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Gudermann
Christoph Gudermann (25 March 1798 – 25 September 1852) was a German mathematician noted for introducing the Gudermannian function and the concept of uniform convergence, and for being the teacher of Karl Weierstrass, who was greatly influenced by Gudermann's course on elliptic functions in 1839–1840, the first such course to be taught in any institute. Biography Gudermann was born in Vienenburg. He was the son of a school teacher and became a teacher himself after studying at the University of Göttingen, where his academic advisor was Karl Friedrich Gauss. He began his teaching career in Kleve and then transferred to a school in Münster. Gudermann introduced the concept of uniform convergence in an 1838 paper on elliptic functions, but only observed it informally, neither formalizing it nor using it in his proofs. Instead, Weierstrass elaborated and applied uniform convergence. His researches into spherical geometry 300px, A sphere with a spherical triangl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gudermannian Function
In mathematics, the Gudermannian function relates a hyperbolic angle measure \psi to a circular angle measure \phi called the ''gudermannian'' of \psi and denoted \operatorname\psi. The Gudermannian function reveals a close relationship between the circular functions and hyperbolic functions. It was introduced in the 1760s by Johann Heinrich Lambert, and later named for Christoph Gudermann who also described the relationship between circular and hyperbolic functions in 1830. The gudermannian is sometimes called the hyperbolic amplitude as a limiting case of the Jacobi elliptic amplitude \operatorname(\psi, m) when parameter m=1. The real Gudermannian function is typically defined for -\infty < \psi < \infty to be the integral of the hyperbolic secant The real inverse Gudermannian function can be defined for as the [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karl Weierstrass
Karl Theodor Wilhelm Weierstrass (german: link=no, Weierstraß ; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis". Despite leaving university without a degree, he studied mathematics and trained as a school teacher, eventually teaching mathematics, physics, botany and gymnastics. He later received an honorary doctorate and became professor of mathematics in Berlin. Among many other contributions, Weierstrass formalized the definition of the continuity of a function, proved the intermediate value theorem and the Bolzano–Weierstrass theorem, and used the latter to study the properties of continuous functions on closed bounded intervals. Biography Weierstrass was born into a Roman Catholic family in Ostenfelde, a village near Ennigerloh, in the Province of Westphalia. Weierstrass was the son of Wilhelm Weierstrass, a government official, and Theodora Vonderforst both of whom were catholic Rhinelanders. His int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Convergence
In the mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence. A sequence of functions (f_n) converges uniformly to a limiting function f on a set E if, given any arbitrarily small positive number \epsilon, a number N can be found such that each of the functions f_N, f_,f_,\ldots differs from f by no more than \epsilon ''at every point'' x ''in'' E. Described in an informal way, if f_n converges to f uniformly, then the rate at which f_n(x) approaches f(x) is "uniform" throughout its domain in the following sense: in order to guarantee that f_n(x) falls within a certain distance \epsilon of f(x), we do not need to know the value of x\in E in question — there can be found a single value of N=N(\epsilon) ''independent of x'', such that choosing n\geq N will ensure that f_n(x) is within \epsilon of f(x) ''for all x\in E''. In contrast, pointwise convergence of f_n to f merely guarantees that for any x\in E given ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Convergence
In the mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence. A sequence of functions (f_n) converges uniformly to a limiting function f on a set E if, given any arbitrarily small positive number \epsilon, a number N can be found such that each of the functions f_N, f_,f_,\ldots differs from f by no more than \epsilon ''at every point'' x ''in'' E. Described in an informal way, if f_n converges to f uniformly, then the rate at which f_n(x) approaches f(x) is "uniform" throughout its domain in the following sense: in order to guarantee that f_n(x) falls within a certain distance \epsilon of f(x), we do not need to know the value of x\in E in question — there can be found a single value of N=N(\epsilon) ''independent of x'', such that choosing n\geq N will ensure that f_n(x) is within \epsilon of f(x) ''for all x\in E''. In contrast, pointwise convergence of f_n to f merely guarantees that for any x\in E given ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl Gauss
Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes referred to as the ''Princeps mathematicorum'' () and "the greatest mathematician since antiquity", Gauss had an exceptional influence in many fields of mathematics and science, and he is ranked among history's most influential mathematicians. Also available at Retrieved 23 February 2014. Comprehensive biographical article. Biography Early years Johann Carl Friedrich Gauss was born on 30 April 1777 in Brunswick (Braunschweig), in the Duchy of Brunswick-Wolfenbüttel (now part of Lower Saxony, Germany), to poor, working-class parents. His mother was illiterate and never recorded the date of his birth, remembering only that he had been born on a Wednesday, eight days before the Feast of the Ascension (which occurs 39 days after Easter). Gau ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1798 Births
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 &ndas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karl Friedrich Gauss
Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes referred to as the ''Princeps mathematicorum'' () and "the greatest mathematician since antiquity", Gauss had an exceptional influence in many fields of mathematics and science, and he is ranked among history's most influential mathematicians. Also available at Retrieved 23 February 2014. Comprehensive biographical article. Biography Early years Johann Carl Friedrich Gauss was born on 30 April 1777 in Brunswick (Braunschweig), in the Duchy of Brunswick-Wolfenbüttel (now part of Lower Saxony, Germany), to poor, working-class parents. His mother was illiterate and never recorded the date of his birth, remembering only that he had been born on a Wednesday, eight days before the Feast of the Ascension (which occurs 39 days after Easter). Ga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vienenburg
Vienenburg is a borough of Goslar, capital of the Goslar (district), Goslar district, in Lower Saxony, Germany. The former independent municipality was incorporated in Goslar on 1 January 2014. Geography It is situated in the north of the Harz mountain range and east of the Harly Forest on the Oker River near its confluence with the Radau, about northeast of the Goslar town centre. Neighbouring municipalities are Bad Harzburg in the south and Schladen-Werla in the north. The former township consisted of Vienenburg proper and the surrounding villages Immenrode, Lengde, Weddingen, Lochtum and Wiedelah, all incorporated in 1972. Situated in a mainly agricultural area, it is known for the Harzer cheese, although the production was transferred to Saxony in 2004. History The Harlyberg hill (256m/840 ft) north of the town was the site of a castle built in 1203 by the House of Welf, Welf king Otto IV, Holy Roman Emperor, Otto IV of Germany to threaten the trade route to History of G ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Göttingen
The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded in 1734 by George II, King of Great Britain and Elector of Hanover, and starting classes in 1737, the Georgia Augusta was conceived to promote the ideals of the Enlightenment. It is the oldest university in the state of Lower Saxony and the largest in student enrollment, which stands at around 31,600. Home to many noted figures, it represents one of Germany's historic and traditional institutions. According to an official exhibition held by the University of Göttingen in 2002, 44 Nobel Prize winners had been affiliated with the University of Göttingen as alumni, faculty members or researchers by that year alone. The University of Göttingen was previously supported by the German Universities Excellence Initiative, holds memberships ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Province Of Westphalia
The Province of Westphalia () was a province of the Kingdom of Prussia and the Free State of Prussia from 1815 to 1946. In turn, Prussia was the largest component state of the German Empire from 1871 to 1918, of the Weimar Republic and from 1918 to 1933, and of Nazi Germany from 1933 until 1945. The province was formed and awarded to Prussia at the Congress of Vienna in 1815, in the aftermath of the Napoleonic Wars. It combined some territories that had previously belonged to Prussia with a range of other territories that had previously been independent principalities. The population included a large population of Catholics, a significant development for Prussia, which had hitherto been almost entirely Protestant. The politics of the province in the early nineteenth century saw local expectations of Prussian reforms, increased self-government, and a constitution largely stymied. The Revolutions of 1848 led to an effervescence of political activity in the province, but the failur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
People From Goslar (district)
A person ( : people) is a being that has certain capacities or attributes such as reason, morality, consciousness or self-consciousness, and being a part of a culturally established form of social relations such as kinship, ownership of property, or legal responsibility. The defining features of personhood and, consequently, what makes a person count as a person, differ widely among cultures and contexts. In addition to the question of personhood, of what makes a being count as a person to begin with, there are further questions about personal identity and self: both about what makes any particular person that particular person instead of another, and about what makes a person at one time the same person as they were or will be at another time despite any intervening changes. The plural form " people" is often used to refer to an entire nation or ethnic group (as in "a people"), and this was the original meaning of the word; it subsequently acquired its use as a plural f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1852 Deaths
Year 185 ( CLXXXV) was a common year starting on Friday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Lascivius and Atilius (or, less frequently, year 938 ''Ab urbe condita''). The denomination 185 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * Nobles of Britain demand that Emperor Commodus rescind all power given to Tigidius Perennis, who is eventually executed. * Publius Helvius Pertinax is made governor of Britain and quells a mutiny of the British Roman legions who wanted him to become emperor. The disgruntled usurpers go on to attempt to assassinate the governor. * Tigidius Perennis, his family and many others are executed for conspiring against Commodus. * Commodus drains Rome's treasury to put on gladiatorial spectacles and confiscates property to sup ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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