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George Jerrard
George Birch Jerrard (25 November 1804 – 23 November 1863) was a British mathematician. He studied at Trinity College, Dublin from 1821 to 1827. His main work was on the theory of equations, where he was reluctant to accept the validity of the work of Niels Henrik Abel on the insolubility of the quintic equation by Nth root, radicals. He found a way of using Tschirnhaus transformations to eliminate three of the terms in an equation, which generalised work of Erland Samuel Bring, Erland Bring (1736–1798), and is now called Bring–Jerrard normal form. Works * ''An essay on the resolution of equations'', part 1, London 1858,online. References * External links * English mathematicians 1804 births 1863 deaths Algebraists 19th-century British mathematicians Alumni of Trinity College Dublin {{UK-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trinity College, Dublin
, name_Latin = Collegium Sanctae et Individuae Trinitatis Reginae Elizabethae juxta Dublin , motto = ''Perpetuis futuris temporibus duraturam'' (Latin) , motto_lang = la , motto_English = It will last into endless future times , founder = Queen Elizabeth I , established = , named_for = Trinity, The Holy Trinity.The Trinity was the patron of The Dublin Guild Merchant, primary instigators of the foundation of the University, the arms of which guild are also similar to those of the College. , previous_names = , status = , architect = , architectural_style =Neoclassical architecture , colours = , gender = , sister_colleges = St. John's College, CambridgeOriel College, Oxford , freshman_dorm = , head_label = , head = , master = , vice_head_label = , vice_head = , warden ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theory Of Equations
In algebra, the theory of equations is the study of algebraic equations (also called "polynomial equations"), which are equations defined by a polynomial. The main problem of the theory of equations was to know when an algebraic equation has an algebraic solution. This problem was completely solved in 1830 by Évariste Galois, by introducing what is now called Galois theory. Before Galois, there was no clear distinction between the "theory of equations" and "algebra". Since then algebra has been dramatically enlarged to include many new subareas, and the theory of algebraic equations receives much less attention. Thus, the term "theory of equations" is mainly used in the context of the history of mathematics, to avoid confusion between old and new meanings of "algebra". History Until the end of the 19th century, "theory of equations" was almost synonymous with "algebra". For a long time, the main problem was to find the solutions of a single non-linear polynomial equation in a s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Niels Henrik Abel
Niels Henrik Abel ( , ; 5 August 1802 – 6 April 1829) was a Norwegian mathematician who made pioneering contributions in a variety of fields. His most famous single result is the first complete proof demonstrating the impossibility of solving the general quintic equation in radicals. This question was one of the outstanding open problems of his day, and had been unresolved for over 250 years. He was also an innovator in the field of elliptic functions, discoverer of Abelian functions. He made his discoveries while living in poverty and died at the age of 26 from tuberculosis. Most of his work was done in six or seven years of his working life. Regarding Abel, the French mathematician Charles Hermite said: "Abel has left mathematicians enough to keep them busy for five hundred years." Another French mathematician, Adrien-Marie Legendre, said: "What a head the young Norwegian has!" The Abel Prize in mathematics, originally proposed in 1899 to complement the Nobel Prizes (but ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quintic Equation
In algebra, a quintic function is a function of the form :g(x)=ax^5+bx^4+cx^3+dx^2+ex+f,\, where , , , , and are members of a field, typically the rational numbers, the real numbers or the complex numbers, and is nonzero. In other words, a quintic function is defined by a polynomial of degree five. Because they have an odd degree, normal quintic functions appear similar to normal cubic functions when graphed, except they may possess one additional local maximum and one additional local minimum. The derivative of a quintic function is a quartic function. Setting and assuming produces a quintic equation of the form: :ax^5+bx^4+cx^3+dx^2+ex+f=0.\, Solving quintic equations in terms of radicals (''n''th roots) was a major problem in algebra from the 16th century, when cubic and quartic equations were solved, until the first half of the 19th century, when the impossibility of such a general solution was proved with the Abel–Ruffini theorem. Finding roots of a quintic equa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nth Root
In mathematics, a radicand, also known as an nth root, of a number ''x'' is a number ''r'' which, when raised to the power ''n'', yields ''x'': :r^n = x, where ''n'' is a positive integer, sometimes called the ''degree'' of the root. A root of degree 2 is called a ''square root'' and a root of degree 3, a ''cube root''. Roots of higher degree are referred by using ordinal numbers, as in ''fourth root'', ''twentieth root'', etc. The computation of an th root is a root extraction. For example, 3 is a square root of 9, since 3 = 9, and −3 is also a square root of 9, since (−3) = 9. Any non-zero number considered as a complex number has different complex th roots, including the real ones (at most two). The th root of 0 is zero for all positive integers , since . In particular, if is even and is a positive real number, one of its th roots is real and positive, one is negative, and the others (when ) are non-real complex numbers; if is even and is a negative real numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tschirnhaus Transformation
In mathematics, a Tschirnhaus transformation, also known as Tschirnhausen transformation, is a type of mapping on polynomials developed by Ehrenfried Walther von Tschirnhaus in 1683. Simply, it is a method for transforming a polynomial equation of degree n\ge2 with some nonzero intermediate coefficients, a_1, ..., a_, such that some or all of the transformed intermediate coefficients, a'_1, ..., a'_, are exactly zero. For example, finding a substitutiony(x)=k_1x^2 + k_2x+k_3for a cubic equation of degree n=3,f(x) = x^3+a_2x^2+a_1x+a_0such that substituting x=x(y) yields a new equationf'(y)=y^3+a'_2y^2+a'_1y+a'_0such that a'_1=0, a'_2=0, or both. More generally, it may be defined conveniently by means of field theory, as the transformation on minimal polynomials implied by a different choice of primitive element. This is the most general transformation of an irreducible polynomial that takes a root to some rational function applied to that root. Definition For a generic n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erland Samuel Bring
Erland Samuel Bring (19 August 1736 – 20 May 1798) was a Swedish mathematician. Bring studied at Lund University between 1750 and 1757. In 1762 he obtained a position of a reader in history and was promoted to professor in 1779. At Lund he wrote eight volumes of mathematical work in the fields of algebra, geometry, analysis and astronomy, including ''Meletemata quaedam mathematica circa transformationem aequationum algebraicarum'' (1786). This work describes Bring's contribution to the algebraic solution of equations. Bring had developed an important transformation to simplify a quintic equation to the form x^5 + px + q = 0 (see Bring radical). In 1832–35 the same transformation was independently derived by George Jerrard. However, whereas Jerrard knew from the past work by Paolo Ruffini and Niels Henrik Abel that a general quintic equation can not be solved, this fact was not known to Bring, putting him in a disadvantage.J J O'Connor and E F RobertsoErland Samuel Bring/ref> ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bring–Jerrard Normal Form
In algebra, the Bring radical or ultraradical of a real number ''a'' is the unique real root of the polynomial : x^5 + x + a. The Bring radical of a complex number ''a'' is either any of the five roots of the above polynomial (it is thus multi-valued), or a specific root, which is usually chosen such that the Bring radical is real-valued for real ''a'' and is an analytic function in a neighborhood of the real line. Because of the existence of four branch points, the Bring radical cannot be defined as a function that is continuous over the whole complex plane, and its domain of continuity must exclude four branch cuts. George Jerrard showed that some quintic equations can be solved in closed form using radicals and Bring radicals, which had been introduced by Erland Bring. In this article, the Bring radical of ''a'' is denoted \operatorname(a). For real argument, it is odd, monotonically decreasing, and unbounded, with asymptotic behavior \mathrm(a) \sim -a^ for large ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
English Mathematicians
English usually refers to: * English language * English people English may also refer to: Peoples, culture, and language * ''English'', an adjective for something of, from, or related to England ** English national identity, an identity and common culture ** English language in England, a variant of the English language spoken in England * English languages (other) * English studies, the study of English language and literature * ''English'', an Amish term for non-Amish, regardless of ethnicity Individuals * English (surname), a list of notable people with the surname ''English'' * People with the given name ** English McConnell (1882–1928), Irish footballer ** English Fisher (1928–2011), American boxing coach ** English Gardner (b. 1992), American track and field sprinter Places United States * English, Indiana, a town * English, Kentucky, an unincorporated community * English, Brazoria County, Texas, an unincorporated community * Engli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1804 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] |
1863 Deaths
Events January–March * January 1 – Abraham Lincoln signs the Emancipation Proclamation during the third year of the American Civil War, making the abolition of slavery in the Confederate states an official war goal. It proclaims the freedom of 3.1 million of the nation's four million slaves and immediately frees 50,000 of them, with the rest freed as Union armies advance. * January 2 – Lucius Tar Painting Master Company (''Teerfarbenfabrik Meirter Lucius''), predecessor of Hoechst, as a worldwide chemical manufacturing brand, founded in a suburb of Frankfurt am Main, Germany. * January 4 – The New Apostolic Church, a Christian and chiliastic church, is established in Hamburg, Germany. * January 7 – In the Swiss canton of Ticino, the village of Bedretto is partly destroyed and 29 killed, by an avalanche. * January 8 ** The Yorkshire County Cricket Club is founded at the Adelphi Hotel, in Sheffield, England. ** American Civil War &ndash ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
