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Thomas Clausen (mathematician)
Thomas Clausen (16 January 1801, Snogbæk, Sottrup Municipality, Duchy of Schleswig (now Denmark) – 23 May 1885, Dorpat, Imperial Russia (now Estonia)) was a Danish mathematician and astronomer. Clausen learned mathematics at home. In 1820, he became a trainee at the Munich Optical Institute and in 1824, at the Altona Observatory after he showed Heinrich Christian Schumacher his paper on calculating longitude by the occultation of stars by the moon. He eventually returned to Munich, where he conceived and published his best known works on mathematics. In 1842 Clausen was hired by the staff of the Tartu Observatory, becoming its director in 1866-1872. Works by Clausen include studies on the stability of Solar System, comet movement, ABC telegraph code and calculation of 250 decimals of pi (later, only 248 were confirmed to be correct). In 1840 he discovered the Von Staudt–Clausen theorem. Also in 1840 he also found two compass and straightedge constructions of lunes w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas Clausen
{{Hndis, Clausen, Thomas ...
Thomas Clausen may refer to: * Thomas Clausen (educator) (1939–2002), educator from Baton Rouge, Louisiana *Thomas Clausen (musician) (born 1949), Danish jazz pianist *Thomas Clausen (mathematician) (1801–1885), Danish mathematician and astronomer See also *Clausen Clausen is a Danish language, Danish patronymic surname, literally meaning ''child of Claus'', Claus being a German language, German form of the Greek language, Greek Νικόλαος, Nikolaos, (cf. Nicholas), used in Denmark at least since the 16t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Comet
A comet is an icy, small Solar System body that, when passing close to the Sun, warms and begins to release gases, a process that is called outgassing. This produces a visible atmosphere or coma, and sometimes also a tail. These phenomena are due to the effects of solar radiation and the solar wind acting upon the nucleus of the comet. Comet nuclei range from a few hundred meters to tens of kilometers across and are composed of loose collections of ice, dust, and small rocky particles. The coma may be up to 15 times Earth's diameter, while the tail may stretch beyond one astronomical unit. If sufficiently bright, a comet may be seen from Earth without the aid of a telescope and may subtend an arc of 30° (60 Moons) across the sky. Comets have been observed and recorded since ancient times by many cultures and religions. Comets usually have highly eccentric elliptical orbits, and they have a wide range of orbital periods, ranging from several years to potentially several mill ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1885 Deaths
Events January–March * January 3– 4 – Sino-French War – Battle of Núi Bop: French troops under General Oscar de Négrier defeat a numerically superior Qing Chinese force, in northern Vietnam. * January 4 – The first successful appendectomy is performed by Dr. William W. Grant, on Mary Gartside. * January 17 – Mahdist War in Sudan – Battle of Abu Klea: British troops defeat Mahdist forces. * January 20 – American inventor LaMarcus Adna Thompson patents a roller coaster. * January 24 – Irish rebels damage Westminster Hall and the Tower of London with dynamite. * January 26 – Mahdist War in Sudan: Troops loyal to Mahdi Muhammad Ahmad conquer Khartoum; British commander Charles George Gordon is killed. * February 5 – King Leopold II of Belgium establishes the Congo Free State, as a personal possession. * February 9 – The first Japanese arrive in Hawaii. * February 16 – Charles Dow publishes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1801 Births
Eighteen or 18 may refer to: * 18 (number), the natural number following 17 and preceding 19 * one of the years 18 BC, AD 18, 1918, 2018 Film, television and entertainment * ''18'' (film), a 1993 Taiwanese experimental film based on the short story ''God's Dice'' * ''Eighteen'' (film), a 2005 Canadian dramatic feature film * 18 (British Board of Film Classification), a film rating in the United Kingdom, also used in Ireland by the Irish Film Classification Office * 18 (''Dragon Ball''), a character in the ''Dragon Ball'' franchise * "Eighteen", a 2006 episode of the animated television series ''12 oz. Mouse'' Music Albums * ''18'' (Moby album), 2002 * ''18'' (Nana Kitade album), 2005 * '' 18...'', 2009 debut album by G.E.M. Songs * "18" (5 Seconds of Summer song), from their 2014 eponymous debut album * "18" (One Direction song), from their 2014 studio album ''Four'' * "18", by Anarbor from their 2013 studio album '' Burnout'' * "I'm Eighteen", by Alice Cooper common ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Für Die Reine Und Angewandte Mathematik
''Crelle's Journal'', or just ''Crelle'', is the common name for a mathematics journal, the ''Journal für die reine und angewandte Mathematik'' (in English: ''Journal for Pure and Applied Mathematics''). History The journal was founded by August Leopold Crelle (Berlin) in 1826 and edited by him until his death in 1855. It was one of the first major mathematical journals that was not a proceedings of an academy. It has published many notable papers, including works of Niels Henrik Abel, Georg Cantor, Gotthold Eisenstein, Carl Friedrich Gauss and Otto Hesse. It was edited by Carl Wilhelm Borchardt from 1856 to 1880, during which time it was known as ''Borchardt's Journal''. The current editor-in-chief is Rainer Weissauer (Ruprecht-Karls-Universität Heidelberg) Past editors * 1826–1856 August Leopold Crelle * 1856–1880 Carl Wilhelm Borchardt * 1881–1888 Leopold Kronecker, Karl Weierstrass * 1889–1892 Leopold Kronecker * 1892–1902 Lazarus Fuchs * 1903–1928 Kurt Hens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clausen Function
In mathematics, the Clausen function, introduced by , is a transcendental, special function of a single variable. It can variously be expressed in the form of a definite integral, a trigonometric series, and various other forms. It is intimately connected with the polylogarithm, inverse tangent integral, polygamma function, Riemann zeta function, Dirichlet eta function, and Dirichlet beta function. The Clausen function of order 2 – often referred to as ''the'' Clausen function, despite being but one of a class of many – is given by the integral: :\operatorname_2(\varphi)=-\int_0^\varphi \log\left, 2\sin\frac \\, dx: In the range 0 :\operatorname_2\left(-\frac+2m\pi \right) =-1.01494160 \ldots The following properties are immediate consequences of the series definition: :\operatorname_2(\theta+2m\pi) = \operatorname_2(\theta) :\operatorname_2(-\theta) = -\operatorname_2(\theta) See . General definition More generally, one defines the two generalized Clausen fu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clausen's Formula
In mathematics, Clausen's formula, found by , expresses the square of a Gaussian hypergeometric series as a generalized hypergeometric series. It states :\;_F_1 \left begin a & b \\ a+b+1/2 \end ; x \right2 = \;_F_2 \left begin 2a & 2b &a+b \\ a+b+1/2 &2a+2b \end ; x \right/math> In particular it gives conditions for a hypergeometric series to be positive. This can be used to prove several inequalities, such as the Askey–Gasper inequality used in the proof of de Branges's theorem In complex analysis, de Branges's theorem, or the Bieberbach conjecture, is a theorem that gives a necessary condition on a holomorphic function in order for it to map the open unit disk of the complex plane injectively to the complex plane. It was .... References * * * For a detailed proof of Clausen's formula: {{Citation , last1=Milla , first1=Lorenz , title= A detailed proof of the Chudnovsky formula with means of basic complex analysis , arxiv=1809.00533 , year=2018 Special functions [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermat Number
In mathematics, a Fermat number, named after Pierre de Fermat, who first studied them, is a positive integer of the form :F_ = 2^ + 1, where ''n'' is a non-negative integer. The first few Fermat numbers are: : 3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, ... . If 2''k'' + 1 is prime and ''k'' > 0, then ''k'' must be a power of 2, so 2''k'' + 1 is a Fermat number; such primes are called Fermat primes. , the only known Fermat primes are ''F''0 = 3, ''F''1 = 5, ''F''2 = 17, ''F''3 = 257, and ''F''4 = 65537 ; heuristics suggest that there are no more. Basic properties The Fermat numbers satisfy the following recurrence relations: : F_ = (F_-1)^+1 : F_ = F_ \cdots F_ + 2 for ''n'' ≥ 1, : F_ = F_ + 2^F_ \cdots F_ : F_ = F_^2 - 2(F_-1)^2 for ''n'' ≥ 2. Each of these relations can be proved by mathematical induction. From the second equation, we can deduce Goldbach's theorem (named after Christian Goldbach): no two Fermat numbers share a common integer factor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galois Theory
In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to group theory, which makes them simpler and easier to understand. Galois introduced the subject for studying roots of polynomials. This allowed him to characterize the polynomial equations that are solvable by radicals in terms of properties of the permutation group of their roots—an equation is ''solvable by radicals'' if its roots may be expressed by a formula involving only integers, th roots, and the four basic arithmetic operations. This widely generalizes the Abel–Ruffini theorem, which asserts that a general polynomial of degree at least five cannot be solved by radicals. Galois theory has been used to solve classic problems including showing that two problems of antiquity cannot be solved as they were stated (doubling the cub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Monthly
''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an expository journal intended for a wide audience of mathematicians, from undergraduate students to research professionals. Articles are chosen on the basis of their broad interest and reviewed and edited for quality of exposition as well as content. In this the ''American Mathematical Monthly'' fulfills a different role from that of typical mathematical research journals. The ''American Mathematical Monthly'' is the most widely read mathematics journal in the world according to records on JSTOR. Tables of contents with article abstracts from 1997–2010 are availablonline The MAA gives the Lester R. Ford Awards annually to "authors of articles of expository excellence" published in the ''American Mathematical Monthly''. Editors *2022– ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hippocrates Of Chios
Hippocrates of Chios ( grc-gre, Ἱπποκράτης ὁ Χῖος; c. 470 – c. 410 BC) was an ancient Greek mathematician, geometer, and astronomer. He was born on the isle of Chios, where he was originally a merchant. After some misadventures (he was robbed by either pirates or fraudulent customs officials) he went to Athens, possibly for litigation, where he became a leading mathematician. On Chios, Hippocrates may have been a pupil of the mathematician and astronomer Oenopides of Chios. In his mathematical work there probably was some Pythagorean influence too, perhaps via contacts between Chios and the neighboring island of Samos, a center of Pythagorean thinking: Hippocrates has been described as a 'para-Pythagorean', a philosophical 'fellow traveler'. "Reduction" arguments such as ''reductio ad absurdum'' argument (or proof by contradiction) have been traced to him, as has the use of power to denote the square of a line.W. W. Rouse Ball, A Short Account of the Hist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lune Of Hippocrates
In geometry, the lune of Hippocrates, named after Hippocrates of Chios, is a lune (mathematics), lune bounded by Circular arc, arcs of two circles, the smaller of which has as its diameter a Chord (geometry), chord spanning a right angle on the larger circle. Equivalently, it is a non-Convex set, convex plane region bounded by one 180-degree circular arc and one 90-degree circular arc. It was the first curved figure to have its exact area calculated mathematically.. Translated from Postnikov's 1963 Russian book on Galois theory. History Hippocrates wanted to solve the classic problem of squaring the circle, i.e. constructing a square by means of straightedge and compass, having the same area as a given circle. He proved that the lune bounded by the arcs labeled ''E'' and ''F'' in the figure has the same area as triangle ''ABO''. This afforded some hope of solving the circle-squaring problem, since the lune is bounded only by arcs of circles. Thomas Little Heath, Heath concl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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