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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] |
Sweden
Sweden, formally the Kingdom of Sweden,The United Nations Group of Experts on Geographical Names states that the country's formal name is the Kingdom of SwedenUNGEGN World Geographical Names, Sweden./ref> is a Nordic country located on the Scandinavian Peninsula in Northern Europe. It borders Norway to the west and north, Finland to the east, and is connected to Denmark in the southwest by a bridgetunnel across the Öresund. At , Sweden is the largest Nordic country, the third-largest country in the European Union, and the fifth-largest country in Europe. The capital and largest city is Stockholm. Sweden has a total population of 10.5 million, and a low population density of , with around 87% of Swedes residing in urban areas in the central and southern half of the country. Sweden has a nature dominated by forests and a large amount of lakes, including some of the largest in Europe. Many long rivers run from the Scandes range through the landscape, primarily ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lund University
, motto = Ad utrumque , mottoeng = Prepared for both , established = , type = Public research university , budget = SEK 9 billion Facts and figures Lund University web site. , head_label = , head = Erik Renström , academic_staff = 4,780 (2022) (academic staff, researchers and employed research students) , administrative_staff = 2,890 (2022) , students = 46 000 (29 000 full-time e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bring's Curve
In mathematics, Bring's curve (also called Bring's surface) is the curve given by the equations :v+w+x+y+z=v^2+w^2+x^2+y^2+z^2=v^3+w^3+x^3+y^3+z^3=0. It was named by after Erland Samuel Bring who studied a similar construction in 1786 in a Promotionschrift submitted to the University of Lund. The automorphism group of the curve is the symmetric group ''S''5 of order 120, given by permutations of the 5 coordinates. This is the largest possible automorphism group of a genus 4 complex curve. The curve can be realized as a triple cover of the sphere branched in 12 points, and is the Riemann surface associated to the small stellated dodecahedron. It has genus 4. The full group of symmetries (including reflections) is the direct product S_\times\mathbb_, which has order 240. Fundamental domain and systole Bring's curve can be obtained as a Riemann surface by associating sides of a hyperbolic icosagon (see fundamental polygon). The identification pattern is given in the adjoining ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bring Radical
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] |
Algebraic Solution
A solution in radicals or algebraic solution is a closed-form expression, and more specifically a closed-form algebraic expression, that is the solution of a polynomial equation, and relies only on addition, subtraction, multiplication, division, raising to integer powers, and the extraction of th roots (square roots, cube roots, and other integer roots). A well-known example is the solution :x=\frac of the quadratic equation :ax^2 + bx + c =0. There exist more complicated algebraic solutions for cubic equations and quartic equations. The Abel–Ruffini theorem,Jacobson, Nathan (2009), Basic Algebra 1 (2nd ed.), Dover, and, more generally Galois theory, state that some quintic equations, such as :x^5-x+1=0, do not have any algebraic solution. The same is true for every higher degree. However, for any degree there are some polynomial equations that have algebraic solutions; for example, the equation x^ = 2 can be solved as x=\pm\sqrt 0. The eight other solutions are nonreal ... [...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] |
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] |
Paolo Ruffini (mathematician)
Paolo Ruffini (Valentano, 22 September 1765 – Modena, 10 May 1822) was an Italian mathematician and philosopher. Education and Career By 1788 he had earned university degrees in philosophy, medicine/surgery and mathematics. His works include developments in algebra: * an incomplete proof (Abel–Ruffini theorem) that quintic (and higher-order) equations cannot be solved by radicals (1799), * Ruffini's rule which is a quick method for polynomial division, * contributions to group theory. He also wrote on probability and the quadrature of the circle. He was a professor of mathematics at the University of Modena and a medical doctor including scientific work on typhus. Group theory In 1799 Ruffini marked a major improvement for group theory, developing Joseph Louis Lagrange's work on permutation theory ("Réflexions sur la théorie algébrique des équations", 1770–1771). Lagrange's work was largely ignored until Ruffini established strong connections between permutat ... [...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] |
1736 Births
Events January–March * January 12 – George Hamilton, 1st Earl of Orkney, becomes the first Field Marshal of Great Britain. * January 23 – The Civil Code of 1734 is passed in Sweden. * January 26 – Stanislaus I of Poland abdicates his throne. * February 12 – Francis I, Holy Roman Emperor marries Maria Theresa of Austria, ruler of the Habsburg Empire. * March 8 – Nader Shah, founder of the Afsharid dynasty, is crowned Shah of Iran on a date selected by court astrologers. * March 31 – Bellevue Hospital is founded in New York. April–June * April 14 – The Porteous Riots erupt in Edinburgh (Scotland), after the execution of smuggler Andrew Wilson, when town guard Captain John Porteous orders his men to fire at the crowd. Porteous is arrested later. * April 14 – German adventurer Theodor Stephan Freiherr von Neuhoff is crowned King Theodore of Corsica, 25 days after his arrival on Corsica on March 20. His reign ends on No ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1798 Deaths
Events January–June * January – Eli Whitney contracts with the U.S. federal government for 10,000 muskets, which he produces with interchangeable parts. * January 4 – Constantine Hangerli enters Bucharest, as Prince of Wallachia. * January 22 – A coup d'état is staged in the Netherlands ( Batavian Republic). Unitarian Democrat Pieter Vreede ends the power of the parliament (with a conservative-moderate majority). * February 10 – The Pope is taken captive, and the Papacy is removed from power, by French General Louis-Alexandre Berthier. * February 15 – U.S. Representative Roger Griswold (Fed-CT) beats Congressman Matthew Lyon (Dem-Rep-VT) with a cane after the House declines to censure Lyon earlier spitting in Griswold's face; the House declines to discipline either man.''Harper's Encyclopaedia of United States History from 458 A. D. to 1909'', ed. by Benson John Lossing and, Woodrow Wilson (Harper & Brothers, 1910) p171 * March &nd ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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