty string has 0 lengths. This has been a guide to LEN in Excel. Here we discuss the LENGTH Formula in excel and how to use the LEN Excel function along with excel example and downloadable excel templates. You may also look at these useful functions in excel –
creep. In the brittle zone, stress builds up as the rocks deform elastically, just as if they were giant blocks of rubber. Saponite forms where serpentinite meets and reacts with ordinary sedimentary rocks. A line on a geologic map that represents the intersection of a fault with the Earth's surface. Faults may also displace slowly, by aseismic creep. On the Hayward fault, creep rates are no greater than a few millimeters per year. For example, we now know that creep rates are sensitive to stress changes in the crust induced by moderate to large earthquakes on neighboring faults in the region (Galehouse, 1997; Lienkaemper et al.,1997, 2001), and such stress changes can act to either advance or delay the timing of future earthquakes on a fault (e.g., Toda and Stein, 2002). Define reverse fault. Andrew Alden is a geologist based in Oakland, California. Careful studies of fault creep, then, can give us hints of where locked zones lie below. At a _, one colliding plate will be forced beneath another because of differences in density. reverse fault synonyms, reverse fault pronunciation, reverse fault translation, English dictionary definition of reverse fault. The array is designed so that the IS-ES bearing is as close to perpendicular to fault strike as possible. Fault creep. A fault plane is the plane that represents the fracture surface of a fault. McFarland, F.S., Lienkaemper, J.J., and Caskey, S.J. Inferences drawn from two decades of alinement array measurements of creep on faults in the San Francisco Bay region, Bull. The precision of the method is such that we can confidently detect any movement greater than 1-2 mm between successive surveys. The intersection of a fault with Earth's surface, often as seen in the field, on an aerial photo or on a satellite image. Where the fault plane is sloping, as with normal and reverse faults, the upper side is the hanging wall and the lower side is the footwall. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Similar climatic effects on the creep signal have been documented along the Parkfield segment of the San Andreas fault (Roeloffs, 2001). noun Geology. Deformation creep takes place within mineral grains as rocks become warped and folded. This section of the San Andreas provides a rare opportunity to observe the Earth’s tectonic plates in motion. So, as often happens in Earth science, everyone seems to be right. Creep models have been applied toward the solution of a variety of engineering problems, such as the closure of and loads on tunnels, chambers, and pillars in creep-sensitive materials, such as salt, shale, and fault zones. Most faults remain locked during the interval between earthquakes as elastic shear strain in the upper crust builds to a critical stress threshold when elastic strain energy is ultimately released by seismic fault slip (i.e., earthquakes) (Figure 1). Figure 7 illustrates how site noise and short-term records of apparent creep are influenced by variations soil moisture content. Highly stressed and creep sensitive ground encountered in … (2001) used variations in creep rate along the Hayward fault to model changes in locking depth. (1997). Galehouse (2001). Two sets of initial azimuth readings are initially taken alternately from the instrument (IS) to the orientation and end points (OS and ES, respectively; Figure 3). The SAFOD drilling project succeeded in sampling the rock right on the San Andreas fault in its creeping section, at a depth of almost 3 kilometers. When the fault plane is … Creep measurement error increases with increasing IS-ES distance (Figure 4). Faults allow the blocks to move relative to each other. Res. Soc. All creep rates reported on this website are least squares average rates determined by linear regression. Creep meters can obtain micron precision (e.g., Bilham et al., 2004) and provide continuous records of the precise timing of creep. Lett. called "seismic creep" to distinguish it from the slumping of rock or soil on slopes (which is also known as creep), and sometimes called "aseismic creep", since it does not trigger events greater than This map provides a starting point for planners by showing locations of fault creep and trench exposures of active traces. En echelon shears crossing street, Hayward Hayward, California. What is the geologic definition of a stream? Measuring creep is an intricate art because it occurs near the surface. This definition also satisfies the legal definition of active fault used in the implementation of the Alquist- Priolo Act of 1972 (Hart, 1990). Res. A fault on which the two blocks slide past one another. Movement is caused by shear stress sufficient to produce permanent deformation, but too small to produce shear failure. The graph shows, nearly without exception, that the onset of the rainy season marks the transitions from apparent left-lateral creep recorded during the dry Summer and early Fall months to apparent levels of right-lateral creep recorded after the ground begins to moisten with the first rains. A third target is centered and leveled over an (end) point (ES) on the opposite side of the fault. A fault is a break in Earth’s crust where the blocks of rock overcome friction to move past each other in opposite directions. Galehouse, J.S. 93 (6), 2415-243. 28, 2269-2272. (http://pubs.usgs.gov/of/2009/1119/). Seism. Effect of Loma Prieta earthquake on surface slip along the Calaveras fault in the Hollister area, Geophys. These include the Hayward fault in the east side of San Francisco Bay, the Calaveras fault just to the south, the creeping segment of the San Andreas fault in central California, and part of the Garlock fault in southern California. Measurements are made by repeated surveys along lines of permanent marks, which may be as simple as a row of nails in a street pavement or as elaborate as creepmeters emplaced in tunnels. Inferred depth of creep on the Hayward fault, central California, J. Geophys. Strain builds on locked fault for long period. 17, 1219-1222. Fault creep is aseismic fault slip that occurs in the uppermost part of the earth's crust during the time interval between large stress-releasing earthquakes on a fault or as "afterslip" in the days to years following an earthquake. Alinement arrays (Figure 3) provide the most accurate and complete measurements of creep because they are generally wide enough (typically 130 m) to span the entire creeping zone, but narrow enough to exclude significant elastic strain away from the fault. Their models suggest that locking depths vary along fault strike from 4-12 km. A fault zone is a cluster of parallel faults. Galehouse, J.S. ... fault creep. In Hayward, creep along the Hayward Fault is splitting the city hall in half. The many strike-slip faults of California include several that are creeping. At the Earth’s surface, earthquakes manifest themselves by shaking and sometimes displacement of the ground. Galehouse, and R.W. An alinement array consists of three fixed points marked on permanent survey monuments (or in some cases, nails driven into concrete or pavement). The faults are separated into five categories: historic, Holocene, late Quaternary, Quaternary, and pre-Quaternary. Down deep, the rocks on a fault are so hot and soft that the fault faces simply stretch past each other like taffy. A fault trace or fault line is a place where the fault can be … Because it happens over immense time scales, geologic change is most often undramatic and unnoticed. Faults may range in length from a few millimeters to thousands of kilometers. Res. Depending on the balance between locked and unlocked zones, the speed of creep can vary. Fault creep, also called aseismic creep, happens at the Earth's surface on a small fraction of faults. The theodolite is then flipped vertically 180 degrees and the process is repeated producing a total of 4 angle measurements. We shade the instrument with a canopy during surveys to minimize instrument drift related to fluctuating temperatures. The greater this lithostatic pressure, the more strain that the fault can accumulate. Now we can make sense of fault creep: it happens near the surface where lithostatic pressure is low enough that the fault is not locked. Prof. Pap. A fault trace is also the line commonly plotted on geologic maps to represent a fault. The creep rate expressed at the earth's surface depends on the rate of elastic strain in the lower crust, the fault's ability (or lack thereof) to resist against the building shear stress, and the depth at which the fault remains locked (i.e., the locking depth) where essentially no creep occurs (Savage and Lisowski, 1993) (Figure 2). Res. ... A _ fault is created when the hanging wall moves up relative to the footwall. At most locations, creep surges whenever moisture from storms penetrates into the soil in California that means the winter rainy season. Why is a scientific puzzle. Criterion 2 allows the definition of a critical length, at which a shear crack undergoes unstable failure (Andrews, 1976), where τ 0 is the static shear stress on the fault, τ p = µ p σ n is the peak stress, µ p is the peak friction coefficient, and τ r = µ r σ n is the shear stress after weakening where µ … Faults may also displace slowly, by aseismic creep . Lienkaemper, J.J., J.S. A fault trace is also the line commonly plotted on … Inspection of the 1 sigma error bars indicates that the site noise is not an artifact of measurement uncertainties and that the error estimates are very small relative to the overall creep signal. Fault Trace. Active earthquake faults can produce both earthquakes and creep. Surv. We employ a high-precision Wild T2002 theodolite/total station to conduct our surveys. This proceedure is designed to account for instrumental and target setup errors as much as possible. Above the ductile zone, rocks change from ductile to brittle. The amount of right-lateral creep (u) ~parallel to fault strike (i.e., perpendicular to the IS-ES direction) is calculated by the IS-ES distance times the tan(delta-theta) . … US agency authorized to issue warnings of impending earthquakes and other geologic events: Term. There are generally three types of creep: We make multiple sets of measurements during each survey at a site to quantify measurement uncertainties. n. Geology A fault in which the hanging wall has moved upward relative to the footwall. Fault, in geology, a planar or gently curved fracture in the rocks of Earth’s crust, where compressional or tensional forces cause relative displacement of the rocks on the opposite sides of the fracture. Simpson, R.W., J.J. Liekaemper, and J.S. fault creep —a fault that displays gradual movement (displacement) over time, keeping pace with regional plate-tectonic related movement in a area. Reverse, Strike-Slip, Oblique, and Normal Faults, B.A., Earth Sciences, University of New Hampshire. Lett. Even the maximum is just a fraction of the total tectonic movement, and the shallow zones that creep would never collect much strain energy in the first place. 75 (4), 481-492. Roeloffs, E.A. The next ingredient in this picture is the second force that holds the fault locked: pressure generated by the weight of the rocks. Another factor may be underground water trapped in sediment pores. While … Bodin, P., R. Bilham, J. Behr, J. Gomberg, and K. Hednut (1994). See creep. The image is an oblique aerial photo of the Banning Fault in the northern portion of the Coachella Valley of California. The graph also illustrates how long-term monitoring of creep is necessary to accurately characterize creep rates and to potentially recognize anomalous creep behavior. A site near a fault defined as active by Caltrans criterion also requires a review of surface rupture potential. We monitor creep with theodolite surveys of alinement arrays. Start studying Chapter 8 Geology. The displacements may have been associated with earthquakes or may have been the result of gradual creep along the fault surface. Standard deviations (1-sigma uncertainties) are then calculated from the 8 angle measurements and these error estimates are then applied to the calculations of creep. Creep is steady fault movement, varying from continuous to episodic with creep events lasting minutes to days. The line it makes on the Earth's surface is the fault trace. Lett. Facebook Twitter Google Email Earthquakes Hazards Data Education Monitoring Research. Lett. No large earthquakes have ever been recorded on it. The causes of fault creep have been the subject of much study, but are most commonly attributed to factors such as low frictional strength on the fault, the low values of normal stress acting on the fault in the shallow crust, and elevated pore-fluid pressures, which act to decrease the effective normal stress on a fault. A fault trace or fault line is a place where the fault can be seen or mapped on the surface. Fault creep is the name for the slow, constant slippage that can occur on some active faults without there being an earthquake. 1550-D, D193-D207. If we assume the fault slip rate of 1 mm yr −1, the recurrence interval of ∼5000 years, and the surface creep rate of ∼0.1 mm yr −1, the total shallow creep during the interseismic period is 0.5 m, accounting for up to ∼10 per cent of the average coseismic slip . 28, 2265-2268. (1990). Creep rate changes at Parkfield, California, 1966-1999: seasonal, precipitation induced, and tectonic, J. Geophys. A fault trace or fault line is a place where the fault can be seen or mapped on the surface. In geology, aseismic creep is measurable surface displacement along a fault in the absence of notable earthquakes. Soil creep is the name for the gentlest form of landsliding. (2009), Data from theodolite measurements of creep rates on San Francisco Bay region faults, California, 1979-2009; USGS Open-file Report 2009-1119. Bilham, R, N. Suszek, and S. Pinkney (2004). When people learn about it, they often wonder if fault creep can defuse future earthquakes, or make them smaller. Find more ways to say fault, along with related words, antonyms and example phrases at Thesaurus.com, the world's most trusted free thesaurus. Another word for fault. Creep, in geology, slow downslope movement of particles that occurs on every slope covered with loose, weathered material. Am. Tectonic Landforms: Escarpments, Ridges, Valleys, Basins, Offsets. The azimuth readings to each of the the two points must must agree to within 0.00060 degrees before two angle measurements between the two azimuths are acceptable and recorded. Earthquakes happen when brittle rocks release that elastic strain and snap back to their relaxed, unstrained state. Fault creep is the name for the slow, constant slippage that can occur on some active faults without there being an earthquake. Questions or comments? When the epicenter of a large earthquake is located offshore, the seabed may be displaced sufficiently to cause a tsunami.Earthquakes can also trigger landslides, and occasionally volcanic activity. We then rotate horizontally the tribraches (i.e., mounts) of the theodolite and both targets 180 degrees, re-level the setups, and repeat the previous proceedure, producing a total of 8 angle measurements. A fault plane is the plane that represents the fracture surface of a fault. The IS-ES distance does not change significantly over time, but has been precisely measured with the electronic distance measurer (EDM) compontent of the T2002 total station.. Variations in creep rate along the Hayward fault, California, interpreted as changes in depth of creep, Geophys. Creeping behavior happens on all kinds of faults, but it's most obvious and easiest to visualize on strike-slip faults, which are vertical cracks whose opposite sides move sideways with respect to each other. Seis. When people learn about it, they often wonder if fault creep can defuse future earthquakes, or make them smaller. fault gouge » fault creep. Subduction Zone _ is the scientific study of fossils. California creep meters, Seism. Generally creep occurs without any associated earthquake activity (i.e., aseismic.) Res. But in the lab, high-pressure tests of the core material showed that it was very weak because of the presence of a clay mineral called saponite. Differences between creep rates (measured locally along a fault) and elastic strain rates (measured by more regional geodetic data) are also a proxy indicators of locking depth, so creep data can be used to modify seismic hazard estimations, which rely on knowing the thickness of crust that will likely experience the greatest strain release (i.e., slip) during earthquakes. Geodetic monitoring of fault creep is usually accomplished using surveys of alinement arrays or trilateration networks or with creep meters. The Fremont site (above) exhibits an average creep rate of ~6.4 mm/yr during this time interval, but also shows considerable site noise. While this is happening, the sides of the fault are locked together. However, creep meters commonly span distances of only a few tens of meters and can significantly underestimate creep if they don't span the entire width of the creeping zone. Fault creep arises from the differences in strain behavior at different depths on a fault. The San Andreas Fault is an … Effect of Loma Prieta earthquake on fault creep rates in the San Francisco Bay region, U.S. Geol. Geologic Faults What Is It? Simpson et al. When the cores were first unveiled, the presence of serpentinite was obvious. Creep is the imperceptibly slow, steady, downward movement of slope-forming soil or rock. From that, we may gain clues about how tectonic strain is building up along a fault, and maybe even win some insight into what kind of earthquakes may be coming. Am. 107. Slow, more or less continuous movement occurring on faults due to ongoing tectonic deformation. In geology, "creep" is used to describe any movement that involves a steady, gradual change in shape. One factor may be the presence of abundant clay or serpentinite rock along the fault zone. displacement along a fault that is so slow and gradual that little seismic activity occurs. Creep response of the Hayward fault to stress changes caused by the Loma Prieta earthquake, Science 276, 2014-2016. seismograph: 1 n a measuring instrument for detecting and measuring the intensity and direction and duration of movements of the ground (as an earthquake) Type of: measuring device , measuring instrument , measuring system instrument that shows the extent or … This movement may occur rapidly, in the form of an earthquake - or may occur slowly, in the form of creep . Alternatively, the site noise is almost certainly related to the response of soil (i.e., regolith) to annual rainfall and variations in water saturation (Figure 7). Caltrans’ broader definition of active faults results in other areas that also need to be addressed for surface rupture. Faults that are creeping do not tend to have large earthquakes. Soc. What are the Different Kinds? Creeping zones there are overwhelmingly outweighed by the size of the locked zone. The movement of creep, measured in millimeters per year, is slow and constant and ultimately arises from plate tectonics. Presumably, it happens on the enormous subduction-related faults that give rise to the largest earthquakes, but we can't measure those underwater movements well enough yet to tell. This instrument has a specified accuracy of ±0.5 arcsecond (±0.000139 degrees). So if an earthquake that might be expected around every 200 years, on average, occurs a few years later because creep relieves a bit of strain, no one could tell. Finally, creep-rate anomalies that may show up with continued monitoring might have potential for actually predicting the location and timing of future earthquakes. Galehouse, J.S., and J.J. Lienkaemper (2003). Response of the San Andreas fault to the 1983 Coalinga-Nunez earthquakes: an application of interaction-based probabilities for Parkfield, J. Geophys. The creeping segment of the San Andreas fault is unusual. It's a part of the fault, about 150 kilometers long, that creeps at around 28 millimeters per year and appears to have only small locked zones if any. Although researchers have long thought that the creeping section may stop large ruptures from spreading across it, recent studies have cast that into doubt. Energy release associated with rapid movement on active faults is the cause of most earthquakes. When fault slips, releases a lot of energy - More dangerous than fault creep b/c fault creep is slow, gradual, smooth movement, no seismic energy released He works as a research guide for the U.S. Geological Survey. Even soil covered with close-knit sod creeps downslope, as indicated by slow but persistent tilting of trees, poles, gravestones, and other objects set into the ground on hillsides. ... another definition of an earthquake. An aseismic creep exists along the Calaveras fault in Hollister, California. Strike-slip fault. A fault plane is the plane that represents the fracture surface of a fault. Lon-term monitoring of creep rate along the Hayward fault and evidence for a lasting creep response to the 1989 Loma Prieta earthquake, Geophys. Lienkaemper, J.J., J.S. A fault is a fracture or zone of fractures between two blocks of rock. Clay is very effective at trapping pore water. Stein (2002). Res. Relatively slow, quiet movement along a fault. This movement can generate earthquakes if it occurs rapidly, or it can occur slowly as fault creep. (If you understand earthquakes as "elastic strain release in brittle rocks," you have the mind of a geophysicist.). (2001). Simpson (1997). See more at Wikipedia.org... © This article uses material from Wikipedia ® and is licensed under the GNU Free Documentation License and under … And just to make things a little more complex, it may be that creep is a temporary thing, limited in time to the early part of the earthquake cycle. Because creep is an indicator of the shear strain on a fault, knowing how creep rates vary temporally and spatially along faults in the San Francisco Bay area has important implications for forecasting the timing, locations, and potential sizes of future earthquakes and for understanding the mechanics of fault behavior. Galehouse, and R.W. ucorrected is always greater than u, and is determined by dividing the uncorrrected creep (u) by the cos(90 degrees minus alpha) [or the sin(alpha)], where alpha is the acute angle between the IS-ES direction and fault strike. Fault creep: Slow ground displacement occurring … If the IS-ES direction is not perpendicular to fault strike, then u must be trigonometrically corrected so that ucorrected is resolved in a direction that is parallel to fault strike. Simpson (2001). Many of our data plots show this type of site noise, and in most cases, the noise is probably due to this same phenomenon. Faults may also displace slowly, by aseismic creep. For simplicity we do not show measurement errors for the creep data plots on this website. However, an example of how the standard deviations commonly compare to the creep measurement signal is shown below for data collected at site H8 (HRKT on map of creep measurement sites) on the Hayward fault in Fremont between 1993 and 2004 (Figure 6). The most important process producing creep, aside from direct gravitational influences, is frost … Tectonic movements exert a force (stress) on the rocks, which respond with a change in shape (strain). Toda, S., and R.S. Creep is the "aseismic" movement of a fault (without detectable earthquakes). The amount of creep is determined from the change in the angle between the IS-ES and IS-OS directions (delta-theta) that occurs between successive surveys at the site (Figure 4). Res. Savage, J.C., and M. Lisowski (1993). 84, 806-816. 98, 787-793. In geology, aseismic creep or fault creep is measurable surface displacement along a fault in the absence of notable earthquakes. That is, the rocks undergo ductile strain, which constantly relieves most of the tectonic stress. A high-precision theodolite (Wild T2002) is centered and leveled over a point (IS) on one side of the fault and a second target is centered and leveled over an (orientation) point (OS) on the same side of the fault as the theodolite. a fault in which the rock above the fault plane is displaced upward relative to the rock below the fault plane (opposed to normal fault). 106, 16,525-16,547. Search. (However, creeping faults are generally rare.) ... signs of creep include: Definition. It is a flat surface that may be vertical or sloping. Slip triggered on the southern California faults by the Landers earthquake sequence, Bull. Researchers are looking at other factors that may be lubricating the fault here. 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Plots on this website are least squares average rates determined by linear regression vertical or.. People learn about it, they often wonder if fault creep is oblique. May show up with continued monitoring might have potential for actually predicting the and... Movements exert a force ( stress ) on the southern California faults by the Loma Prieta earthquake fault... Arrays or trilateration networks or with creep meters: Term subduction zone is! The 1983 Coalinga-Nunez earthquakes: an application of interaction-based probabilities for Parkfield, J. Geophys second force that holds fault... Strain, which constantly relieves most of the Hayward fault, central California, J. Geophys Data monitoring... Recorded on it are separated into five categories: historic, Holocene, late Quaternary, and J.S fault or... Suggest that locking depths vary along fault strike as possible so hot and soft that the IS-ES bearing as. 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Equal circles can be arranged so that each circle touches four or six others. What percentage of the plane is covered by circles in each packing pattern? ... A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle Pythagoras of Samos was a Greek philosopher who lived from about 580 BC to about 500 BC. Find out about the important developments he made in mathematics, astronomy, and the theory of music. The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle. A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded? You are given a circle with centre O. Describe how to construct with a straight edge and a pair of compasses, two other circles centre O so that the three circles have areas in the ratio 1:2:3. Semicircles are drawn on the sides of a rectangle ABCD. A circle passing through points ABCD carves out four crescent-shaped regions. Prove that the sum of the areas of the four crescents is equal to. . . . A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing? Which is a better fit, a square peg in a round hole or a round peg in a square hole? Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star. Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas. Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other. Find the area of the annulus in terms of the length of the chord which is tangent to the inner circle. How many right-angled triangles are there with sides that are all integers less than 100 units? Three circular medallions fit in a rectangular box. Can you find the radius of the largest one? Read all about Pythagoras' mathematical discoveries in this article written for students. A 10x10x10 cube is made from 27 2x2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner. It's easy to work out the areas of most squares that we meet, but what if they were tilted? This article for pupils and teachers looks at a number that even the great mathematician, Pythagoras, found terrifying. Liethagoras, Pythagoras' cousin (!), was jealous of Pythagoras and came up with his own theorem. Read this article to find out why other mathematicians laughed at him. A tennis ball is served from directly above the baseline (assume the ball travels in a straight line). What is the minimum height that the ball can be hit at to ensure it lands in the service area? The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest. . . . A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly? Can you work out the dimensions of the three cubes? A fire-fighter needs to fill a bucket of water from the river and take it to a fire. What is the best point on the river bank for the fire-fighter to fill the bucket ?. Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases? What is the same and what is different about these circle questions? What connections can you make? A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground? If the altitude of an isosceles triangle is 8 units and the perimeter of the triangle is 32 units.... What is the area of the triangle? The ten arcs forming the edges of the "holly leaf" are all arcs of circles of radius 1 cm. Find the length of the perimeter of the holly leaf and the area of its surface. The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius? It is obvious that we can fit four circles of diameter 1 unit in a square of side 2 without overlapping. What is the smallest square into which we can fit 3 circles of diameter 1 unit? What remainders do you get when square numbers are divided by 4? A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be? A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical? If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction. Draw two circles, each of radius 1 unit, so that each circle goes through the centre of the other one. What is the area of the overlap? Three squares are drawn on the sides of a triangle ABC. Their areas are respectively 18 000, 20 000 and 26 000 square centimetres. If the outer vertices of the squares are joined, three more. . . . Prove that the shaded area of the semicircle is equal to the area of the inner circle. Which has the greatest area, a circle or a square inscribed in an isosceles, right angle triangle? The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . . Two semi-circles (each of radius 1/2) touch each other, and a semi-circle of radius 1 touches both of them. Find the radius of the circle which touches all three semi-circles. ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR? The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it? ABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF. If a ball is rolled into the corner of a room how far is its centre from the corner? Is the sum of the squares of two opposite sloping edges of a rectangular based pyramid equal to the sum of the squares of the other two sloping edges? A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't. . . . A napkin is folded so that a corner coincides with the midpoint of an opposite edge . Investigate the three triangles formed . Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.
Few people today could recite the scientific accomplishments of 19th century physician Julius Petri. But almost everybody has heard of his dish. For more than a century, microbiologists have studied bacteria by isolating, growing and observing them in a petri dish. That palm-sized plate has revealed the microbial universe — but only a fraction, the easy stuff, the scientific equivalent of looking for keys under the lamppost. But in the light — that is, the greenhouse-like conditions of a laboratory — most bacteria won’t grow. By one estimate, a staggering 99 percent of all microbial species on Earth have yet to be discovered, remaining in the shadows. They’re known as “microbial dark matter,” a reference to astronomers’ description of the vast invisible matter in space that makes up most of the mass in the cosmos. In the last decade or so, though, scientists have developed new tools for growing bacteria and collecting genetic data, allowing faster and better identifications of microbes without ever removing them from natural conditions. A device called the iChip, for instance, encourages bacteria to grow in their home turf. (That device led to the discovery of a potential new antibiotic, in a time when infections are fast outwitting all the old drugs.) Recent genetic explorations of land, water and the human body have raised the prospect of finding hundreds of thousands of new bacterial species. Already, the detection of these newfound organisms is challenging what scientists thought they knew about the chemical processes of biology, the tree of life and the manner in which microbes live and grow. The secrets of microbial dark matter may redefine how life evolved and exists, and even improve the understanding of, and treatments, for many diseases. “Everything is changing,” says Kelly Wrighton, a microbiologist at Ohio State University in Columbus. “The whole field is full of enthusiasm and discovery.” Microbiologists have in the past discovered new organisms without petri dishes, but those experiments were slow going. In one of her first projects, Tanja Woyke analyzed the bacterial community huddled inside a worm that lives in the Mediterranean Sea. Woyke, a microbiologist at the U.S. Department of Energy’s Joint Genome Institute in Walnut Creek, Calif., and colleagues published the report in Nature in 2006. It was two years in the making. They relied on metagenomics, which involves gathering a sample of DNA from the environment — in soil, water or, in this case, worm insides. After extracting the genetic material of every microbe the worm contained, Woyke and colleagues determined the order, or sequences, of all the DNA units, or bases. Analyzing that sequence data allowed the researchers to infer the existence of four previously unknown microbes. It was a bit like obtaining boxes of jigsaw puzzle pieces that need assembly without knowing what the pictures look like or how many different puzzles they belong to, she says. The project involved 300 million bases and cost more than $100,000, using the time-consuming methods available at the time. of all microbial species on Earth have yet to be discovered Just as Woyke was wrapping up the worm endeavor, new technology came online that gave genetic analysis a turbo boost. Sequencing a genome — the entirety of an organism’s DNA — became faster and cheaper than most scientists ever predicted. With next-generation sequencing, Woyke can analyze more than 100 billion bases in the time it takes to turn around an Amazon order, she says, and for just a few thousand dollars. By scooping up random environmental samples and searching for DNA with next-generation sequencing, scientists have turned up entirely new phyla of bacteria in practically every place they look. In 2013 in Nature, Woyke and her colleagues described more than 200 members of almost 30 previously unknown phyla. Finding so many phyla, the first big groupings within a kingdom, tells biologists that there’s a mind-boggling amount of uncharted diversity. Woyke has shifted from these broad genetic fishing expeditions to working on individual bacterial cells. Gently breaking them open, she catalogs the DNA inside. Many of the organisms she has found defy previous rules of biological chemistry. Two genomes taken from a hydrothermal vent in the Pacific Ocean, for example, contained the code UGA, which stands for the bases uracil, guanine and adenine in a strand of RNA. UGA normally separates the genes that code for different proteins, acting like a period at the end of a sentence. In most other known species of animal or microbe, UGA means “stop.” But in these organisms, and one found about the same time in a human mouth, instead of “stop,” the sequence codes for the amino acid glycine. “That was something we had never seen before,” Woyke says. “The genetic code is not as rigid as we thought.” Other recent finds also defy long-held notions of how life works. This year in the ISME Journal, Ohio State’s Wrighton reported a study of the enzyme RubisCO taken from a new microbial species that had never been grown in a laboratory. RubisCO, considered the most abundant protein on Earth, is key to photosynthesis; it helps convert carbon from the atmosphere into a form useful to living things. Because the majority of life on the planet would not exist without it, RubisCO is a familiar molecule — so familiar that most scientists thought they had found all the forms it could take. Yet, Wrighton says, “we found so many new versions of this protein that were entirely different from anything we had seen before.” The list of oddities goes on. Some newly discovered organisms are so small that they barely qualify as bacteria at all. Jillian Banfield, a microbiologist at the University of California, Berkeley, has long studied the microorganisms in the groundwater pumped out of an aquifer in Rifle, Colo. To filter this water, she and her colleagues used a mesh with openings 0.2 micrometers wide — tiny enough that the water coming out the other side is considered bacteria-free. Out of curiosity, Banfield’s team decided to use next-generation sequencing to identify cells that might have slipped through. Sure enough, the water contained extremely minuscule sets of genes.<img alt="" class="caption" src="http://www.buyereaders.org/images/201701/091716_darkmatter_bacteria1_free.jpg" style="width: 300px; height: 280px; float: right;" title="This tiny groundwater bacterium can slip through filters. ~~ B. Luef et al/Nature Communications 2015″ /> “We realized these genomes were really, really tiny,” Banfield says. “So we speculated if something has a tiny genome, the cells are probably pretty tiny, too.” And she has pictures to prove it. Last year in Nature Communications, she and her team published the first images (taken with an electron microscope) and detailed description of these ultrasmall microbes (see, right). They are probably difficult to isolate in a petri dish, Banfield says, because they are slow-growing and must scavenge many of the essential nutrients they need from the environment around them. Part of the price of a minigenome is that you don’t have room for the DNA to make everything you need to live. Relationship status: It’s complicated Banfield predicts that an “unimaginably large number” of species await in every cranny of the globe — soil, rocks, air, water, plants and animals. The human microbiome alone is probably teeming with unfamiliar microbial swarms. As a collection of organisms that live on and in the body, the human microbiome affects health in ways that science is just beginning to comprehend (SN: 2/6/16, p. 6). Scientists from UCLA, the University of Washington in Seattle and colleagues recently offered the most detailed descriptions yet of a human mouth bacterium belonging to a new phylum: TM7. (TM stands for “Torf, mittlere Schicht,” German for a middle layer of peat; organisms in this phylum were first detected in the mid-1990s in a bog in northern Germany.) German scientists found TM7 by sifting through soil samples, using a test that’s specific for the genetic information in bacteria. In the last decade, TM7 species have been found throughout the human body. An overabundance of TM7 appears to be correlated with inflammatory bowel disease and gum disease, plus other conditions. Until recently, members of TM7 have stubbornly resisted scientists’ efforts to study them. In 2015, Jeff McLean, a microbiologist at the University of Washington, and his collaborators finally isolated a TM7 species in a lab and deciphered its full genome. To do so, the team combined the best of old and new technology: First the researchers figured out how to grow most known oral bacteria together, and then they gradually thinned down the population until only two species remained: TM7 and a larger organism. “The really remarkable thing is we finally found out how it lives,” McLean says, and why it wouldn’t grow in the lab. They discovered that this species of TM7, like the miniature bacteria in Colorado groundwater, doesn’t have the cellular machinery to get by on its own. Even more unusual, these bacteria pilfer missing amino acids and whatever else they need by latching on, like parasites, to a larger bacterium. Eventually they can kill their host. “We think this is the first example of a bacterium that lives in this manner,” McLean says. He expects to see more unusual relationships among microbes as the dark matter comes to light. Many have evaded detection, he suspects, because of their small size (sometimes perhaps mistaken for bacterial debris) and dependence on other organisms for survival. In 2013 in the Proceedings of the National Academy of Sciences, McLean and colleagues were the first to describe a member of another uncultivated phylum, TM6. They found this group growing in the slime in a hospital sink drain. Later studies determined that the organism lives by tucking itself inside an amoeba. <img alt="" class="caption" src="http://www.buyereaders.org/images/201701/091716_darkmatter_bacteria_free.jpg" style="height: 180px; font-size: 16px; width: 400px; float: right;" title="Some bacteria live in untraditional ways. One, from a newly discovered phylum called TM7 (left, red dots), lives parasitically on another bacterium. Another, from phylum TM6 (right, dark blobs), lives in an amoeba. ~~ From left: Batbileg Bor and Xuesong He/UCLA; V. Delafont et al/Environmental Microbial Reports 2015″ /> One of the greatest hopes for microbial dark matter exploration is that newly found microbes might provide desperately needed antibiotics. From the 1940s to the 1960s, scientists discovered 10 new classes of drugs by testing chemicals found in soil and elsewhere for action against common infections. But only two classes of medically important antibiotics have been discovered in the last 30 years, and none since 1997. Some major infections are at the brink of being unstoppable because they’ve become resistant to most existing drugs (SN Online: 5/27/16). Many experts think that natural sources of antibiotics have been exhausted. Maybe not. In 2015, a research team led by scientists from Northeastern University in Boston captured headlines after describing in Nature a new chemical extracted from a ground-dwelling bacterium in Maine. The scientists isolated the organism using the iChip, a thumb-sized tool that contains almost 400 separate wells, each large enough to hold only an individual bacterial cell plus a smidgen of its home dirt. The bacteria grow on this scaffold in part because they never leave their natural surroundings. In lauding the discovery, Francis Collins, director of the National Institutes of Health, called the iChip “an ingenious approach that enhances our ability to search one of nature’s richest sources of potential antibiotics: soil.” So far, the research team has discovered about 50,000 new strains of bacteria. One strain held an antibiotic, named teixobactin (SN: 2/7/15, p. 10). In laboratory experiments, it killed two major pathogens in a way that did not appear easily vulnerable to the development of resistance. Most antibiotics work by disrupting a microbe’s survival mechanism. Over time, the bacteria genetically adapt, find a work-around and overcome the threat. This new antibiotic, however, prevents a microbe from assembling the molecules it needs to form an outer wall. Since the antibiotic interrupts a mechanical process and not just a specific chemical reaction, “there’s no obvious molecular target” for resistance, says Kim Lewis, a microbiologist at Northeastern. The small reveal For more than a century, bacteria — the few scientists managed to culture — were grown on petri dishes or in flasks. Recent technological advances now allow scientists to quickly and cheaply reveal a microbe’s genetic identity without ever having to grow the organism in a laboratory. Source: R.S. Lasken and J.S. McLean/Nature Reviews Genetics 2014 Everything is illuminated Some microbiologists feel like astronomers who, after years of staring up into the dark, were just handed the Hubble Space Telescope. Billions of galaxies are coming into view. Banfield expects this new microbial universe to be mapped over the next few years. Then, she says, an even more exciting era begins, as science explores how these dark matter bacteria make a living. “They are doing a lot of things, and we have no idea what,” she says. Part of the excitement comes from knowing that microbes have a history of granting unexpected solutions to problems that scientists never expected to solve. Consider that the enzyme that makes the laboratory technique PCR possible came from organisms that live inside the thermal vents at Yellowstone National Park. PCR, which works like a photocopier to make multiple copies of DNA segments, is now used across a range of situations, from diagnosing cancer to paternity testing. CRISPR, a powerful gene-editing technology, relies on “molecular scissors” that were found in bacteria (SN: 9/3/16, p. 22). Banfield estimates that 30 to 50 percent of newly discovered organisms contain proteins that never met a petri dish. Their function in the chemistry of life is an obscure mystery. Since microbes are the world’s most abundant organism, Banfield says, “the vast majority of life consists of biochemistry we don’t understand.” But once we do, the future could be very bright. This article appears in the September 17, 2016, issue of Science News with the headline, “Out of the dark.” L. Solden et al. The bright side of microbial dark matter: lessons learned from the uncultivated majority. Current Opinion in Microbiology. Vol. 31, Published online May 16, 2016, p. 217. doi: 10.1038/nature12352. T. Woyke et al. Symbiosis insights through metagenomics analysis of a microbial consortium. Nature. Vol. 443, October 26, 2006, p. 950. doi: 10.1038/nature12352. C. Rinke et al. Insights into the phylogeny and coding potential of microbial dark matter. Nature. Vol. 499, July 25, 2013, p. 431. 10.1038/nature12352. B. Leuf et al. Diverse uncultivated ultra-small bacterial cells in groundwater. Nature Communications. Vol. 6, Published online February 27, 2015, p. 6372. doi: 10.1038/ncomms7372. X. He et al. Cultivation of a human-associated TM7 phylotype reveals a reduced genome and epibiotic parasitic lifestyle. Proceedings of the National Academy of Sciences. Vol. 1, January 6, 2015, p. 244. doi: 10.1073/pnas.1419038112. V. Delafont et al. Shedding light on microbial dark matter: a TM6 bacterium as natural endosymbiont of a free-living amoeba. Environmental Microbiology Reports. Vol. 7, December 2015. p. 970. doi:10.1111/1758-2229.12343 L. Ling et al. A new antibiotic kills pathogens without detectable resistance. Nature. Vol. 517, January 22, 2015, p. 455. doi: 10.1038/nature14098. L. Katz and R.H. Baltz. Natural product discovery: past, present, and future. Journal of Industrial Microbiology & Biotechnology. Vol. 43, March 2016, p. 155. doi: 10.1007/s10295-015-1723-5. S. Milius. When it comes to antimicrobial resistance, watch out for wildlife. Science News. Vol. 190, September 17, 2016, p. 10. S. Milius. Yeasts hide in many lichen partnerships. Science News. Vol. 190, August 20, 2016, p. 9. S. Sumner. Underwater city was built by microbes, not people. Science News. Vol. 190, August 6, 2016, p. 5. L. Beil. Benign-turned-deadly bacterium baffles scientists. Science News. Vol. 190, July 23, 2016, p. 11. T.H. Saey. Will we know ET when we see it? Science News. Vol. 189, April 30, 2016, p. 28.
Astrophysicists have found an out-of-place supermassive black hole -- 12 billion times more enormous than the sun -- that mysteriously formed when the cosmos was less than 900 million years old. Such behemoths are usually found in the more modern cosmos, which seemingly offers more feeding material. Black holes are areas of space so condensed with matter that not even photons of light can discharge their gravitational fists. They are sensed as they pull and eat neighbouring stars and dust, making a cosmic zoo of noticeable phenomenon, such gas jets and rapidly spinning accretion disks. “Before this finding the most enormous black hole identified within 1 billion years after the Big Bang was about 5 billion solar mass, less than half the mass of the new discovery,” Bram Venemans, research staff researcher with Max Planck Institute for Astronomy in Germany, wrote in an email to Discovery News. The finding, reported in this week’s Nature, offers a serious challenge to theories about how black holes grew in the early cosmos. Researchers previously expected young black holes started off with between 100 and 100,000 times the mass of the sun and matured from there by consuming in intergalactic matter and/or merging with other black holes. “It may need either very extraordinary ways to grow the black hole within a very short time, or the presence of a huge seed black hole when the first generation of stars and galaxies formed,” lead scientist Xue-Bing Wu, with China’s Peking University in Beijing, said in an email to Discovery News. Neither clarification fits with present theories. “A very stimulating feature of this work is that the outcomes hint that in the early cosmos the supermassive black holes and their host galaxies did not co-evolve,” said astrophysicist Akos Bogdan, with the Harvard-Smithsonian Center for Astrophysics in Cambridge, Mass., who was not involved in the study. It is improbable the black hole’s parent galaxy would be as big as what calculations based on existing theories would conclude. “This would propose that -- at least in this case -- the black hole is developing faster than the galaxy, questioning the often expected co-evolution of galaxies and their central black holes through cosmic time,” added Venemans. The newly discovered black hole exists in in an enormously bright quasar that existed when the cosmos was about 857 million years old – about 6% of the cosmos’s current 13.8-billion-year age. “We can comparatively easily sense this object because it is brighter than others at the same distance,” Wu said. Observations with numerous ground- and space-based telescopes carry on, as well as a search for any comparable giant siblings. “These objects are so far away from us so most of them look (very) faint even if their inherent brightness is large,” Wu said. This post was written by Usman Abrar. To contact the writer write to firstname.lastname@example.org. Follow on Facebook
The discovery of the double-helical nature of DNA by Watson & Crick explained how genetic information could be duplicated and passed on to succeeding generations. The strands of the double helix can separate and serve as templates for the synthesis of daughter strands. In conservative replication the two daughter strands would go to one daughter cell and the two parental strands would go to the other daughter cell. In semiconservative replication one parental and one daughter strand would go to each of the daughter cells. Through experimentation it was determined that DNA replicates via a semiconservative mechanism. There are three possible mechanisms that can explain DNA's semiconservative replication. (a) DNA synthesis starts at a specific place on a chromosome called an origin. In the first mechanism one daughter strand is initiated at an origin on one parental strand and the second is initiated at another origin on the opposite parental strand. Thus only one strand grows from each origin. Some viruses use this type of mechanism. (b) In the second mechanism replication of both strands is initiated at one origin. The site at which the two strands are replicated is called the replication fork. Since the fork moves in one direction from the origin this type of replication is called unidirectional. Some types of bacteria use this type of mechanism. (c) In the third mechanism two replication forks are initiated at the origin and as synthesis proceeds the two forks migrate away from one another. This type of replication is called bi-directional. Most organisms, including mammals, use bi-directional replication. Requirements for DNA Synthesis There are four basic components required to initiate and propagate DNA synthesis. They are: substrates, template, primer and enzymes. Four deoxyribonucleotide triphosphates (dNTP's) are required for DNA synthesis (note the only difference between deoxyribonucleotides and ribonucleotides is the absence of an OH group at position 2' on the ribose ring). These are dATP, dGTP, dTTP and dCTP. The high energy phosphate bond between the a and b phosphates is cleaved and the deoxynucleotide monophosphate is incorporated into the new DNA strand. Ribonucleoside triphosphates (NTP's) are also required to initiate and sustain DNA synthesis. NTP's are used in the synthesis of RNA primers and ATP is used as an energy source for some of the enzymes needed to initiate and sustain DNA synthesis at the replication fork. The nucleotide that is to be incorporated into the growing DNA chain is selected by base pairing with the template strand of the DNA. The template is the DNA strand that is copied into a complementary strand of DNA. The enzyme that synthesizes DNA, DNA polymerase, can only add nucleotides to an already existing strand or primer of DNA or RNA that is base paired with the template. An enzyme, DNA polymerase, is required for the covalent joining of the incoming nucleotide to the primer. To actually initiate and sustain DNA replication requires many other proteins and enzymes which assemble into a large complex called a replisome. It is thought that the DNA is spooled through the replisome and replicated as it passes through. DNA Synthesis, 5' to 3' The major catalytic step of DNA synthesis is shown below. Notice that DNA synthesis always occurs in a 5' to 3' direction and that the incoming nucleotide first base pairs with the template and is then linked to the nucleotide on the primer. DNA Synthesis is Semidiscontinuous Since all known DNA polymerases can synthesize only in a 5' to 3' direction a problem arises in trying to replicate the two strands of DNA at the fork. Notice that the top strand must be discontinuously replicated in short stretches thus the replication of both parental strands is a semidiscontinuous process. The strand that is continuously synthesized is called the leading strand while the strand that is discontinuously synthesized is called the lagging strand. Leading Strand Synthesis DNA synthesis requires a primer usually made of RNA. A primase synthesizes the ribonucleotide primer ranging from 4 to 12 nucleotides in length. DNA polymerase then incorporates a dNMP onto the 3' end of the primer initiating leading strand synthesis. Only one primer is required for the initiation and propagation of leading strand synthesis. Lagging Strand Synthesis Lagging strand synthesis is much more complex and involves five steps. 1. As the leading strand is synthesized along the lower parental strand the top parental strand becomes exposed. The strand is then recognized by a primase which synthesizes a short RNA primer. 2. DNA polymerase then incorporates a dNMP onto the 3" end of the primer and initiates lagging strand synthesis. The polymerase extends the primer for about 1,000 nucleotides until it comes in contact with the 5' end of the preceding primer. These short segments of RNA/DNA are known as Okazaki fragments. 3. When the DNA polymerase encounters the preceding primer it dissociates. The RNA is then removed by a specialized DNA polymerase or by an enzyme called RNaseH. Ribonucleotides are then excised one at a time in a 5' to 3' direction. The RNaseH leaves a phosphate group at the 5' end of the adjoining DNA segment thus leaving a gap. 4. The gap is filled by a DNA polymerase which uses an Okazaki fragment as a primer. 5. The 3' hydroxyl group on the 3' nucleotide terminus is then covalently joined, using DNA ligase, to the free 5' phosphate of the previously made lagging segment. Structure of DNA There are many types of DNA polymerases which can excise, fill gaps, proofread, repair and replicate. Other Factors Required for DNA Synthesis Origins: Origins are unique DNA sequences that are recognized by a protein that builds the replisome. Origins have been found in bacterial, plasmid, viral, yeast and mitochondrial DNA and have recently been discovered in mammalian DNA. Specific origins are used for initiating DNA replication in humans. Most origins have a site that is recognized and bound by an origin-binding protein. When the origin-binding protein binds to the origin the A + T rich sequence becomes partially denatured allowing other replication factors known as cis-acting factors to bind and initiate DNA replication. Origin-binding Protein: binds and partially denatures the origin DNA while binding to another enzyme called helicase. Helicases: unwind double stranded DNA. Single-stranded DNA Binding Protein (SSB): enhances the activity of the helicase and prevents the unwound DNA from renaturing. Primase: synthesize the RNA primers required for initiating leading and lagging strand synthesis. DNA Polymerase: recognizes the RNA primers and extends them in the 5' to 3' direction. Processivity Factors: help load the polymerase onto the primer-template while anchoring the polymerase to the DNA. Topoisomerase: removes the positive supercoils that form as the fork is unwound by the helicase. RNaseH: removes RNA portions from Okazaki fragments. Ligase: seals the nicks after filling in the gaps left by DNA polymerase. Coordination of Leading and Lagging Strand Synthesis Leading and lagging strand synthesis is thought to be coordinated at a replication fork. The two polymerases are held together by another set of proteins, tg, which are near the fork that is being unwound and simultaneously primed by helicase-primase. Both polymerases are bound by a processivity factor, b. Upon completing an Okazaki fragment the lagging strand polymerase release the b factor and dissociates from the DNA. The tg complex then loads the new b factor/primer complex onto the lagging strand polymerase which initiates a new round..... Leading strand synthesis can proceed all the way to the end of a chromosome however lagging strand synthesis can not. Consequently the 3' tips of each daughter chromosome would not be replicated. Telomerase ( also AKA telomere terminal transferase) extends the 3' ends of a chromosome by adding numerous repeats of a six base pair sequence until the 3' end of the lagging strand is long enough to be primed and extended by DNA polymerase. Telomerase recognizes the tips of chromosomes also know as telomeres. The DNA sequences of telomeres have been determined in several organisms and consist of numerous repeats of a 6 to 8 base long sequence, [TTGGGG]n. Telomeres have been found to progressively shorten in certain types of cells. These cells appear to lack Telomerase activity. When telomeric length shortens to a critical point the cell dies. Cells derived from rapidly proliferating tissues, such as tumors, have telomeres that are unusually long. This indicates that Telomerase activity may be necessary for the proliferation of tumor cells. Telomerase activity is found in ovarian cancer cells but not in normal ovarian tissue. Thus it may be possible to develop anti-tumor drugs that function to inhibit telomerase activity. Chemical Inhibitors of DNA Replication Some types of drugs function by inhibiting DNA replication. Substrate Analogs: analogs of dNTP's which function as chain terminators can be incorporated into DNA. These analogs are usually either missing the 3' hydroxyl group or have a chemical group, other than hydroxyl, in the 3' position. Cytosine Arabinoside: is an anticancer drug used to treat leukemia. Azidothymidine (AZT): was used as an anti-HIV drug that, while effective in tissue culture experiments, proved to be ineffective for treating HIV in humans. Acyclovir: is an effective anti-herpes virus drug. Intercalating Agents: are compounds with fused aromatic ring systems that can wedge (intercalate) between the stacked base pairs of DNA. This disrupts the structure of the DNA so that the replicative enzymes have difficulty in synthesizing DNA past the "intercalated" sites. Anthracycline glycosides and Actinomycin D are intercalators used to treat a variety of cancers. DNA Damaging Agents: a variety of compounds such as Cisplatin, cause chemical damage to DNA and are used in the treatment of cancers. Topoisomerase Inhibitors: Nalidixic acid and Fluoroquinolones are antibiotics used to inhibit bacterial topoisomerases. DNA Mutation and Repair A mutation, which may arise during replication and/or recombination, is a permanent change in the nucleotide sequence of DNA. Damaged DNA can be mutated either by substitution, deletion or insertion of base pairs. Mutations, for the most part, are harmless except when they lead to cell death or tumor formation. Because of the lethal potential of DNA mutations cells have evolved mechanisms for repairing damaged DNA. Types of Mutations There are three types of DNA Mutations: base substitutions, deletions and insertions. 1. Base Substitutions Single base substitutions are called point mutations, recall the point mutation Glu -----> Val which causes sickle-cell disease. Point mutations are the most common type of mutation and there are two types. Transition: this occurs when a purine is substituted with another purine or when a pyrimidine is substituted with another pyrimidine. Transversion: when a purine is substituted for a pyrimidine or a pyrimidine replaces a purine. Point mutations that occur in DNA sequences encoding proteins are either silent, missense or nonsense. Silent: If abase substitution occurs in the third position of the codon there is a good chance that a synonymous codon will be generated. Thus the amino acid sequence encoded by the gene is not changed and the mutation is said to be silent. Missence: When base substitution results in the generation of a codon that specifies a different amino acid and hence leads to a different polypeptide sequence. Depending on the type of amino acid substitution the missense mutation is either conservative or nonconservative. For example if the structure and properties of the substituted amino acid are very similar to the original amino acid the mutation is said to be conservative and will most likely have little effect on the resultant proteins structure / function. If the substitution leads to an amino acid with very different structure and properties the mutation is nonconservative and will probably be deleterious (bad) for the resultant proteins structure / function (i.e. the sickle cell point mutation). Nonsense: When a base substitution results in a stop codon ultimately truncating translation and most likely leading to a nonfunctional protein. A deletion, resulting in a frameshift, results when one or more base pairs are lost from the DNA (see Figure above). If one or two bases are deleted the translational frame is altered resulting in a garbled message and nonfunctional product. A deletion of three or more bases leave the reading frame intact. A deletion of one or more codons results in a protein missing one or more amino acids. This may be deleterious or not. The insertion of additional base pairs may lead to frameshifts depending on whether or not multiples of three base pairs are inserted. Combinations of insertions and deletions leading to a variety of outcomes are also possible. Causes of Mutations Errors in DNA Replication On very, very rare occasions DNA polymerase will incorporate a noncomplementary base into the daughter strand. During the next round of replication the missincorporated base would lead to a mutation. This, however, is very rare as the exonuclease functions as a proofreading mechanism recognizing mismatched base pairs and excising them. Errors in DNA Recombination DNA often rearranges itself by a process called recombination which proceeds via a variety of mechanisms. Occasionally DNA is lost during replication leading to a mutation. Chemical Damage to DNA Many chemical mutagens, some exogenous, some man-made, some environmental, are capable of damaging DNA. Many chemotherapeutic drugs and intercalating agent drugs function by damaging DNA. Gamma rays, X-rays, even UV light can interact with compounds in the cell generating free radicals which cause chemical damage to DNA. Damaged DNA can be repaired by several different mechanisms. Sometimes DNA polymerase incorporates an incorrect nucleotide during strand synthesis and the 3' to 5' editing system, exonuclease, fails to correct it. These mismatches as well as single base insertions and deletions are repaired by the mismatch repair mechanism. Mismatch repair relies on a secondary signal within the DNA to distinguish between the parental strand and daughter strand, which contains the replication error. Human cells posses a mismatch repair system similar to that of E. coli, which is described here. Methylation of the sequence GATC occurs on both strands sometime after DNA replication. Because DNA replication is semi-conservative, the new daughter strand remains unmethylated for a very short period of time following replication. This difference allows the mismatch repair system to determine which strand contains the error. A protein, MutS recognizes and binds the mismatched base pair. Another protein, MutL then binds to MutS and the partially methylated GATC sequence is recognized and bound by the endonuclease, MutH. The MutL/MutS complex then links with MutH which cuts the unmethylated DNA strand at the GATC site. A DNA Helicase, MutU unwinds the DNA strand in the direction of the mismatch and an exonuclease degrades the strand. DNA polymerase then fills in the gap and ligase seals the nick. Defects in the mismatch repair genes found in humans appear to be associated with the development of hereditary colorectal cancer. Nucleotide Excision Repair (NER) NER in human cells begins with the formation of a complex of proteins XPA, XPF, ERCC1, HSSB at the lesion on the DNA. The transcription factor TFIIH, which contains several proteins, then binds to the complex in an ATP dependent reaction and makes an incision. The resulting 29 nucleotide segment of damaged DNA is then unwound, the gap is filled (DNA polymerase) and the nick sealed (ligase). Direct Repair of Damaged DNA Sometimes damage to a base can be directly repaired by specialized enzymes without having to excise the nucleotide. This mechanism enables a cell to replicate past the damage and fix it later. Regulation of Damage Control DNA repair is regulated in mammalian cells by a sensing mechanism that detects DNA damage and activates a protein called p53. p53 is a transcriptional regulatory factor that controls the expression of some gene products that affect cell cycling, DNA replication and DNA repair. Some of the functions of p53, which are just being determined, are: stimulation of the expression of genes encoding p21 and Gaad45. Loss of p53 function can be deleterious, about 50% of all human cancers have a mutated p53 gene. The p21 protein binds and inactivates a cell division kinase (CDK) which results in cell cycle arrest. p21 also binds and inactivates PCNA resulting in the inactivation of replication forks. The PCNA/Gaad45 complex participates in excision repair of damaged DNA. Some examples of the diseases resulting from defects in DNA repair mechanisms. Hereditary nonpolyposis colorectal cancer © Dr. Noel Sturm 2021 Disclaimer: The views and opinions expressed on unofficial pages of California State University, Dominguez Hills faculty, staff or students are strictly those of the page authors. The content of these pages has not been reviewed or approved by California State University, Dominguez Hills.
Unit 1: Facing Prejudice: All American Boys Students explore the American experience through the eyes of two young men - one white and one Black - connected through an incident of police brutality. This first 8th grade unit kicks off students’ year-long study of injustice and how people respond to forces of oppression. In this unit, students will explore issues of racial justice (and injustice) in the United States. The core text, All American Boys, is a 2015 novel written by two authors—one white and one Black—that tells the story of two teenage boys—one white and one Black. Their lives intersect unexpectedly when Quinn, who is white, watches as Rashad, a Black classmate, is beaten by a police officer outside a local convenience store. Quinn is suddenly forced to face the reality of racial injustice in his own community, while Rashad faces the harsh reality that the (white) world judges him primarily by his race. Both young men must grapple with how to respond to the event and the responsibility they have to stand up when injustice has occurred. In addition to the core text, students will read diverse nonfiction texts, including a history of the Say Her Name movement, a TED Talk about growing up Black in America, and an excerpt from the United States Constitution. Throughout the unit, students will gain vocabulary and schema related to racial justice with the hope that they will come out better equipped to engage meaningfully with these issues in their own lives. Fishtank Plus for ELA Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress. Some of the links below are Amazon affiliate links. This means that if you click and make a purchase, we receive a small portion of the proceeds, which supports our non-profit mission. Book: All American Boys by Jason Reynolds and Brendan Kiely Article: “What is White Privilege, Really?” by Cory Collins (Teaching Tolerance) Video: “A Conversation about Growing Up Black” by The New York Times (YouTube) Video: “How to Raise a Black Son in America” by Clint Smith (TED Talk) Website: The Constitution of the United States Website: Right to Peaceful Assembly: United States (Library of Congress) Article: “The ‘Say Her Name’ Movement Started for a Reason: We Forget Black Women Killed by Police” by Precious Fondren (Teen Vogue) Speech: “Why Black Lives Matter” by Alicia Garza (Open Transcripts) Book: Flying Lessons & Other Stories by Ellen Oh (Crown Books for Young Readers, 2017) Assessment Text: “My Father Died in Afghanistan, and I Support Colin Kaepernick” by Kelly Mchugh-Stewart This assessment accompanies Unit 1 and should be given on the suggested assessment day or after completing the Download Content Assessment Download Content Assessment Answer Key Suggestions for how to prepare to teach this unit Prepare to teach this unit by immersing yourself in the texts, themes, and core standards. Unit Launches include a series of short videos, targeted readings, and opportunities for action planning. The central thematic questions addressed in the unit or across units Literary terms, text-based vocabulary, idioms and word parts to be taught with the text point of view/perspective To see all the vocabulary for Unit 1, view our 8th Grade Vocabulary Glossary. In order to ensure that all students are able to access the texts and tasks in this unit, it is incredibly important to intellectually prepare to teach the unit prior to launching the unit. Use the intellectual preparation protocol and the Unit Launch to determine which support students will need. To learn more, visit the Supporting all Students teacher tool. Notes to help teachers prepare for this specific unit Fishtank ELA units related to the content in this unit. Define significant terms related to racial justice. Explain how specific events and sections of text in All American Boys reveal aspects of Rashad’s character and his perspective. Explain how specific events and sections of text in All American Boys reveal aspects of Quinn’s character and his perspective. Explain how racism and racial bias shape the way that characters in All American Boys—and people more generally—are viewed. Explain how Smith uses figurative language in his TED Talk to develop and support his central idea. Explain how authors Reynolds and Kiely use figurative language and word choice to provide insight into characters’ emotions. Explain how events and lines of text reveal characters’ perspectives of themselves and others in All American Boys. Explain the impact of Rashad’s assault on characters and their perspectives in All American Boys. Plan and outline a free verse poem that explores fear, anger, or forgiveness. Interpret an experience of fear, anger, or forgiveness through a free verse poem. Explain how events in All American Boys reveal and challenge characters' beliefs. Analyze the ways that the authors explore the topic of invisibility through Rashad and Quinn's stories. Explain how specific events in All American Boys reveal and/or change Rashad's perspective. Explain how Quinn makes the decision to attend the rally, and the impact of this decision in All American Boys. Determine the technical meaning of words using context clues and reference texts to develop an understanding of the First Amendment of the United States Constitution. Draw conclusions about Quinn and Rashad’s perspectives based on what they say and do in All American Boys. Describe the structure of All American Boys and explain how it contributes to the text’s meaning. Determine themes in All American Boys and explain how they are developed over the course of the text. Determine Precious Fondren’s purpose in her article. Clearly and succinctly present information about a Black woman killed by police. Explain how writers use figurative language and make structural choices to develop and support key ideas. Engage in a Socratic Seminar with classmates, drawing evidence from unit texts, and carefully explaining reasoning. Translate the expectations of the writing task and analyze a mentor text. Outline a short story that explores the power of perspective. Apply some of the storytelling strategies they studied in All American Boys to a narrative. Compose a complete narrative and revise for transitions, mechanics, and organization. Assessment – 2 days Create a free account to access thousands of lesson plans. Already have an account? Sign In The content standards covered in this unit — Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. — Explain the function of verbals (gerunds, participles, infinitives) in general and their function in particular sentences. — Determine or clarify the meaning of unknown and multiple-meaning words or phrases based on grade 8 reading and content, choosing flexibly from a range of strategies. — Use context (e.g., the overall meaning of a sentence or paragraph; a word's position or function in a sentence) as a clue to the meaning of a word or phrase. — Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech. — Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary). — Demonstrate understanding of figurative language, word relationships, and nuances in word meanings. — Interpret figures of speech (e.g. verbal irony, puns) in context. — Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression. — Determine a central idea of a text and analyze its development over the course of the text, including its relationship to supporting ideas; provide an objective summary of the text. — Analyze how a text makes connections among and distinctions between individuals, ideas, or events (e.g., through comparisons, analogies, or categories). — Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the impact of specific word choices on meaning and tone, including analogies or allusions to other texts. — Determine an author's point of view or purpose in a text and analyze how the author acknowledges and responds to conflicting evidence or viewpoints. — Determine a theme or central idea of a text and analyze its development over the course of the text, including its relationship to the characters, setting, and plot; provide an objective summary of the text. — Analyze how particular lines of dialogue or incidents in a story or drama propel the action, reveal aspects of a character, or provoke a decision. — Determine the meaning of words and phrases as they are used in a text, including figurative and connotative meanings; analyze the impact of specific word choices on meaning and tone, including analogies or allusions to other texts. — Compare and contrast the structure of two or more texts and analyze how the differing structure of each text contributes to its meaning and style. — Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 8 topics, texts, and issues, building on others' ideas and expressing their own clearly. — Come to discussions prepared, having read or researched material under study; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion. — Follow rules for collegial discussions and decision-making, track progress toward specific goals and deadlines, and define individual roles as needed. — Present claims and findings, emphasizing salient points in a focused, coherent manner with relevant evidence, sound valid reasoning, and well-chosen details; use appropriate eye contact, adequate volume, and clear pronunciation. — Write arguments to support claims with clear reasons and relevant evidence. — Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences. — Engage and orient the reader by establishing a context and point of view and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically. — Use narrative techniques, such as dialogue, pacing, description, and reflection, to develop experiences, events, and/or characters. — Use a variety of transition words, phrases, and clauses to convey sequence, signal shifts from one time frame or setting to another, and show the relationships among experiences and events. — Use precise words and phrases, relevant descriptive details, and sensory language to capture the action and convey experiences and events. — Provide a conclusion that follows from and reflects on the narrated experiences or events. — Draw evidence from literary or informational texts to support analysis, reflection, and research. — Apply grade 8 Reading standards to literature (e.g., "Analyze how a modern work of fiction draws on themes, patterns of events, or character types from myths, traditional stories, or religious works such as the Bible, including describing how the material is rendered new"). Standards that are practiced daily but are not priority standards of the unit — Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. — Use punctuation (comma, ellipsis, dash) to indicate a pause or break. — Use an ellipsis to indicate an omission. — Spell correctly. — Use knowledge of language and its conventions when writing, speaking, reading, or listening. — Use verbs in the active and passive voice and in the conditional and subjunctive mood to achieve particular effects (e.g., emphasizing the actor or the action; expressing uncertainty or describing a state contrary to fact). — Use common, grade-appropriate Greek or Latin affixes and roots as clues to the meaning of a word (e.g., precede, recede, secede). — Use the relationship between particular words to better understand each of the words. — Distinguish among the connotations (associations) of words with similar denotations (definitions) (e.g., bullheaded, willful, firm, persistent, resolute). — Cite the textual evidence that most strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text. — Analyze in detail the structure of a specific paragraph in a text, including the role of particular sentences in developing and refining a key concept. — Evaluate the advantages and disadvantages of using different mediums (e.g., print or digital text, video, multimedia) to present a particular topic or idea. — By the end of the year, read and comprehend literary nonfiction at the high end of the grades 6—8 text complexity band independently and proficiently. — Cite the textual evidence that most strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text. — Analyze how differences in the points of view of the characters and the audience or reader (e.g., created through the use of dramatic irony) create such effects as suspense or humor. — Analyze how a modern work of fiction draws on themes, patterns of events, or character types from myths, traditional stories, or religious works such as the Bible, including describing how the material is rendered new. — By the end of the year, read and comprehend literature, including stories, dramas, and poems, at the high end of grades 6—8 text complexity band independently and proficiently. — Analyze the purpose of information presented in diverse media and formats (e.g., visually, quantitatively, orally) and evaluate the motives (e.g., social, commercial, political) behind its presentation. — Delineate a speaker's argument and specific claims, evaluating the soundness of the reasoning and relevance and sufficiency of the evidence and identifying when irrelevant evidence is introduced. — Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate. — Introduce claim(s), acknowledge and distinguish the claim(s) from alternate or opposing claims, and organize the reasons and evidence logically. — Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text. — Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), counterclaims, reasons, and evidence. — Establish and maintain a formal style. — Provide a concluding statement or section that follows from and supports the argument presented. — Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content — Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. — With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on how well purpose and audience have been addressed. — Use technology, including the Internet, to produce and publish writing and present the relationships between information and ideas efficiently as well as to interact and collaborate with others. — Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation. — Apply grade 8 Reading standards to literary nonfiction (e.g., "Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient; recognize when irrelevant evidence is introduced"). — Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. Encountering Evil: Night
- Angles are classified by how many degrees they contain. - An acute angle is less than 90°. - A right angle is exactly 90°. - An obtuse angle is larger than 90° but less than 180°. - A straight line is exactly 180°. - A reflex angle is larger than 180° but less than 360° - A full turn is exactly 360° - The first angle is 315° which is between 180° and 360°. It is a reflex angle. - The second angle is exactly 90°. It is a right angle. - The third angle is exactly 360°. It is a full turn. - The fourth angle is exactly 180°. It is a straight line. - The fifth angle is 150°, which is between 90° and 180°. It is an obtuse angle. - The final angle is 40°, which is less than 90°. It is an acute angle. Classifying Angles Worksheets and Answers Classifying Different Types of Angles What are the Different Types of Angle? There are 7 main different types of angle: - Zero Angles - Acute Angles - Right Angles - Obtuse Angles - Straight Lines Obtuse Angles - Full Turns The different types of angle are classified by their size in the table below. \|Type of Angle\|\|Size in Degrees\| \|Zero Angle\|\|Exactly 0°\| \|Acute Angle\|\|Less than 90°\| \|Right Angle\|\|Exactly 90°\| \|Obtuse Angle\|\|Larger than 90° and less than 180°\| \|Straight Angle\|\|Exactly 180°\| \|Reflex Angle\|\|Larger than 180° and less than 360°\| \|Full Turn\|\|Exactly 360°\| How to Classify an Angle To classify an angle, first measure its size in degrees. Then compare this angle to the following values: - If the angle is less than 90°, it is an acute angle. - If the angle is exactly 90°, it is a right angle. - If the angle is between 90° and 180°, it is an obtuse angle. - If the angle is exactly 180°, it is a straight line. - If the angle is exactly 360°, then it is a full turn. Although you can turn through an angle that is larger than 360°, there is no new name for an angle that is larger than 360°. For example, turning 360° completes ones full turn and completing 720° is two full turns because 2 lots of 360° is 720°. Here is a summary table of the different angle types. Here are some examples of identifying angle types. The angle in the top left is 315°. This angle is larger than 180° but it is less than 360°. This means that it opens wider than a straight line but it is not quite a full turn. The angle is a reflex angle. The angle in the top right shows a turn that has gone all the way around back to where it started. It shows a full turn. A full turn is 360°. The angle in the middle is a right angle. This is because it is exactly 90°. It is also marked with a square in the corner of the angle which tells us that it is a right angle. The angle at the bottom left is a straight line. Straight lines are exactly 180°. The angle in the bottom middle is 150°. 150° is larger than 90° but it is less than 180°. It is larger than a right angle but it is not as large as a straight line angle. This is an obtuse angle. The angle in the bottom right is 40°. 40° is less than 90° and so, this angle is an acute angle. Here is another example of classifying an angle. This angle is 60°. This angle is less than 90° and so, this angle is classified as an acute angle. Apart from a zero angle, there is no smaller angle than an acute angle. Since zero angles look like a straight line, they are difficult to work with and are not commonly found in typical angle classification questions. Here is another example of identifying an angle type. Here we have a 280° angle. 280° is larger than a straight line angle of 180° and it is less than a full turn of 360°. It is a reflex angle. It is important to make sure that you measure the correct angle when measuring reflex angles. We are measuring the marked arrow shown in red on the diagram. We have rotated all the way around past a straight line to get to this point. Acute angles refer to any angle that is less than 90°. This means that an acute angle is smaller than a right angle. Here are some examples of acute angles. When teaching acute angles, we can remember that these are the smallest type of angle classification and so, they are ‘a cute’ angle. Linking the idea of being small and being cute can make this name easy to remember. Acute angles along with right angles are probably the easiest type of angles to learn first because they are most commonly seen in day-to-day life. Right angles measure exactly 90°. They are a quarter of a full turn and are shown with a small square in the corner of the angle. Right angles are commonly found around the home such as on the corners of tables, shelves, books and boxes. For this reason, they can be one of the easiest types of angle to teach first. The name of right angle orignally comes from the latin words for it,’angulus rectus’. Rectus means upright. When measured from horizontal position, a right angle is upright and hence the name right angle. An obtuse angle is larger than 90° but less than 180°. Therefore an obtuse angle is larger than a right angle but is not as large as a straight line. Here are some examples of obtuse angles. A common real life example of an obtuse angle is the tip of a roof of a house. A straight angle is exactly 180° and is called this because it looks like a straight line. When an object rotates through a straight angle, it has turned through 180° and therefore it has reversed its original direction. Here is a picture of a straight angle. A straight angle, or straight line must be exactly 180. If it is slightly more or less than this, then there will be a deviation at the corner of the angle and it will not be a straight line. Straight lines are found everywhere and children may find it difficult to think of straight line angles as angles rather than lines. To teach straight line angles, it is helpful to mark the centre of the straight line as the corner of the angle. It is also useful to show an angle rotating around between 179° and 181°. In between must be 180°. Reflex angles are larger than 180° and less than 360°. This means that reflex angles open wider than a straight line but are not large enough to complete a full turn. Here are some examples of reflex angles. Reflex angles are sometimes confused in name with obtuse angles. These are the two most commonly mixed up names when teaching angle classification. It is useful to show examples of both reflex and obtuse angles when teaching them. It can be helpful to compare both angles to a straight line, perhaps using a ruler, which can help us decide if the angle is less than or larger than 180°. A full turn is exactly 360°. After completing a full turn, an object is facing the same direction that it was originally. Here is a diagram showing a full rotation. Full rotations can sometimes hard to draw or explain since the two arms of the angle are directly on top of each other. Now try our lesson on Why Angles in a Triangle Add to 180 Degrees where we learn about angles in a triangle.
Sixteenth Amendment Facts The Sixteenth Amendment to the United States Constitution was ratified on February 3, 1913. It gave the federal government the power to collect income tax. Income is the amount of money a person earns at their job. Income tax is a percentage of this money that is collected by the government to help pay for government services, national defense, health care, education, and other national needs. What does the Sixteenth Amendment say? “The Congress shall have power to lay and collect taxes on incomes, from whatever source derived, without apportionment among the several States, and without regard to any census or enumeration.” Taxation Before the Sixteenth Amendment Article I, Section 8 of the Constitution says that Congress has the power to collect taxes to “provide for the common defense and general welfare of the United States.” Article I, Section 9 said that no “direct tax” could be laid “unless in proportion to the census or enumeration herein before directed to be taken.” This means that if a tax is a direct tax, it must be divided among the states based on population. So, a state that makes up 1/10 of the total population will pay 1/10 of the tax. Even if one state had a lot of whatever was being taxed (like valuable land), and another state had very little, the state would still have to pay its fair share based on population. This made direct taxation very challenging. The definition of “direct tax” has been debated. Generally, it is a tax on a person or property instead of on a good or service. It is paid directly to the government. So, before the Sixteenth Amendment, there were many limitations on direct taxation, but few limitations on indirect taxation. Most of the government’s money came from taxes on goods. The Revenue Act of 1862 In some instances, the government had charged income tax before the Sixteenth Amendment was passed. The Revenue Act of 1862 charged citizens who earned more than $600 per year 3% of their income. People who paid more than $10,000 paid a 5% income tax. This money was used to pay for the Civil War. Rates were raised in 1864, but the law expired in 1872. Pollock v. Farmer’s Loan and Trust Co. The government attempted to tax income again in 1894. People who earned more than $4,000 would pay a 2% tax on their earnings. This tax was challenged in the Supreme Court by a man from Massachusetts named Charles Pollock. In Pollock v. Farmer’s Loan and Trust Co., the Supreme Court ruled that this tax was unconstitutional. A direct tax would have to be “apportioned among the states,” meaning each state would need to be assigned an amount to raise based on population and/or representation in the House of Representatives. This would mean that a poor state with a large population would be required to pay more tax than a wealthy state with a smaller population, which would not work well in practice. The Sixteenth Amendment removed this requirement (by saying that apportionment was not required) and made income tax possible. Ratifying the Sixteenth Amendment Income tax was supposed to be fairer than the consumption taxes that were the government’s main source of revenue. Consumption taxes put a great burden on people who did not have much money. Income taxes would charge people who earned more money a higher percentage. It was supported mostly by states in the South and West, where consumption taxes were raising the cost of living. The ruling in Pollock, which struck down the 1894 income tax, was met with outrage. Some people wanted the direct tax clause to be repealed. But Nebraska Senator Norris Brown instead chose to give Congress a clear power to “enact taxes on incomes” without having to apportion the tax between the states. Congress passed the resolution in 1909, and the amendment was ratified four years later. In 1913, Congress enacted a nationwide individual income tax. The United States has had one ever since, and the Sixteenth Amendment has very rarely been brought up in the Supreme Court. Other Interesting Facts About the Sixteenth Amendment Alabama was the first state to ratify the Sixteenth Amendment. It came into force when Delaware became the 36th state to ratify it on February 3, 1913. The first income tax schedule consisted of seven tax brackets. Rates ranged from 1% on the first $20,000 of income to 7% on income of more than $500,000. That year, the government earned $28.3 million on income tax. Today, the U.S. government collects about two trillion dollars each year from income taxes. The Sixteenth Amendment is significant because it changed the U.S. government from a modest central government to a much more powerful, modern government earning vast amounts of money from income tax.

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