wikipedia_id stringlengths 2 8 | wikipedia_title stringlengths 1 243 | url stringlengths 44 370 | contents stringlengths 53 2.22k | id int64 0 6.14M |
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74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
thought there was an obstacle near this point known as the Table Jump, which may have resembled a bank similar to those still seen at Punchestown in Ireland. In the 1840s the Melling Road was also flanked by hedges and the runners had to jump into the road and then back out of it.
- Fence 13 & 29
Heigh... | 38,600 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
continue around the course to negotiate two fences which are only jumped once:
- Fence 15 – The Chair
Height: , preceded by a 6 ft (1.83 m) wide ditch
This fence is the site of the accident that claimed the only human life in the National's history: in 1862, Joe Wynne fell here and died from his injur... | 38,601 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
any horse that had not passed him before the previous runner passed the finishing post as "distanced", meaning a non-finisher. The practice was done away with in the 1850s, but the monument where the chair stood is still there. The ground on the landing side is six inches higher than on the takeoff side,... | 38,602 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
a great jumping spectacle for those in the stands and was always a major feature in the newsreels' coverage of the race. As the newsreels made way for television in the 1960s, so in turn did the Water Jump fall under the shadow of its neighbour, The Chair, in popularity as an obstacle.
On the final lap,... | 38,603 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
snatched away, such as Devon Loch in 1956, Crisp in 1973, What's Up Boys in 2002 and Sunnyhillboy in 2012.
# Records.
Leading horse:
- Red Rum – 3 wins (1973, 1974, 1977)
Leading jockey:
- George Stevens – 5 wins (Freetrader, 1856; Emblem 1863; Emblematic, 1864; The Colonel, 1869, 1870)
Leading tra... | 38,604 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
(Red Rum, 1973, 1974, 1977)
- Trevor Hemmings - 3 wins (Hedgehunter, 2005; Ballabriggs, 2011, Many Clouds, 2015)
- Gigginstown House Stud - 3 wins (Rule The World, 2016; Tiger Roll, 2018, 2019)
- Fastest winning time: Mr. Frisk (1990); 8:47.80
- Slowest winning time: Lottery (1839); 14:53
- Oldest w... | 38,605 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
all 100/1
- Shortest odds winner: Poethlyn (1919); 11/4
- Largest field: 66 runners (1929)
- Smallest field: 10 runners (1883)
- Most horses to finish: 23 (1984)
- Fewest horses to finish: 2 (1928)
- Most rides in the race: 21 (Richard Johnson, 1997-2019)
- Most rides without winning: 21 (Richard ... | 38,606 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
for hire. Throughout the Victorian era the line between the amateur and professional sportsman existed only in terms of the rider's status, and the engagement of an amateur to ride in the race was rarely considered a handicap to a contender's chances of winning. Many gentleman riders won the race prior t... | 38,607 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
on Mr Frisk in 1990. By the 21st century however, openings for amateur riders had become very rare with some years passing with no amateur riders at all taking part. Those that do in the modern era are most usually talented young riders who are often close to turning professional. In the past, such amate... | 38,608 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
Act 1975 made it possible for female jockeys to enter the race. The first female jockey to enter the race was Charlotte Brew on the 200/1 outsider Barony Fort in the 1977 race. The first female jockey to complete the race was Geraldine Rees on Cheers in 1982. The 21st century has not seen a significant i... | 38,609 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
the Grand National, her best placing being seventh in 2010.
Professionals now hold dominance in the Grand National and better training, dietary habits and protective clothing has ensured that riders' careers last much longer and offer more opportunities to ride in the race. Of the 34 riders who have enj... | 38,610 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
of the 34 never tasted the glory of winning the race. McCoy is the only rider to successfully remove himself from the list after winning at the 15th attempt in 2010. Richard Johnson set a record of 21 failed attempts to win the race from 1997–2019, having finished second twice, but is still competing. Th... | 38,611 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
second once in 14 attempts
- Bill Parvin (1926–1939): finished second once in 14 attempts
- Robert Thornton (1997–2011): never in first three in 14 attempts
- Andrew Thornton (1996–2016): never in first three in 14 attempts
- Chris Grant (1980–1994): finished second thrice in 13 attempts
- Stan Mell... | 38,612 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
that he officially competed in twelve Nationals.
Many other well-known jockeys have failed to win the Grand National. These include champion jockeys such as Terry Biddlecombe, John Francome, Josh Gifford, Stan Mellor, Jonjo O'Neill (who never finished the race) and Fred Rimell. Three jockeys who led ove... | 38,613 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
when well in front only 40 yards from the winning post. Pitman's son Mark also led over the last fence, only to be pipped at the post when riding Garrison Savannah in 1991. David Dick luckily won the 1956 Grand National on E.S.B. when Devon Loch collapsed and he also holds the record for the number of cl... | 38,614 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
in the Grand National are higher than the average steeplechase, with six deaths per 439 horses between 2000 and 2010. Due to the high number of injuries and deaths suffered by participating horses, animal rights groups have campaigned to have the race modified or abolished.
Over the years, Aintree offic... | 38,615 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
and in better surroundings. Those requiring more specialist care can be transported by specialist horse ambulances, under police escort, to the nearby Philip Leverhulme Equine Hospital at the University of Liverpool at Leahurst. A mobile on-course X-ray machine assists in the prompt diagnosis of leg inju... | 38,616 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
while still preserving them as formidable obstacles. After the 1989 Grand National, in which two horses died in incidents at Becher's Brook, Aintree began the most significant of its modifications to the course. The brook on the landing side of Becher's was filled in and, after the 2011 race which also s... | 38,617 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
jockeys to spread out along the fence, rather than take the tight left-side route. Additionally, work has been carried out to smooth the core post infrastructure of the fences with protective padding to reduce impact upon contact, and the height of the toe-boards on all fences has been increased to . The... | 38,618 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
contenders around those fences on the final lap.
Welfare groups have suggested a reduction in the size of the field (currently limited to a maximum of 40 horses) should be implemented. Opponents point to previous unhappy experience with smaller fields such as only 29 runners at the 1954 Grand National, ... | 38,619 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
have argued that the lowering of fences and the narrowing of ditches, primarily designed to increase horse safety, has had the adverse effect by encouraging the runners to race faster. During the 1970s and 1980s, the Grand National saw a total of 12 horses die (half of which were at Becher's Brook); in t... | 38,620 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
same course. The animal welfare charity League Against Cruel Sports counts the number of horse deaths over the three-day meeting from the year 2000 to 2013 at 40. There were no equine fatalities in the main Grand National race for seven years until 2019, when one horse died at the first fence.
# Grand N... | 38,621 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
the unlikely winners in 1967;
- Manifesto, who holds the record for most runs in the race, eight including two victories;
- Jenny Pitman, the first woman to train the winner of the race in 1983; and
- Sir Peter O'Sullevan, the commentator who called home the winners of fifty Grand Nationals on radio a... | 38,622 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
took his name after 1839; and
- Edward Topham, who was assigned the task of framing the weights for the handicap from 1847 and whose descendants played a major role in the race for the next 125 years.
In 2011, nine additional legends were added:
- Bob Champion and Aldaniti, the winners of the 1981 Gra... | 38,623 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
trained three consecutive winners of the race in the 1950s;
- Tom Olliver, who rode in nineteen Nationals, including seventeen consecutively, and won three times, as well as finishing second three times and third once;
- Count Karl Kinsky, the first international winner of the race, and at his first at... | 38,624 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
during the 1970s and 1980s;
- Edie Roche, a Melling Road resident, who opened her home to jockeys, spectators and members of the media when the course was evacuated following a bomb threat in 1997;
- Ian Stewart, a fan who had travelled from Coventry every year to watch the race and was attending his f... | 38,625 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
people to the course.
A public vote announced at the 2012 Grand National saw five more additions to the Legends hall:
- Fred Winter, who rode two National winners and trained two more;
- Carl Llewellyn, jockey who won two Nationals including on Party Politics in 1992, and Earth Summit in 1998, the lat... | 38,626 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
Tommy Carberry, the jockey who stopped Red Rum's attempt at a third success in 1975 by winning on L'Escargot, also finished second and third before going on to train the winner in 1999.
The selection panel also inducted three more competitors:
- Tommy Pickernell, who rode in seventeen Grand Nationals i... | 38,627 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
Rimell trained four National winners, starting with Lottery in the first official Grand National in 1839.
# Notes.
## Favourites.
In the 70 races of the post-war era (excluding the void race in 1993), the favourite or joint-favourite have only won the race ten times (in 1950, 1960, 1973, 1982, 1996, 1... | 38,628 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
Coin (1951)
## Greys.
Three greys have won:
- The Lamb (1868, 1871)
- Nicolaus Silver (1961)
- Neptune Collonges (2012)
## Female jockeys.
Since 1977, women have ridden in 20 Grand Nationals. Geraldine Rees became the first to complete the course, in 1982. In 2012 Katie Walsh became the first fema... | 38,629 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
horse to win the race. He is also the joint-second oldest horse to win, at age 13, alongside Why Not (1884). The U.S.-bred Battleship, son of the famous Man o' War, became the first (and so far only) horse to have won both the Grand National (in 1938) and the American Grand National (which he won four ye... | 38,630 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
was won by a horse named Seagram, bred in New Zealand. 1997 saw another New Zealand-bred winner in Lord Gyllene.
## Other British winners.
- The only Welsh-trained horse to win was Kirkland in 1905.
- Rubstic, trained by John Leadbetter in Roxburghshire, became the first Scottish-trained winner, with ... | 38,631 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
had her first runner in the race in Monaveen, who finished fifth. Six years later she would witness her Devon Loch collapse on the run-in, just yards from a certain victory.
The favourite for the 1968 race, Different Class, was owned by actor Gregory Peck.
The 1963 winner Ayala and the 1976 winner Rag ... | 38,632 |
74730 | Grand National | https://en.wikipedia.org/w/index.php?title=Grand%20National | Grand National
reddie Starr.
What A Friend ran in 2011 and 2013 when part-owned by Alex Ferguson, the former manager of Manchester United.
# See also.
- Horse racing in Great Britain
- List of British National Hunt races
# References.
- Racing Post:
- , , , , , , , , , ,
- Timeform:
- 2017
Notes
- Winners 18... | 38,633 |
3807460 | Teversal F.C. | https://en.wikipedia.org/w/index.php?title=Teversal%20F.C. | Teversal F.C.
Teversal F.C.
Teversal Football Club are a semi-professional football club based in Teversal, near Mansfield, Nottinghamshire, England. They play in the East Midlands Counties League.
# History.
A previous club, Teversal Miners Welfare, had existed in the town since the 1918s, playing at the same Carna... | 38,634 |
3807460 | Teversal F.C. | https://en.wikipedia.org/w/index.php?title=Teversal%20F.C. | Teversal F.C.
Teversal Grange Sports and Social Centre. The football club followed suit, changing the name to Teversal Grange. A further name-change took place in 2000 when they dropped the "Grange" to become simply Teversal F.C.
Upon formation, Miners Welfare Teversal joined the Central Midlands League, winning that ... | 38,635 |
3807460 | Teversal F.C. | https://en.wikipedia.org/w/index.php?title=Teversal%20F.C. | Teversal F.C.
facilities available led to promotion to the Supreme Division in 2001, where they again consolidated for a period, this time four years, again without picking up the league title. Their third place in 2004–05 was enough however to merit a further promotion, and they commenced the 2006–07 campaign in the N... | 38,636 |
3807462 | Allan Scott (businessman) | https://en.wikipedia.org/w/index.php?title=Allan%20Scott%20(businessman) | Allan Scott (businessman)
Allan Scott (businessman)
Archibald Allan Scott, AO (1923–28 October 2008) was a South Australian businessman, most well known for his Mount Gambier-based transport, property, and media interests.
# Career.
Scott was best known for founding the truck organisation Scott's Transport in Mount ... | 38,637 |
3807462 | Allan Scott (businessman) | https://en.wikipedia.org/w/index.php?title=Allan%20Scott%20(businessman) | Allan Scott (businessman)
(OAM) in June 1986 and made an Officer of the Order of Australia (AO) in June 2006 for "service to the development of the transport industry, focusing on heavy vehicle driver safety training and through lobbying for improved infrastructure and development of an integrated freight network, and ... | 38,638 |
3807462 | Allan Scott (businessman) | https://en.wikipedia.org/w/index.php?title=Allan%20Scott%20(businessman) | Allan Scott (businessman)
became a major sponsor of Port Adelaide Football Club upon their entry into the Australian Football League. In early 2004, Scott criticised Port Adelaide coach Mark Williams, stating that Williams would never coach Port to an AFL premiership. Following Port Adelaide's victory in the 2004 AFL G... | 38,639 |
3807456 | Claude Carter | https://en.wikipedia.org/w/index.php?title=Claude%20Carter | Claude Carter
Claude Carter
Claude Pagdett Carter, sometimes known as Claude Paget Carter (23 April 1881 in Durban, Natal – 8 November 1952 in Durban, Natal) was a South African cricketer who played in 10 Tests from 1912 to 1924.
Shortly after leaving the Durban Boys' Model School at the age of 16, Carter began playi... | 38,640 |
3807456 | Claude Carter | https://en.wikipedia.org/w/index.php?title=Claude%20Carter | Claude Carter
) was a South African cricketer who played in 10 Tests from 1912 to 1924.
Shortly after leaving the Durban Boys' Model School at the age of 16, Carter began playing first-class cricket for Natal, and eventually played for them from 1898 to 1923, except for a season with Transvaal in 1910-11. He toured En... | 38,641 |
3807496 | Harold Baumgartner | https://en.wikipedia.org/w/index.php?title=Harold%20Baumgartner | Harold Baumgartner
Harold Baumgartner
Harold Vane Baumgartner (17 November 1883 – 8 April 1938), was a South African cricketer who was born in Henley-on-Thames, Oxfordshire, England, educated at Bedford School, and died in Accra, Gold Coast. He played in one Test in 1913. | 38,642 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
Torus
In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle.
If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution. If the axis of rev... | 38,643 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
of revolution include swim rings and inner tubes. Eyeglass lenses that combine spherical and cylindrical correction are toric lenses.
A torus should not be confused with a "solid torus", which is formed by rotating a disk, rather than a circle, around an axis. A solid torus is a torus plus the volume inside the ... | 38,644 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
but another way to do this is the Cartesian product of the embedding of "S" in the plane with itself. This produces a geometric object called the Clifford torus, a surface in 4-space.
In the field of topology, a torus is any topological space that is topologically equivalent to a torus. A coffee cup and a doughn... | 38,645 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
When , the surface will be the familiar ring torus or anchor ring.
- corresponds to the horn torus, which in effect is a torus with no "hole".
- describes the self-intersecting spindle torus.
- When , the torus degenerates to the sphere.
When , the interior
of this torus is diffeomorphic (and, hence, homeomo... | 38,646 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
around the center of the tube. The losses in surface area and volume on the inner side of the tube exactly cancel out the gains on the outer side.
Expressing the surface area and the volume by the distance of an outermost point on the surface of the torus to the center, and the distance of an innermost point (so... | 38,647 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
are moved; measures the same angle as it does in the spherical system, but is known as the "toroidal" direction. The center point of is moved to the center of , and is known as the "poloidal" direction. These terms were first used in a discussion of the Earth's magnetic field, where "poloidal" was used to denote ... | 38,648 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
torus. In fact, "S" is filled out by a family of nested tori in this manner (with two degenerate circles), a fact which is important in the study of "S" as a fiber bundle over "S" (the Hopf bundle).
The surface described above, given the relative topology from R, is homeomorphic to a topological torus as long as... | 38,649 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
"ABA""B".
The fundamental group of the torus is just the direct product of the fundamental group of the circle with itself:
Intuitively speaking, this means that a closed path that circles the torus' "hole" (say, a circle that traces out a particular latitude) and then circles the torus' "body" (say, a circle t... | 38,650 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
and longitude interchanged. This is equivalent to building a torus from a cylinder, by joining the circular ends together, in two ways: around the outside like joining two ends of a garden hose, or through the inside like rolling a sock (with the toe cut off). Additionally, if the cylinder was made by gluing two ... | 38,651 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
structure on the 2-torus can be represented as a two-sheeted cover of the 2-sphere. The points on the torus corresponding to the ramification points are the Weierstrass points. In fact, the conformal type of the torus is determined by the cross-ratio of the four points.
# "n"-dimensional torus.
The torus has a ... | 38,652 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
And similar to the 2-torus, the "n"-torus, T can be described as a quotient of R under integral shifts in any coordinate. That is, the "n"-torus is R modulo the action of the integer lattice Z (with the action being taken as vector addition). Equivalently, the "n"-torus is obtained from the "n"-dimensional hyperc... | 38,653 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
multiplication.
Toroidal groups play an important part in the theory of compact Lie groups. This is due in part to the fact that in any compact Lie group "G" one can always find a maximal torus; that is, a closed subgroup which is a torus of the largest possible dimension. Such maximal tori "T" have a controllin... | 38,654 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
with determinant ±1. Making them act on R in the usual way, one has the typical "toral automorphism" on the quotient.
The fundamental group of an "n"-torus is a free abelian group of rank "n". The "k"-th homology group of an "n"-torus is a free abelian group of rank "n" choose "k". It follows that the Euler char... | 38,655 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
Symbolically, T = ("S"). The configuration space of "unordered", not necessarily distinct points is accordingly the orbifold T/"S", which is the quotient of the torus by the symmetric group on "n" letters (by permuting the coordinates).
For "n" = 2, the quotient is the Möbius strip, the edge corresponding to the... | 38,656 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
face corresponds to points with 2 coordinates equal and the 3rd different, while the 1-dimensional edge corresponds to points with all 3 coordinates identical.
These orbifolds have found significant applications to music theory in the work of Dmitri Tymoczko and collaborators (Felipe Posada, Michael Kolinas, et ... | 38,657 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
identifications . This particular flat torus (and any uniformly scaled version of it) is known as the "square" flat torus.
This metric of the square flat torus can also be realised by specific embeddings of the familiar 2-torus into Euclidean 4-space or higher dimensions. Its surface has zero Gaussian curvature ... | 38,658 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
embedding of a rectangular flat torus (more general than the square one) is as follows:
where "R" and "P" are constants determining the aspect ratio. It is diffeomorphic to a regular torus but not isometric. It can not be analytically embedded (smooth of class ) into Euclidean 3-space. Mapping it into "3"-space ... | 38,659 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
the torus will partition the 3-sphere into two congruent solid tori subsets with the aforesaid flat torus surface as their common boundary. One example is the torus T defined by
Other tori in "S" having this partitioning property include the square tori of the form "Q"⋅T, where "Q" is a rotation of 4-dimensional... | 38,660 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
must be a tangency. But that would imply that part of the torus, since it has zero curvature everywhere, must lie strictly outside the sphere, which is a contradiction.) On the other hand, according to the Nash-Kuiper theorem, proven in the 1950s, an isometric "C" embedding exists. This is solely an existence pro... | 38,661 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
it does have defined surface normals. It "is" a flat torus in the sense that as metric spaces, it is isometric to a flat square torus. (These infinitely recursive corrugations are used only for embedding into three dimensions; they are not an intrinsic feature of the flat torus.) This is the first time that any s... | 38,662 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
along the boundary circles. To form the connected sum of more than two surfaces, sum two of them at a time until they are all connected. In this sense, a genus "g" surface resembles the surface of "g" doughnuts stuck together side by side, or a 2-sphere with "g" handles attached.
As examples, a genus zero surfac... | 38,663 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
the sphere or the connect sum of some number of tori, disks, and real projective planes.
# Toroidal polyhedra.
Polyhedra with the topological type of a torus are called toroidal polyhedra, and have Euler characteristic "V" − "E" + "F" = 0. For any number holes, the formula generalizes to "V" − "E" + "F" = 2 − 2... | 38,664 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
GL("n", Z) of invertible integer matrices, and can be realized as linear maps on the universal covering space R that preserve the standard lattice Z (this corresponds to integer coefficients) and thus descend to the quotient.
At the level of homotopy and homology, the mapping class group can be identified as the... | 38,665 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
the mapping class group reflects that all homotopy equivalences can be realized by homeomorphisms – every homotopy equivalence is homotopic to a homeomorphism – and that homotopic homeomorphisms are in fact isotopic (connected through homeomorphisms, not just through homotopy equivalences). More tersely, the map ... | 38,666 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
product,
The mapping class group of higher genus surfaces is much more complicated, and an area of active research.
# Coloring a torus.
The torus's Heawood number is seven, meaning every graph that can be embedded on the torus has a chromatic number of at most seven. (Since the complete graph formula_17 can be... | 38,667 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
first 11 numbers of parts, for 0 ≤ "n" ≤ 10 (including the case of "n" = 0, not covered by the above formulas), are as follows:
# Notes.
- "Nociones de Geometría Analítica y Álgebra Lineal", , Author: Kozak Ana Maria, Pompeya Pastorelli Sonia, Verdanega Pedro Emilio, Editorial: McGraw-Hill, Edition 2007, 744 pa... | 38,668 |
74800 | Torus | https://en.wikipedia.org/w/index.php?title=Torus | Torus
s:
# Notes.
- "Nociones de Geometría Analítica y Álgebra Lineal", , Author: Kozak Ana Maria, Pompeya Pastorelli Sonia, Verdanega Pedro Emilio, Editorial: McGraw-Hill, Edition 2007, 744 pages, language: Spanish
- Allen Hatcher. "Algebraic Topology". Cambridge University Press, 2002. .
- V. V. Nikulin, I. R. Sh... | 38,669 |
3807469 | Methods of divination | https://en.wikipedia.org/w/index.php?title=Methods%20of%20divination | Methods of divination
Methods of divination
Methods of divination can be found around the world, and many cultures practice the same methods under different names. During the Middle Ages, scholars coined terms for many of these methods—some of which had hitherto been unnamed—in Medieval Latin, very often utilizing the... | 38,670 |
3807469 | Methods of divination | https://en.wikipedia.org/w/index.php?title=Methods%20of%20divination | Methods of divination
like haruspication, while others (such as megapolisomancy or coffee-based tasseomancy) originated in the 20th and 21st centuries.
The chapter "How Panurge consulteth with Herr Trippa" of "Gargantua and Pantagruel", a parody on occult treatises of Heinrich Cornelius Agrippa, contains a list of ove... | 38,671 |
3807469 | Methods of divination | https://en.wikipedia.org/w/index.php?title=Methods%20of%20divination | Methods of divination
see (metathesis of "hydromancy")
- aeromancy : by atmospheric conditions (Greek , air + , prophecy)
- agalmatomancy : by statues (Greek [], statue + , prophecy)
- aichmomancy : by sharp objects (Greek , spearhead + , prophecy)
- ailuromancy/aeluromancy → see
- alectormancy/alectromancy : by r... | 38,672 |
3807469 | Methods of divination | https://en.wikipedia.org/w/index.php?title=Methods%20of%20divination | Methods of divination
: by walking (Latin , to walk + Greek , prophecy)
- amniomancy : by placenta (Greek , amnion + , prophecy)
- anemoscopy/anemomancy : by wind (Greek , wind + , observation)
- anthomancy : by flowers (Greek , flower + , prophecy)
- anthracomancy : by burning coals (Greek [], charcoal + , prophec... | 38,673 |
3807469 | Methods of divination | https://en.wikipedia.org/w/index.php?title=Methods%20of%20divination | Methods of divination
als (Greek [], charcoal + , prophecy)
- anthropomancy : by human sacrifice (Greek , human being + , prophecy)
- anthroposcopy : by physical appearance (Greek , human being + , observation)
- apantomancy : by chance encounters with animals (Greek , to encounter + , prophecy)
- arachnomancy : by... | 38,674 |
3807465 | Sira, Norway | https://en.wikipedia.org/w/index.php?title=Sira,%20Norway | Sira, Norway
Sira, Norway
Sira is a village in Flekkefjord municipality in Vest-Agder county, Norway. The village is located immediately east of the county border of Vest-Agder and Rogaland. The European route E39 highway passes by the village and the Sørlandet Line runs right through the village, stopping at Sira Sta... | 38,675 |
3807465 | Sira, Norway | https://en.wikipedia.org/w/index.php?title=Sira,%20Norway | Sira, Norway
llage in Flekkefjord municipality in Vest-Agder county, Norway. The village is located immediately east of the county border of Vest-Agder and Rogaland. The European route E39 highway passes by the village and the Sørlandet Line runs right through the village, stopping at Sira Station. The village has a po... | 38,676 |
3807448 | Tommy Ward (cricketer) | https://en.wikipedia.org/w/index.php?title=Tommy%20Ward%20(cricketer) | Tommy Ward (cricketer)
Tommy Ward (cricketer)
Thomas Alfred Ward (2 August 1887 in Rawalpindi, India – 16 February 1936 in East Springs, Transvaal) was a South African cricketer who played in 23 Tests from 1912 to 1924.
A wicket-keeper and useful batsman, Ward made his Test debut on 27 May 1912, the opening Test of t... | 38,677 |
3807448 | Tommy Ward (cricketer) | https://en.wikipedia.org/w/index.php?title=Tommy%20Ward%20(cricketer) | Tommy Ward (cricketer)
Africa fell well short of the Australians' first innings total and were forced to follow on. In South Africa's second innings, Matthews again got two wickets in two balls, Herbie Taylor (21) and Reginald Schwarz, caught and bowled for 0. Ward for the second time in his debut match found himself w... | 38,678 |
3807448 | Tommy Ward (cricketer) | https://en.wikipedia.org/w/index.php?title=Tommy%20Ward%20(cricketer) | Tommy Ward (cricketer)
' first innings total and were forced to follow on. In South Africa's second innings, Matthews again got two wickets in two balls, Herbie Taylor (21) and Reginald Schwarz, caught and bowled for 0. Ward for the second time in his debut match found himself walking to the crease to face Matthews on ... | 38,679 |
74678 | Playoffs | https://en.wikipedia.org/w/index.php?title=Playoffs | Playoffs
Playoffs
The playoffs, play-offs, postseason and/or finals of a sports league are a competition played after the regular season by the top competitors to determine the league champion or a similar accolade. Depending on the league, the playoffs may be either a single game, a series of games, or a tournament, ... | 38,680 |
74678 | Playoffs | https://en.wikipedia.org/w/index.php?title=Playoffs | Playoffs
season, teams play more games in their division than outside it, but the league's best teams might not play against each other in the regular season. Therefore, in the postseason a playoff series is organized. Any group-winning team is eligible to participate, and as playoffs became more popular they were expa... | 38,681 |
74678 | Playoffs | https://en.wikipedia.org/w/index.php?title=Playoffs | Playoffs
season compete to decide the final promotion spot to the Premier League.
# American football.
## National Football League.
Evidence of playoffs in professional football dates to at least 1919, when the "New York Pro Championship" was held in Western New York (it is possible one was held in 1917, but that is... | 38,682 |
74678 | Playoffs | https://en.wikipedia.org/w/index.php?title=Playoffs | Playoffs
scheduled "de facto" championship matchups) did not adopt the New York league's playoff format, opting for a championship based on regular season record for its first twelve seasons; as a result, four of the first six "championships" were disputed. Technically, a vote of league owners was all that was required... | 38,683 |
74678 | Playoffs | https://en.wikipedia.org/w/index.php?title=Playoffs | Playoffs
game between division winners. In 1950 the NFL absorbed three teams from the rival All-America Football Conference, and the former "Divisions" were now called "Conferences", echoing the college use of that term. In 1967, the NFL expanded and created four divisions under the two conferences, which led to the in... | 38,684 |
74678 | Playoffs | https://en.wikipedia.org/w/index.php?title=Playoffs | Playoffs
its 32nd team, the Houston Texans, and significantly reshuffled its divisional alignment. The league went from 6 division winners and 6 wild card spots to 8 division winners and only 4 wild card qualifiers. The winners of each division automatically earn a playoff spot and a home game in their first rounds, an... | 38,685 |
74678 | Playoffs | https://en.wikipedia.org/w/index.php?title=Playoffs | Playoffs
championships, and the winners of those conference championship games then face each other in the Super Bowl.
## College football.
### Division I NCAA Football FBS.
The College Football Playoff National Championship is a post-season college football bowl game, used to determine a national champion of the NC... | 38,686 |
74678 | Playoffs | https://en.wikipedia.org/w/index.php?title=Playoffs | Playoffs
the BCS championship, the participating teams in the College Football Playoff National Championship are determined by two semi-final bowls—hosted by two of the consortium's six member bowls yearly—and the top two teams as determined by the selection committee do not automatically advance to the game in lieu of... | 38,687 |
74678 | Playoffs | https://en.wikipedia.org/w/index.php?title=Playoffs | Playoffs
the title game in the same year.
The winner of the game is awarded a new championship trophy instead of the "crystal football", which has been given by the American Football Coaches Association (AFCA) since 1986; officials wanted a new trophy that was unconnected with the previous BCS championship system. The... | 38,688 |
74678 | Playoffs | https://en.wikipedia.org/w/index.php?title=Playoffs | Playoffs
of the NCAA Division I Football Championship Subdivision (FCS). Prior to 2006, the game was known as the NCAA Division I-AA Football Championship. The FCS is the highest division in college football to hold a playoff tournament sanctioned by the NCAA to determine its champion. The four-team playoff system used... | 38,689 |
74678 | Playoffs | https://en.wikipedia.org/w/index.php?title=Playoffs | Playoffs
"NCAA College Division" and a poll determined the final champion.
The National Championship game was held at Sacramento, California from 1973 to 1975. It was in Wichita Falls, Texas in 1976 and 1977. The game was played in Longview, Texas in 1978. For 1979 and 1980, Albuquerque, New Mexico hosted the game. Mc... | 38,690 |
74678 | Playoffs | https://en.wikipedia.org/w/index.php?title=Playoffs | Playoffs
III NCAA Football.
The NCAA Division III Football Championship began in 1973. Before 1973, most of the schools now in Division III competed either in the NCAA College Division or the National Association of Intercollegiate Athletics (NAIA). NCAA Divisions II and III were created by splitting the College Divis... | 38,691 |
74678 | Playoffs | https://en.wikipedia.org/w/index.php?title=Playoffs | Playoffs
1993. It was previously played in Phenix City, Alabama at Garrett-Harrison Stadium (1973–1982, 1985–1989), at the College Football Hall of Fame, when the Hall was located in Kings Island, Ohio at Galbreath Field (1983–1984), and Bradenton, Florida at Hawkins Stadium (1990–1992).
# Association football.
As a ... | 38,692 |
74678 | Playoffs | https://en.wikipedia.org/w/index.php?title=Playoffs | Playoffs
to determine champions, although in some countries such systems are used to determine teams to be promoted to higher leagues (e.g., England) or qualifiers for European club competitions (such as Greece and the Netherlands), usually between teams that didn't perform well enough to earn an automatic spot.
A "te... | 38,693 |
74678 | Playoffs | https://en.wikipedia.org/w/index.php?title=Playoffs | Playoffs
mini league where all participants play each other or teams only play those from the other league. The winner of the test match series play in the higher league the following season, and the loser in the lower league.
## International playoffs.
In international football, playoffs were a feature of the 1954 a... | 38,694 |
74678 | Playoffs | https://en.wikipedia.org/w/index.php?title=Playoffs | Playoffs
earned the most points against teams in the top six of their individual groups, the remaining six second-placed teams entered playoffs to select three teams for the finals.
- The winners of the Oceania qualifying tournament, Australia played the fifth placed team from the South American qualifying tournament,... | 38,695 |
74678 | Playoffs | https://en.wikipedia.org/w/index.php?title=Playoffs | Playoffs
are open to many teams — 92 clubs compete for the League Cup, and hundreds compete for the FA Cup. These competitions run concurrently with the "regular season" league competitions and are not regarded as playoffs.
## Argentina.
In Argentine football, playoffs in the style of the English leagues occur in the... | 38,696 |
74678 | Playoffs | https://en.wikipedia.org/w/index.php?title=Playoffs | Playoffs
its traditional Apertura and Clausura format in 2015 in favor of an expanded single season, there was no playoff between the Apertura and Clausura winners. As a result, the league crowned two champions each year. After each Clausura, the two teams with the lowest points-per-game total for the previous six tour... | 38,697 |
74678 | Playoffs | https://en.wikipedia.org/w/index.php?title=Playoffs | Playoffs
to either Primera B Metropolitana or Torneo Argentino A for non-Buenos Aires clubs. From 2015 onward, relegation from the Primera División will be based solely on league position at the end of the season (which, effective in 2016–17, changed from a February–December format to an August–June format).
## Austra... | 38,698 |
74678 | Playoffs | https://en.wikipedia.org/w/index.php?title=Playoffs | Playoffs
Page playoff system. The top two teams at the end of league play were matched in one semifinal, with the winner advancing directly to the Grand Final and the loser going into the Preliminary Final. The next two teams played a semifinal for a place in the Preliminary Final, whose winner took the other place in ... | 38,699 |
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