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Routh's Theorem
In geometry, Routh's theorem determines the ratio of areas between a given triangle and a triangle formed by the pairwise intersections of three cevians. The theorem states that if in triangle ABC points D, E, and F lie on segments BC, CA, and AB, then writing \tfrac = x, \tfrac = y, and \tfrac = z, the signed area of the triangle formed by the cevians AD, BE, and CF is : S_ \frac, where S_ is the area of the triangle ABC. This theorem was given by Edward John Routh on page 82 of his ''Treatise on Analytical Statics with Numerous Examples'' in 1896. The particular case x = y = z = 2 has become popularized as the one-seventh area triangle. The x = y = z = 1 case implies that the three medians are concurrent (through the centroid). Proof Suppose that the area of triangle ABC is 1. For triangle ABD and line FRC using Menelaus's theorem, We could obtain: :\frac \times \frac \times \frac = 1 Then \frac = \frac \times \frac = \frac So the area of triangle ARC is: :S_ = \frac S_ = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Routh Theorem2
Routh may refer to: Places * Routh, East Riding of Yorkshire, a village in England People * Brandon Routh (born 1979), American actor * Camilla Belle Routh (born 1986), American actress * Edward Routh (1831–1907), British mathematician * Francis Routh, Francis John Routh (1927–2021), English composer and author * Jonathan Routh (1927–2008), British humourist * Josh Routh (born 1978), contemporary American circus artist * Martin Joseph Routh, or Martin Routh (1755-1854), British classical scholar * C.R.N. Routh, wrote ''Who's Who in Tudor England 1485-1603'' {{disambig, surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stomachion
''Ostomachion'', also known as ''loculus Archimedius'' (Archimedes' box in Latin) and also as ''syntomachion'', is a mathematical treatise attributed to Archimedes. This work has survived fragmentarily in an Arabic version and a copy, the ''Archimedes Palimpsest'', of the original ancient Greek text made in Byzantine times.Darling, David (2004). ''The universal book of mathematics: from Abracadabra to Zeno's paradoxes''. John Wiley and Sons, p. 188. The word Ostomachion has as its roots in the Greek Ὀστομάχιον, which means "bone-fight", from ὀστέον (''osteon''), "bone" and μάχη (''mache''), "fight, battle, combat". Note that the manuscripts refer to the word as "Stomachion", an apparent corruption of the original Greek. Ausonius gives us the correct name "Ostomachion" (''quod Graeci ostomachion vocavere,'' "which the Greeks called ostomachion"). The Ostomachion which he describes was a puzzle similar to tangrams and was played perhaps by several persons w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Wolfram Demonstrations Project
The Wolfram Demonstrations Project is an organized, open-source collection of small (or medium-size) interactive programs called Demonstrations, which are meant to visually and interactively represent ideas from a range of fields. It is hosted by Wolfram Research, whose stated goal is to bring computational exploration to a large population. At its launch, it contained 1300 demonstrations but has grown to over 10,000. The site won a Parents' Choice Award in 2008. Technology The Demonstrations run in '' Mathematica'' 6 or above and in '' Wolfram CDF Player'' which is a free modified version of Wolfram's ''Mathematica'' and available for Windows, Linux and macOS and can operate as a web browser plugin. They typically consist of a very direct user interface to a graphic or visualization, which dynamically recomputes in response to user actions such as moving a slider, clicking a button, or dragging a piece of graphics. Each Demonstration also has a brief description of the c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Magazine
''Mathematics Magazine'' is a refereed bimonthly publication of the Mathematical Association of America. Its intended audience is teachers of collegiate mathematics, especially at the junior/senior level, and their students. It is explicitly a journal of mathematics rather than pedagogy. Rather than articles in the terse "theorem-proof" style of research journals, it seeks articles which provide a context for the mathematics they deliver, with examples, applications, illustrations, and historical background. Paid circulation in 2008 was 9,500 and total circulation was 10,000. ''Mathematics Magazine'' is a continuation of ''Mathematics News Letter'' (1926-1934) and ''National Mathematics Magazine'' (1934-1945.) Doris Schattschneider became the first female editor of ''Mathematics Magazine'' in 1981. .. The MAA gives the Carl B. Allendoerfer Awards annually "for articles of expository excellence" published in ''Mathematics Magazine''. See also *''American Mathematical Mont ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ivan Niven
Ivan Morton Niven (October 25, 1915 May 9, 1999) was a Canadian-American mathematician, specializing in number theory and known for his work on Waring's problem. He worked for many years as a professor at the University of Oregon, and was president of the Mathematical Association of America. He was the author of several books on mathematics. Life Niven was born in Vancouver. He did his undergraduate studies at the University of British Columbia and was awarded his doctorate in 1938 from the University of Chicago. He was a member of the University of Oregon faculty from 1947 to his retirement in 1981. He was president of the Mathematical Association of America (MAA) from 1983 to 1984. He died in 1999 in Eugene, Oregon. Research Niven gave a proof that \pi is irrational in 1947. Niven completed the solution of most of Waring's problem in 1944. This problem, based on a 1770 conjecture by Edward Waring, consists of finding the smallest number g(n) such that every positive integer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crux Mathematicorum
''Crux Mathematicorum'' is a scientific journal of mathematics published by the Canadian Mathematical Society. It contains mathematical problems for secondary school and undergraduate students. , its editor-in-chief is Kseniya Garaschuk. The journal was established in 1975, under the name ''Eureka'', by the Carleton-Ottawa Mathematics Association, with Léo Sauvé as its first editor-in-chief. It took the name ''Crux Mathematicorum'' with its fourth volume, in 1978, to avoid confusion with another journal ''Eureka'' published by the Cambridge University Mathematical Society. The Canadian Mathematical Society took over the journal in 1985, and soon afterwards G.W. (Bill) Sands became its new editor. Bruce L. R. Shawyer took over as editor in 1996. In 1997 it merged with another journal founded in 1988, ''Mathematical Mayhem'', to become ''Crux Mathematicorum with Mathematical Mayhem''. Jim Totten became editor in 2003, and Václav (Vazz) Linek replaced him in 2008. Ross Honsberger ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Murray S
Murray may refer to: Businesses * Murray (bicycle company), an American manufacturer of low-cost bicycles * Murrays, an Australian bus company * Murray International Trust, a Scottish investment trust * D. & W. Murray Limited, an Australian wholesale drapery business * John Murray (publishing house), a British publishing house Fictional characters * Murray Monster, a muppet in ''Sesame Street'' *Little Murray Sparkles, a cat in ''Sesame Street'' * Murray (''Monkey Island''), a character in the video game series * Murray (''Sly Cooper''), a character in the video game series *Murray Slaughter, a regular character in ''The Mary Tyler Moore Show'' *Murray, the mascot of the band Dio *Murray, in the 2015 Netflix series '' Richie Rich'' *Murray, a ''Hotel Transylvania'' character *Murray the Cop, in ''Fat Pizza'' *Murray Smith, in ''Swift and Shift Couriers'' People *Murray (surname) *Murray (given name) Places Australia * Division of Murray, federal electoral district in Victo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Virginia
Virginia, officially the Commonwealth of Virginia, is a state in the Mid-Atlantic and Southeastern regions of the United States, between the Atlantic Coast and the Appalachian Mountains. The geography and climate of the Commonwealth are shaped by the Blue Ridge Mountains and the Chesapeake Bay, which provide habitat for much of its flora and fauna. The capital of the Commonwealth is Richmond; Virginia Beach is the most-populous city, and Fairfax County is the most-populous political subdivision. The Commonwealth's population was over 8.65million, with 36% of them living in the Baltimore–Washington metropolitan area. The area's history begins with several indigenous groups, including the Powhatan. In 1607, the London Company established the Colony of Virginia as the first permanent English colony in the New World. Virginia's state nickname, the Old Dominion, is a reference to this status. Slave labor and land acquired from displaced native tribes fueled the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Williamsburg, Virginia
Williamsburg is an Independent city (United States), independent city in the Commonwealth (U.S. state), Commonwealth of Virginia. As of the 2020 United States census, 2020 census, it had a population of 15,425. Located on the Virginia Peninsula, Williamsburg is in the northern part of the Hampton Roads metropolitan area. It is bordered by James City County, Virginia, James City County on the west and south and York County, Virginia, York County on the east. English settlers founded Williamsburg in 1632 as Middle Plantation (Virginia), Middle Plantation, a fortified settlement on high ground between the James River, James and York River (Virginia), York rivers. The city functioned as the capital of the Colony of Virginia, Colony and Commonwealth of Virginia from 1699 to 1780 and became the center of political events in Virginia leading to the American Revolution. The College of William & Mary, established in 1693, is the second-oldest institution of higher education in the United ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
College Of William & Mary
The College of William & Mary (officially The College of William and Mary in Virginia, abbreviated as William & Mary, W&M) is a public research university in Williamsburg, Virginia. Founded in 1693 by letters patent issued by King William III and Queen Mary II, it is the second-oldest institution of higher education in the United States and the ninth-oldest in the English-speaking world. Institutional rankings have placed it among the best public universities in the United States. The college educated American presidents Thomas Jefferson, James Monroe, and John Tyler. It also educated other key figures pivotal to the development of the United States, including the first President of the Continental Congress Peyton Randolph, the first U.S. Attorney General Edmund Randolph, the fourth U.S. Supreme Court Chief Justice John Marshall, Speaker of the House of Representatives Henry Clay, Commanding General of the U.S. Army Winfield Scott, sixteen members of the Continental Con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wrangler (University Of Cambridge)
At the University of Cambridge in England, a "Wrangler" is a student who gains first-class honours in the final year of the university's degree in mathematics. The highest-scoring student is the Senior Wrangler, the second highest is the Second Wrangler, and so on. At the other end of the scale, the person who achieves the lowest exam marks while still earning a third-class honours degree (that is, while still earning an honours degree at all) is known as the wooden spoon. Until 1909, the university made the rankings public. Since 1910, it has publicly revealed only the class of degree gained by each student. An examiner reveals the identity of the Senior Wrangler "unofficially" by tipping his hat when reading out the person's name, but other rankings are communicated to each student privately. Therefore, the names of only some 20th-century Senior Wranglers (such as Crispin Nash-Williams, Christopher Budd, Frank P. Ramsey, Donald Coxeter, Kevin Buzzard, Jayant Narlikar, Georg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Potts
Robert Frederick Potts, known as Fred Potts (born 1893) was an English professional footballer who played as a right back. Career Born in Congleton, Potts played for Bacup Borough, Bradford City and Congleton Town. For Bradford City, he made 136 appearances in the Football League; he also made 11 FA Cup The Football Association Challenge Cup, more commonly known as the FA Cup, is an annual knockout football competition in men's domestic English football. First played during the 1871–72 season, it is the oldest national football compet ... appearances.Frost, p. 387 Sources * References 1893 births People from Congleton Year of death missing English footballers Bacup Borough F.C. players Bradford City A.F.C. players Congleton Town F.C. players English Football League players Association football defenders {{England-footy-defender-1890s-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
