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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1055334 | Equatorial mount | https://en.wikipedia.org/w/index.php?title=Equatorial%20mount | Equatorial mount
design disadvantage of English or Yoke mounts by replacing the polar bearing with an open "horseshoe" structure to allow the telescope to access Polaris and stars near it. The Hale telescope is the most prominent example of a Horseshoe mount in use.
## Cross-axis mount.
The Cross-axis or English cros... | 25,800 |
1055334 | Equatorial mount | https://en.wikipedia.org/w/index.php?title=Equatorial%20mount | Equatorial mount
uatorial axis. It achieves this by having a surface that pivots about a "virtual polar axis". This gives equatorial tracking to anything sitting on the platform, from small cameras up to entire observatory buildings. These platforms are often used with altazimuth mounted amateur astronomical telescopes... | 25,801 |
1055319 | Bullet with Butterfly Wings | https://en.wikipedia.org/w/index.php?title=Bullet%20with%20Butterfly%20Wings | Bullet with Butterfly Wings
Bullet with Butterfly Wings
"Bullet with Butterfly Wings" is a song by the American alternative rock band The Smashing Pumpkins and the lead single from their 1995 double album "Mellon Collie and the Infinite Sadness". The song won the Grammy Award for Best Hard Rock Performance. This song ... | 25,802 |
1055319 | Bullet with Butterfly Wings | https://en.wikipedia.org/w/index.php?title=Bullet%20with%20Butterfly%20Wings | Bullet with Butterfly Wings
song was named the 91st best hard rock song of all time by VH1 in 2009 and ranked number 70 on the 2008 list of "The 100 Greatest Guitar Songs of All Time" of "Rolling Stone". The song came second in the Triple J Hottest 100, 1995, was later voted number 51 in the Triple J Hottest 100 of All... | 25,803 |
1055319 | Bullet with Butterfly Wings | https://en.wikipedia.org/w/index.php?title=Bullet%20with%20Butterfly%20Wings | Bullet with Butterfly Wings
on an acoustic guitar during the same session that "Landslide" was recorded. The lyrics "Can you fake it, for just one more show?" may refer to the band's experience headlining the 1994 Lollapalooza festival, with Corgan calling it the "old job". Along with other parts of the album, Corgan a... | 25,804 |
1055319 | Bullet with Butterfly Wings | https://en.wikipedia.org/w/index.php?title=Bullet%20with%20Butterfly%20Wings | Bullet with Butterfly Wings
debut their new glam rock wardrobes - notably, Billy Corgan's black shirt with the word "Zero" written in silver, and silver pants. The video also marks the last filmed appearance of Billy Corgan prior to his decision to shave his head.
When asked why the band chose Bullet for the first vid... | 25,805 |
1055319 | Bullet with Butterfly Wings | https://en.wikipedia.org/w/index.php?title=Bullet%20with%20Butterfly%20Wings | Bullet with Butterfly Wings
single
# Cover versions.
- Scranton punk rock band The Menzingers closed many of the shows on their 2013 tour with a cover of the song.
- Melodic hardcore band Four Year Strong covered this song on their 2009 album "Explains It All" which is a cover album tributing songs that were made fa... | 25,806 |
1055319 | Bullet with Butterfly Wings | https://en.wikipedia.org/w/index.php?title=Bullet%20with%20Butterfly%20Wings | Bullet with Butterfly Wings
a one-off single in 2009.
- Hawthorne Heights made a cover of this song, released as part of a 2007 Smashing Pumpkins tribute album from MySpace Records.
- Taking Back Sunday made a cover as apart of charity compilation called "Songs That Saved My Life."
- Karen O made a cover of this son... | 25,807 |
1055319 | Bullet with Butterfly Wings | https://en.wikipedia.org/w/index.php?title=Bullet%20with%20Butterfly%20Wings | Bullet with Butterfly Wings
tuary. The song is also used in the "South Park" episode "Whale Whores", which parodies "Whale Wars".
"Weird Al" Yankovic performed the chorus in "The Alternative Polka" from his "Bad Hair Day" album.
The song was featured as a playable track in the video game "Guitar Hero 5".
It was also... | 25,808 |
1055365 | Sangaku | https://en.wikipedia.org/w/index.php?title=Sangaku | Sangaku
Sangaku
Sangaku or San Gaku (算額; lit. translation: calculation tablet) are Japanese geometrical problems or theorems on wooden tablets which were placed as offerings at Shinto shrines or Buddhist temples during the Edo period by members of all social classes.
# History.
The Sangaku were painted in color on w... | 25,809 |
1055365 | Sangaku | https://en.wikipedia.org/w/index.php?title=Sangaku | Sangaku
of prominence, published the first collection of "sangaku" problems, his "Shimpeki Sampo" (Mathematical problems Suspended from the Temple) in 1790, and in 1806 a sequel, the "Zoku Shimpeki Sampo".
During this period Japan applied strict regulations to commerce and foreign relations for western countries so th... | 25,810 |
1055365 | Sangaku | https://en.wikipedia.org/w/index.php?title=Sangaku | Sangaku
on an 1824 tablet in the Gunma Prefecture, covers the relationship of three touching circles with a common tangent. Given the size of the two outer large circles, what is the size of the small circle between them? "The answer is:"
## In the west.
Soddy's hexlet, thought previously to have been discovered in t... | 25,811 |
1055365 | Sangaku | https://en.wikipedia.org/w/index.php?title=Sangaku | Sangaku
). "Japanese temple geometry problems = Sangaku". Winnipeg: Charles Babbage. ; OCLC 474564475
- __________ and Dan Pedoe. (1991) Tōkyō : Mori Kitashuppan. ; OCLC 47500620
- __________ and Tony Rothman. (2008). "Sacred Mathematics: Japanese Temple Geometry." Princeton: Princeton University Press. ; OCLC 181142... | 25,812 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
Travel class
A travel class is a quality of accommodation on public transport. The accommodation could be a seat or a cabin for example. Higher travel classes are designed to be more comfortable and are typically more expensive.
# Airliners.
Traditionally, an airliner is divided to, from the top, first,... | 25,813 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
change or refund policy, etc.
# Buses.
In Mexico, bus services often have designated levels of service, the top of which is "de lujo" or "clase lujo", followed by "plus clase", "primera clase", and "segunda clase".
# Ocean liners.
Before cruise ships dominated the passenger ship trade, ocean liners had... | 25,814 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
with sleeping accommodations, there may be more levels of luxury.
## China.
Traditional trains commonly offer the following classes: soft sleeper, hard sleeper, soft seat and hard seat, depending on the route.
CRH EMUs offer the following classes: soft sleeper (available only on few overnight routes), b... | 25,815 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
class "service" with goods wagons.
In 1949, the first "Limited Express with Reserved Seating" (特快對號車) appeared with the Railway Bureau of Taiwan, and it offered a three-class service, inherited locally from Japanese colonial rule. This structure was the norm for all trains, normal or express, until 1953.
... | 25,816 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
1960, with the reforming of Limited Expresses (the Limited Express with Reserved Seating and Diesel Limited Express merged into one fare), all passenger trains officially offered only one class. Therefore, all expresses had only second class carriages and other trains only third class. As time passes, more... | 25,817 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
and with fewer seating space. In contrast, "third class" only provided wooden benches. While most passenger trains carried just one or two "first class" and "second class" carriages, every other carriage was "third class" only.
Today there are generally two classes, known as "first class" and "second clas... | 25,818 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
and the "third class", with hardly any wooden seatings left, was declared the new "second class".
Trains in Great Britain provide a two-tier class structure, with the higher tier called "first class". The lower tier was re-branded from "third class" to "second class" by British Rail from 3 June 1956, and ... | 25,819 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
side of the aisle); first-class compartments are typically "2+1". In Britain and France, some short-distance Suburban trains use "2+3" for the lower class and "2+2" for first class.
Metro, suburban and local trains are sometimes second-class-only. First-class-only trains were common up to the 1980s (see T... | 25,820 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
Plus on the cross-border Enterprise service. No commuter services have premium classes. Premium benefits can be as limited as a reading light and waiter service; but reach to 2+1 recliner seating and enhanced catering options.
In Germany, there existed a "fourth class" ("4. Klasse") on almost every local ... | 25,821 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
First Class A/C (1A) is the highest rail travel class and is not available on all trains. It offers air-conditioned cubicles in two-bed and four-bed formats with closing doors. There usually is only one 1A bogie (carriage) on a train.
- Two Tier A/C (2A) offers air conditioned cubicles in four-bed + two-b... | 25,822 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
that cover the journey within a day. The seating is usually in 3x3 format.
- Sleeper Class (SL) is configured similarly to 3A but is not air conditioned. There are typically ten to fifteen SL bogies in a train.
- Second Class (Reserved) (2S) similar as CC, without the air-conditioning. These may be reser... | 25,823 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
Similar to Three Tier A/C, however this class have an additional middle berth in the side section of the air conditioned cubicle, making it a six-bed and three-bed format. This type of accommodation is created for less well off people, who desire a comfortable travel at lesser fare.
- First Class (FC), wh... | 25,824 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
"Shatabdi Express" and "Tejas Express" trains, which link major cities located within a day-trip distance.
## Indonesia.
Indonesian trains, operated by the state-owned PT Kereta Api Indonesia (the Indonesian Railways Co.), have now four classes for long-distance travel. All types of carriages are seating... | 25,825 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
Business/second class ("bisnis")–medium class, the fare is around 60% of executive classes, 2–2 seating, fixed 60 degrees seat.
- Premium economy class–the intermediate level between the business and economy classes, the fare is nearly same as business, 2-2 reclining seat configuration.
- Economy/third c... | 25,826 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
passengers require a seat reservation, "except" for commuter trains. All seats can be reserved from 30–90 days before travel date until minutes before departure time when seats are still available.
Medium and long distance trains have onboard cafeteria, flushing toilets (older passenger coaches have squat... | 25,827 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
more time to reach the destination, as they stop on many smaller stations and have to pass all executive and business class traffic going in the same direction (third priority). Many less important routes lack either business or executive service, or both. Some services have more two or three classes mixed... | 25,828 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
route there are "Sriwedari" train services which is air conditioned and has transverse seating and also "Prambanan Express" train which is non air conditioned, has longitudinal seating and more stops. Meanwhile, in Jakarta metropolitan area, there's only one class of service available since mid-2013 which ... | 25,829 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
the few remaining first class carriages were rebranded "special" carriages available for hire, and consequently moved Japan's railway system to a two-class system, of which the original second class became the first, and the original third became second.
In 1969, the class structure was abolished altogeth... | 25,830 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
Car on nearly all of their intercity trains. Additionally, the Central Japan Railway Company (JR Central) and Shikoku Railway Company (JR Shikoku) offer a Green Car on some trains, and a few West Japan Railway Company (JR West) trains also have a Green Car. The alternative to Green Car is the Ordinary Car.... | 25,831 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
leading to/from the train platform. Green Cars also frequently offer slippers and reading materials in Japanese.
Additionally, JR East offers a third category of service, the GranClass, available on its Hayabusa route. Features of GranClass cars include leather seats that recline to a 45 degree angle, rai... | 25,832 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
Britain.
During the Victorian era, most trains in the United Kingdom had three classes of accommodation: first class, second class and third class. From 1875, when the Midland Railway redesignated its second class accommodation as "third class", second class (equivalent to either premium economy or busine... | 25,833 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
meant that boat trains in Britain still often operated with three classes of accommodation after the abolition of second class in the rest of the country. From 3 June 1956 British Railways redesignated third class as "second class", finally (as British Rail) renaming it "standard class" from 11 May 1987, i... | 25,834 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
classes: First Class and Business Class. Amtrak Northeast Regional trains have Business Class and Coach class. Canada's Via Rail has the same classes as Amtrak. Trains with sleeper cars have additional levels. Most commuter trains in USA and Canada generally have a business class and economy class or stand... | 25,835 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
gional trains have Business Class and Coach class. Canada's Via Rail has the same classes as Amtrak. Trains with sleeper cars have additional levels. Most commuter trains in USA and Canada generally have a business class and economy class or standard fare. Although business class is offered it typically is... | 25,836 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
Goal setting
Goal setting involves the development of an action plan designed to motivate and guide a person or group toward a goal. Goal setting can be guided by goal-setting criteria (or rules) such as SMART criteria. Goal setting is a major component of personal-development and management literature.
... | 25,837 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
and task performance.
The theory states that the simplest most direct motivational explanation of why some people perform better than others is because they have different performance goals. The essence of the theory is fourfold. First, difficult specific goals lead to significantly higher performance tha... | 25,838 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
it leads to the setting of and commitment to a specific difficult goal. Fourth, goal-setting, in addition to affecting the three mechanisms of motivation, namely, choice, effort, and persistence, can also have a cognitive benefit. It can influence choice, effort, and persistence to discover ways to attain ... | 25,839 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
have on human activity. Locke developed and refined his goal-setting theory in the 1960s, publishing his first article on the subject, "Toward a Theory of Task Motivation and Incentives", in 1968. This article established the positive relationship between clearly identified goals and performance.
# Concep... | 25,840 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
able to use goal setting to benefit organizational performance. Locke and Latham (2002) have indicated three moderators that indicate goal setting success:
Expanding the three from above, the level of commitment is influenced by external factors. Such as the person assigning the goal, setting the standard... | 25,841 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
level in the work to achieve the goal. What they expect from themselves can either flourish their success, or destroy it. Also, the individual may want to appear superior to their peers or competitors. They want to achieve the goal the best and be known for it. The self-reward of accomplishing a goal, is u... | 25,842 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
to "do their best". "Doing one's best" has no external referent, which makes it useless in eliciting specific behavior. To elicit some specific form of behavior from another person, it is important that this person has a clear view of what is expected from him/her. A goal is thereby of vital importance bec... | 25,843 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
feedback channels it is impossible for employees to adapt or adjust to the required behavior. Managers should keep track of performance to allow employees to see how effective they have been in attaining their goals. Providing feedback on short-term objectives helps to sustain motivation and commitment to ... | 25,844 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
Properly delivered feedback is also very essential, and the following hints may help for providing a good feedback:
Advances in technology can facilitate providing feedback. Systems analysts have designed computer programs that track goals for numerous members of an organization. Such computer systems may... | 25,845 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
and strategies. From an organizational perspective, it is thereby more difficult to successfully attain more difficult goals, since resources become more scarce.
## Honing goal setting using temporal motivation theory.
Locke and Latham (2004) note that goal setting theory lacks "the issue of time perspec... | 25,846 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
expression "the sum of the parts can be greater than the whole", a division of a project into several, immediate, subgoals appears to take advantage of these two elements.
## Employee motivation.
The more employees are motivated, the more they are stimulated and interested in accepting goals. These succe... | 25,847 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
might think (s)he is not making enough progress. This can reduce self-efficacy and thereby harm the performance outcomes in the long run.
# In business.
In business, goal setting encourages participants to put in substantial effort. Also, because every member has defined expectations for their role, litt... | 25,848 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
performance are:
- 1. Goals focus attention toward goal-relevant activities and away from goal-irrelevant activities.
- 2. Goals serve as an energizer: Higher goals induce greater effort, while low goals induce lesser effort.
- 3. Goals affect persistence; constraints with regard to resources affect wor... | 25,849 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
testing scores; the addition of achievable goals appeared to be beneficial to the trainees./ref When goal setting is applied optimally during training processes, both employee motivation and organizational commitment can increase.
Furthermore, training in goal setting has been linked to higher levels of p... | 25,850 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
breaking it up into smaller, more achievable components helps in the planning portion of setting the goal. These smaller, more obtainable objectives promote self-esteem and provide instant feedback to keep the individual on task.
Time management is the practice of systematically finishing tasks assigned b... | 25,851 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
In an organization, a goal of a manager may not align with the goals of the organization as a whole. In such cases, the goals of an individual may come into direct conflict with the employing organization. Without clearly aligning goals between the organization and the individual, overall performance may s... | 25,852 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
the drawback of inhibiting implicit learning: goal setting may encourage simple focus on an outcome without openness to exploration, understanding, or growth. A solution to this limitation is to set "learning" goals as well as "performance" goals, so that learning is expected as part of the process of reac... | 25,853 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
Tunnel vision is a consequence of specific goals; if a person is too focused on attaining a specific goal, he or she may ignore the need to learn new skills or acquire new information. This concept is illustrated well by the "basketball game task" study in which observers watched a video of a group of peop... | 25,854 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
white shirts, only 6 reported noticing the woman carrying the umbrella. When observers watched the video without focusing on a specific task, all of the observers noticed the umbrella woman. In situations where the risk of tunnel vision is high, the best option is to set a "learning goal". A learning goal ... | 25,855 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
is necessary in environments with little or no guidance and structure. Although jobs typically have set goals, individual goals and achievement can benefit from metacognition.
## Framing.
Framing, or how goals are viewed, influences performance. When one feels threatened and or intimidated by a high goal... | 25,856 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
one realm. Success in one's job can compensate for feelings of failure in one's personal life.
## Group goals.
The relationship between group goals and individual goals influences group performance; when goals are compatible there is a positive effect, but when goals are incompatible the effects can be d... | 25,857 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
the two types of goals are "learning goals" and "performance goals"; each possesses different traits associated with the selected goal.
"Learning goals" involve tasks where skills and knowledge can be acquired, whereas "performance goals" involve easy-to-accomplish tasks that will make one appear successf... | 25,858 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
"Control orientation" (extrinsic motivation) is associated with both avoidance and approach goals. Approach goals are associated with higher goal levels and higher performance.
- "Autonomy goals" (intrinsic motivation) leads to mastery goals, enhanced focus, and therefore enhanced performance.
## Macro-l... | 25,859 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
subconscious priming.
The effects of subconscious priming and conscious goals are independent, although a conscious goal has a larger effect. The interaction effect is that priming can enhance the effects of difficult goals, but it has no effect on easy goals. There is also the situation in which priming ... | 25,860 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
whereas typical inaction goals can take the form of having a rest or to stop doing something.
Goal-regulated overall activity and inactivity tendency result from both biological conditions and social-cultural environment. Recent research revealed that most nations hold more favorable attitude towards acti... | 25,861 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
e making decisions among choices where uncertainty could result in negative outcomes, but they prefer action over inaction in their daily behaviors when no deliberation is needed. Timothy D. Wilson and colleagues found that many people "preferred to administer electric shocks to themselves instead of being... | 25,862 |
1055369 | Japanese mathematics | https://en.wikipedia.org/w/index.php?title=Japanese%20mathematics | Japanese mathematics
Japanese mathematics
In the history of mathematics, the development of "wasan" falls outside the Western realms of people, propositions and alternate solutions. At the beginning of the Meiji period (1868–1912), Japan and its people opened themselves to the West. Japanese scholars adopted Western m... | 25,863 |
1055369 | Japanese mathematics | https://en.wikipedia.org/w/index.php?title=Japanese%20mathematics | Japanese mathematics
Chishō, and Takahara Kisshu. These students came to be known to their contemporaries as "the Three Arithmeticians".
Yoshida was the author of the oldest extant Japanese mathematical text. The 1627 work was named "Jinkōki". The work dealt with the subject of soroban arithmetic, including square and... | 25,864 |
1055369 | Japanese mathematics | https://en.wikipedia.org/w/index.php?title=Japanese%20mathematics | Japanese mathematics
development in Europe; but Seki's investigations did not proceed from conventionally shared foundations.
# Select mathematicians.
The following list encompasses mathematicians whose work was derived from "wasan."
- Kambei Mori (early 17th century)
- Yoshida Mitsuyoshi (1598–1672)
- Seki Takaka... | 25,865 |
1055369 | Japanese mathematics | https://en.wikipedia.org/w/index.php?title=Japanese%20mathematics | Japanese mathematics
Isshu (1824–1871)
# See also.
- Japanese theorem for cyclic polygons
- Japanese theorem for cyclic quadrilaterals
- Sangaku, the custom of presenting mathematical problems, carved in wood tablets, to the public in Shinto shrines
- Soroban, a Japanese abacus
# References.
- Campbell, Douglas ... | 25,866 |
1055369 | Japanese mathematics | https://en.wikipedia.org/w/index.php?title=Japanese%20mathematics | Japanese mathematics
47500620
- __________ and Tony Rothman. (2008). "Sacred Mathematics: Japanese Temple Geometry." Princeton: Princeton University Press. ; OCLC 181142099
- Horiuchi, Annick. (1994). "Les Mathematiques Japonaises a L'Epoque d'Edo (1600–1868): Une Etude des Travaux de Seki Takakazu (?-1708) et de Tak... | 25,867 |
1055369 | Japanese mathematics | https://en.wikipedia.org/w/index.php?title=Japanese%20mathematics | Japanese mathematics
Japan from China?", "Historia Scientiarum", Vol.12, No.1.
- Kobayashi, Tatsuhiko. Trigonometry and Its Acceptance in the 18th-19th Centuries Japan.
- Morimoto, Mitsuo. "Infinite series in Japanese Mathematics of the 18th Century".
- Morimoto, Mitsuo. "A Chinese Root of Japanese Traditional Mathe... | 25,868 |
1055369 | Japanese mathematics | https://en.wikipedia.org/w/index.php?title=Japanese%20mathematics | Japanese mathematics
; OCLC 25709270
- Selin, Helaine. (1997). "Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures." Dordrecht: Kluwer/Springer. ; OCLC 186451909
- David Eugene Smith and Yoshio Mikami. (1914). "A History of Japanese Mathematics." Chicago: Open Court Publishing. ... | 25,869 |
1055390 | Sniper and Other Love Songs | https://en.wikipedia.org/w/index.php?title=Sniper%20and%20Other%20Love%20Songs | Sniper and Other Love Songs
Sniper and Other Love Songs
Sniper and Other Love Songs is the second studio album by the American singer/songwriter Harry Chapin, released in 1972. The album's title song is a vaguely fictionalised account of Charles Whitman's shootings from the clocktower of the Main Building of the Unive... | 25,870 |
1055390 | Sniper and Other Love Songs | https://en.wikipedia.org/w/index.php?title=Sniper%20and%20Other%20Love%20Songs | Sniper and Other Love Songs
arles Whitman's shootings from the clocktower of the Main Building of the University of Texas at Austin in August 1966. In 2004 it was released as a double CD package with "Heads & Tales" featuring several previously unreleased out-takes.
The song "Circle" was a major hit for The New Seeker... | 25,871 |
1055391 | Copiague Harbor, New York | https://en.wikipedia.org/w/index.php?title=Copiague%20Harbor,%20New%20York | Copiague Harbor, New York
Copiague Harbor, New York
Copiague Harbor ( ) is an incorporated community in the hamlet of Copiague. It is located south of Merrick Road (or Montauk Highway), off of South Great Neck Road in Suffolk County, New York, USA, on the South Shore of Long Island. It is sometimes referred to as Grea... | 25,872 |
1055391 | Copiague Harbor, New York | https://en.wikipedia.org/w/index.php?title=Copiague%20Harbor,%20New%20York | Copiague Harbor, New York
Shore of Long Island. It is sometimes referred to as Great Neck Landing;
Copiague Harbor is a small, community located on a southern peninsula of Copiague, primarily composed of larger size homes deeded belonging to a homeowner's association; Great South Bay Estates Homeowner's Association (G... | 25,873 |
1055393 | List of wars involving Georgia (country) | https://en.wikipedia.org/w/index.php?title=List%20of%20wars%20involving%20Georgia%20(country) | List of wars involving Georgia (country)
List of wars involving Georgia (country)
The following is an incomplete list of wars involving Georgia, by Georgian people or regular armies during periods when independent Georgian states existed, from antiquity to the present day. It also includes wars fought outside of Georg... | 25,874 |
1055372 | Villers-sur-Mer | https://en.wikipedia.org/w/index.php?title=Villers-sur-Mer | Villers-sur-Mer
Villers-sur-Mer
Villers-sur-Mer is a commune in the Calvados department in Normandy, northwestern France, with a population of 2,765 as of 2016.
# Geography.
The commune is located on the French coast of the English Channel, on the Côte Fleurie, between Deauville and Houlgate, approximately 200km fro... | 25,875 |
1055372 | Villers-sur-Mer | https://en.wikipedia.org/w/index.php?title=Villers-sur-Mer | Villers-sur-Mer
to the Cassini map (drawn in the 18th century), Villers at that time is made up of a church, two farms ("La Motte" and "Fontaine"), and a castle.
# Population.
The town had a population of 2,574 in 2006, posting a growth of just over 150 residents between then and 2016.
# Sights.
Villers-sur-Mer is ... | 25,876 |
1055372 | Villers-sur-Mer | https://en.wikipedia.org/w/index.php?title=Villers-sur-Mer | Villers-sur-Mer
the starting point of the Vaches Noires cliffsa site where many fossils have been discovered. There is a small museum in the enclosure of the office of tourism, which has an outline of the resources and discoveries. It is a place widely known by specialists in the ammonites and other fossils.
# Transpo... | 25,877 |
1055395 | 5th arrondissement | https://en.wikipedia.org/w/index.php?title=5th%20arrondissement | 5th arrondissement
5th arrondissement
5th arrondissement may refer to:
- France:
- 5th arrondissement of Lyon
- 5th arrondissement of Marseille
- 5th arrondissement of Paris
- Benin:
- 5th arrondissement of Porto-Novo
- 5th arrondissement of the Littoral Department | 25,878 |
1055398 | Little Indian River (Michigan) | https://en.wikipedia.org/w/index.php?title=Little%20Indian%20River%20(Michigan) | Little Indian River (Michigan)
Little Indian River (Michigan)
The Little Indian River is a river on the Upper Peninsula of the U.S. state of Michigan. It rises in a small lake on Hiawatha National Forest land in Alger County, Michigan at , flows through a lake district, then on through Schoolcraft County, and into the... | 25,879 |
1055370 | Lucas pseudoprime | https://en.wikipedia.org/w/index.php?title=Lucas%20pseudoprime | Lucas pseudoprime
Lucas pseudoprime
Lucas pseudoprimes and Fibonacci pseudoprimes are composite integers that pass certain tests which all primes and very few composite numbers pass: in this case, criteria relative to some Lucas sequence.
# Baillie-Wagstaff-Lucas pseudoprimes.
Baillie and Wagstaff define Lucas pseud... | 25,880 |
1055370 | Lucas pseudoprime | https://en.wikipedia.org/w/index.php?title=Lucas%20pseudoprime | Lucas pseudoprime
does "not" hold, then "n" is "not" prime.
If "n" is "composite", then this equation "usually" does not hold. These are the key facts that make Lucas sequences useful in primality testing.
Some good references are chapter 8 of the book by Bressoud and Wagon (with Mathematica code), pages 142–152 of t... | 25,881 |
1055370 | Lucas pseudoprime | https://en.wikipedia.org/w/index.php?title=Lucas%20pseudoprime | Lucas pseudoprime
prime test is most useful if "D" is chosen such that the Jacobi symbol formula_2 is −1
(see pages 1401–1409 of, page 1024 of
, or pages 266–269 of
). This is especially important when combining a Lucas test with a strong pseudoprime test, such as the Baillie-PSW primality test. Typically implementa... | 25,882 |
1055370 | Lucas pseudoprime | https://en.wikipedia.org/w/index.php?title=Lucas%20pseudoprime | Lucas pseudoprime
true, then "n" is "likely" to be prime (this justifies the term probable prime), but this does not "prove" that "n" is prime.
As is the case with any other probabilistic primality test, if we perform additional Lucas tests with different "D", "P" and "Q", then unless one of the tests proves that "n" ... | 25,883 |
1055370 | Lucas pseudoprime | https://en.wikipedia.org/w/index.php?title=Lucas%20pseudoprime | Lucas pseudoprime
Lucas pseudoprime.
For the next example, let "n" = 119. We have formula_8 = −1, and we can compute
However, 119 = 7·17 is not prime, so 119 is a Lucas "pseudoprime" for this ("P, Q") pair.
In fact, 119 is the smallest pseudoprime for "P" = 3, "Q" = −1.
We will see below that, in order to check equ... | 25,884 |
1055370 | Lucas pseudoprime | https://en.wikipedia.org/w/index.php?title=Lucas%20pseudoprime | Lucas pseudoprime
one of the conditions
or
for some 0 ≤ "r" "s"; see page 1396 of. A strong Lucas pseudoprime is also a Lucas pseudoprime (for the same ("P, Q") pair), but the converse is not necessarily true.
Therefore, the strong test is a more stringent primality test than equation ().
We can set "Q" = −1, then... | 25,885 |
1055370 | Lucas pseudoprime | https://en.wikipedia.org/w/index.php?title=Lucas%20pseudoprime | Lucas pseudoprime
some formula_19 pair.
# Implementing a Lucas probable prime test.
Before embarking on a probable prime test, one usually verifies that "n", the number to be tested for primality, is odd, is not a perfect square, and is not divisible by any small prime less than some convenient limit. Perfect squares... | 25,886 |
1055370 | Lucas pseudoprime | https://en.wikipedia.org/w/index.php?title=Lucas%20pseudoprime | Lucas pseudoprime
of "D" values, the average number of "D" values that must be tried before we encounter one whose Jacobi symbol is −1 is about 1.79; see, p. 1416.
Once we have "D", we set formula_24 and formula_25.
It is a good idea to check that "n" has no prime factors in common with "P" or "Q".
This method of ch... | 25,887 |
1055370 | Lucas pseudoprime | https://en.wikipedia.org/w/index.php?title=Lucas%20pseudoprime | Lucas pseudoprime
is odd, replace it with formula_38; this is even so it can now be divided by 2. The numerator of formula_39 is handled in the same way. (Adding "n" does not change the result modulo "n".)
Observe that, for each term that we compute in the "U" sequence, we compute the corresponding term in the "V" seq... | 25,888 |
1055370 | Lucas pseudoprime | https://en.wikipedia.org/w/index.php?title=Lucas%20pseudoprime | Lucas pseudoprime
of indices to compute: 1 = 1, 10 = 2, 100 = 4, 101 = 5, 1010 = 10, 1011 = 11, 10110 = 22, 101100 = 44. Therefore, we compute "U", "U", "U", "U", "U", "U", "U", and "U". We also compute the same-numbered terms in the "V" sequence, along with "Q", "Q", "Q", "Q", "Q", "Q", "Q", and "Q".
By the end of th... | 25,889 |
1055370 | Lucas pseudoprime | https://en.wikipedia.org/w/index.php?title=Lucas%20pseudoprime | Lucas pseudoprime
are chosen as described above, the first 10 "strong" Lucas pseudoprimes are: 5459, 5777, 10877, 16109, 18971, 22499, 24569, 25199, 40309, and 58519
To calculate a list of "extra strong" Lucas pseudoprimes, set formula_43.
Then try "P" = 3, 4, 5, 6, ..., until a value of formula_1 is found so that th... | 25,890 |
1055370 | Lucas pseudoprime | https://en.wikipedia.org/w/index.php?title=Lucas%20pseudoprime | Lucas pseudoprime
"n" happens to be composite, these additional conditions may help discover that fact.
If "n" is an odd prime and formula_20, then we have the following (see equation 2 on page 1392 of ):
Although this congruence condition is not, by definition, part of the Lucas probable prime test, it is almost fre... | 25,891 |
1055370 | Lucas pseudoprime | https://en.wikipedia.org/w/index.php?title=Lucas%20pseudoprime | Lucas pseudoprime
to set "Q" = −1, then we can adjust "P" and "Q" so that "D" and formula_2 remain unchanged and "P" = "Q" = 5 (see Lucas sequence-Algebraic relations).
If we use this enhanced method for choosing "P" and "Q", then 913 = 11·83 is the "only" composite less than 10 for which congruence () is true (see pa... | 25,892 |
1055370 | Lucas pseudoprime | https://en.wikipedia.org/w/index.php?title=Lucas%20pseudoprime | Lucas pseudoprime
is the same as the Jacobi symbol).
Therefore, if "n" is prime, we must have
The Jacobi symbol on the right side is easy to compute, so this congruence is easy to check.
If this congruence does not hold, then "n" cannot be prime.
Additional congruence conditions that must be satisfied if "n" is pri... | 25,893 |
1055370 | Lucas pseudoprime | https://en.wikipedia.org/w/index.php?title=Lucas%20pseudoprime | Lucas pseudoprime
two trivial exceptions (see below), the fraction of ("P","Q") pairs (modulo "n") that declare a composite "n" to be probably prime is at most (4/15).
Therefore, "k" applications of the strong Lucas test would declare a composite "n" to be probably prime with a probability at most (4/15).
There are t... | 25,894 |
1055370 | Lucas pseudoprime | https://en.wikipedia.org/w/index.php?title=Lucas%20pseudoprime | Lucas pseudoprime
tests for primality, such as the Baillie–PSW primality test.
# Fibonacci pseudoprimes.
As noted above, when "P" = 1 and "Q" = −1, the numbers in the "U" sequence are the Fibonacci numbers.
A Fibonacci pseudoprime is often
(page 264 of, page 142 of, or
page 127 of )
defined as a composite number ... | 25,895 |
1055370 | Lucas pseudoprime | https://en.wikipedia.org/w/index.php?title=Lucas%20pseudoprime | Lucas pseudoprime
143 and exercise 3.41 on page 168) point out that it is rare for a Fibonacci pseudoprime to also be a Fermat pseudoprime base 2. However, when "n" is congruent to 1 or 4 (mod 5), the opposite is true, with over 12% of Fibonacci pseudoprimes under 10 also being base-2 Fermat pseudoprimes.
If "n" is pr... | 25,896 |
1055370 | Lucas pseudoprime | https://en.wikipedia.org/w/index.php?title=Lucas%20pseudoprime | Lucas pseudoprime
( page 129) ; the latter refers to these as "Bruckman-Lucas" pseudoprimes.
Hoggatt and Bicknell studied properties of these pseudoprimes in 1974. Singmaster computed these pseudoprimes up to 100000. Jacobsen lists all 111443 of these pseudoprimes less than 10.
It has been shown that there are no eve... | 25,897 |
1055370 | Lucas pseudoprime | https://en.wikipedia.org/w/index.php?title=Lucas%20pseudoprime | Lucas pseudoprime
− 1) or 2("p" + 1) | ("n" − "p") for every prime "p" dividing "n".
The smallest example of a strong Fibonacci pseudoprime is 443372888629441 = 17·31·41·43·89·97·167·331.
# Pell pseudoprimes.
A Pell pseudoprime may be defined as a composite number "n" for which equation () above is true with "P" = 2... | 25,898 |
1055370 | Lucas pseudoprime | https://en.wikipedia.org/w/index.php?title=Lucas%20pseudoprime | Lucas pseudoprime
en as:
with ("P", "Q") = (2, −1) again defining "U" as the Pell sequence. The first pseudoprimes are then 169, 385, 741, 961, 1121, 2001, 3827, 4879, 5719, 6215 ...
A third definition uses equation (5) with ("P", "Q") = (2, −1), leading to the pseudoprimes 169, 385, 961, 1105, 1121, 3827, 4901, 6265... | 25,899 |
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