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	Riemann, Georg Friedrich Bernhard - Hutchinson encyclopedia article about Riemann, Georg Friedrich Bernhard
		Georg Riemann showed that in spherical geometry (a form of non-Euclidean geometry), although a parallelogram may have two opposite angles of 90°, it does not necessarily follow that the other two angles are also 90°.
		Riemann took into account the possible interaction between space and the bodies placed in it; until then, space had been treated as an entity in itself, and this new point of view was to become a central concept of 20th-century physics.
		Riemann's paper on the fundamental postulates of Euclidean geometry, written in the early 1850s but not published until 1867, was to open up the whole field of non-Euclidean geometry and become a classic in the history of mathematics.
	encyclopedia.farlex.com /Riemann,%20Georg%20Friedrich%20Bernhard (364 words)

	Bernhard Riemann (Site not responding. Last check: 2007-10-29)
		Georg Friedrich Bernhard Riemann (September 17, 1826 - July 20, 1866) (pronounced REE mahn) was a German mathematician who made important contributions to analysis and differential geometry, some of them paving the way for the later development of general relativity.
		His name is connected with the Riemann zeta function, the Riemann hypothesis, the Riemann integral, the Riemann lemma, Riemannian manifolds, the Riemann mapping theorem, Riemann-Hilbert problems, Riemann surfaces, the Riemann-Roch theorem, the Riemann sphere, and the Cauchy-Riemann equations.
		Riemann held his first lectures in 1854, which not only founded the field of Riemannian geometry but set the stage for Einstein's general relativity.
	www.tocatch.info /en/Bernhard_Riemann.htm (332 words)

	Riemann
		Riemann moved from Göttingen to Berlin University in the spring of 1847 to study under Steiner, Jacobi, Dirichlet and Eisenstein.
		In 1859 Dirichlet died and Riemann was appointed to the chair of mathematics at Göttingen on 30 July.
		Riemann considered a very different question to the one Euler had considered, for he looked at the zeta function as a complex function rather than a real one.
	www-gap.dcs.st-and.ac.uk /~history/Mathematicians/Riemann.html (2606 words)

	Bernhard Riemann - Wikipedija, prosta enciklopedija
		Bernhard je bil drugi sin od šestih luteranskega pastorja Friedricha Bernharda Riemanna.
		Navkljub siromaštvu je bilo družinsko življenje srečno. Riemann je za vedno ohranil svoje najtoplejše spomine in domotožje.
		Riemann se je ukvarjal tudi s funkcijsko teorijo, diferencialnimi enačbami in z osnovami geometrije.
	sl.wikipedia.org /wiki/Bernhard_Riemann (819 words)

	Bernhard Riemann - Wikipedia
		Georg Friedrich Bernhard Riemann (17 de septiembre de 1826 - 20 de junio de 1866) fue un matemático alemán que realizó contribuciones muy importantes en análisis y geometría diferencial, algunas de ellas que allanaron el camino para el desarrollo más avanzado de la relatividad general.
		En 1840 Bernhard fue a Hannover a vivir con su abuela y a visitar el Lyceum.
		Riemann dio sus primeras conferencias en 1854, en las cuales fundó el campo de la geometría de Riemann.
	es.wikipedia.org /wiki/Bernhard_Riemann (499 words)

	GEORG FRIEDRICH BERNHARD RIEMANN - LoveToKnow Article on GEORG FRIEDRICH BERNHARD RIEMANN (Site not responding. Last check: 2007-10-29)
		His father, Friedrich Bernhard Riemann, came from Mecklenburg, had served in the war of freedom, and had finally settled as pastor in Quickborn.
		He showed at an early age wellmarked mathematical powers, and his progress was so rapid in arithmetic and geometry that he was soon beyond the guidance not only of his father but of schoolmaster Schulz, who assisted in the mathematical department of his training.
		In 1846 Riemann entered himself as a student of philology and theology in the university of Gottingen.
	9.1911encyclopedia.org /R/RI/RIEMANN_GEORG_FRIEDRICH_BERNHARD.htm (982 words)

	Encyclopedia: Bernhard Riemann (Site not responding. Last check: 2007-10-29)
		Georg Friedrich Bernhard Riemann (September 17, 1826 - July 20, 1866) was a German mathematician who made important contributions to analysis and differential geometry, some of them paving the way for the later development of general relativity.
		His name is connected with the Riemann zeta function, the Riemann integral, the Riemann lemma, Riemannian manifolds, the Riemann mapping theorem, Riemann-Hilbert problems, and Riemann surfaces.
		In mathematics, the Riemann zeta function, named after Bernhard Riemann (pronounced REE mahn), is a function of paramount importance in number theory, because of its relation to the distribution of prime numbers.
	www.nationmaster.com /encyclopedia/Bernhard-Riemann (1355 words)

	Johanneum Lüneburg Bernhard Riemann Youth and time as a pupil at the Johanneum
		In one of these small villages, Breselenz on the edge of the range of hills Drawehn, Bernhard Riemann was born on the 17th of September 1826 as the second of the vicar's six children.
		Bernhard Georg Friedrich Riemann, born on the 17th of September 1826 in Breselenz, the Quickborn/Dannenberg's vicar Riemann's son, Lutheran of denomination, visited the Hannover Lyzeum for two years, since Easter 1842 the Gymnasium Johanneum, the first class since Easter 1844.
		Bernhard Riemann did now go to Göttingen to read theoology for one semester, as his father wanted him to, but was then able to -probably by referring to the comment in his report- give his undivided attention to mathematics.
	www.fh-lueneburg.de /u1/gym03/englpage/chronik/riemann/jugend/jugend.htm (2771 words)

	Riemann, (Georg Friedrich) Bernhard (1826-1866)
		A German mathematician who was the first person to provide a thorough treatment of non-Euclidean geometry and to see how it might be applied in physics; he thus helped pave the way for the general theory of relativity.
		Among several profound aspects of mathematics now named after him are the Riemann hypothesis and the related Riemann zeta function.
		But even as a child Riemann had shown an tremendous aptitude for mathematics and, in 1847, he persuaded his father to let him go to Berlin to learn mathematics from the likes of Karl Jacobi, Peter Dirichlet, and Jakob Steiner.
	www.daviddarling.info /encyclopedia/R/Riemann.html (206 words)

	Biography of Riemann
		Georg Friedrich Bernhard Riemann was born on September 17, 1826 in Breselenz, Germany to Georg Friedrich Bernhard Riemann and Charlotte Ebell.
		Riemann submitted his thesis in 1851 to Gauss, an impressed Gauss said that Riemann possessed a "Gloriously fertile originality." Thanks to Gauss's recommendation Riemann was appointed to a position at Göttingen.
		Georg Friedrich Bernhard Riemann began his career by working on the theory of functions, but he is best remembered for his development of non-Euclidean geometry.
	www.andrews.edu /~calkins/math/biograph/bioriema.htm (912 words)

	Riemann, Georg Friedrich Bernhard Riemann - Famous mathematicians pictures, posters, gifts items, note cards, greeting ...
		Georg Friedrich Bernhard Riemann was a profoundly original thinker.
		Riemann surfaces, an instance of one overlaying the lower right of Riemann's portrait, are a Riemann invention arising from multi-valued functions -- a not uncommon conundrum in mathematics.
		Riemann examined the properties of the Zeta function, (inscribed at the lower left of Riemann's portrait).
	www.mathematicianspictures.com /Mathematicians/Riemann.htm (396 words)

	Georg Friedrich Bernhard Riemann (Site not responding. Last check: 2007-10-29)
		Georg Friedrich Bernhard Riemann (September 17, 1826 - June 20, 1866) was a German mathematician who made important contributions to analysis and differentialgeometry, some of them paving the way for the later development of general relativity.
		His name is connected with the zeta function, the Riemann integral,the Riemann lemma, Riemannian manifolds and Riemann surfaces.
		Riemann held his first lectures in 1854, which not only founded the field of Riemannian geometry but set the stage for Einstein 's General relativity.
	www.therfcc.org /georg-friedrich-bernhard-riemann-8571.html (257 words)

	Georg Friedrich Bernhard Riemann (Site not responding. Last check: 2007-10-29)
		Bernhard Riemann's father acted as teacher to his children, and he taught Bernhard until he was 10 years old, when he started studying at Hanover.
		In 1846, Riemann enrolled at the University of Göttingen.
		In 1859, Dirichlet died and Riemann was appointed to the chair of mathematics at Göttingen.
	www.stetson.edu /~efriedma/periodictable/html/Rn.html (659 words)

	GEORG FRIEDRICH BERNHARD RIEMANN (Site not responding. Last check: 2007-10-29)
		Georg was accepted into the third class at the Lyceum in Hannover in 1840 at the age of fourteen.
		Riemann left the Lyceum in Hannover in the spring of 1846 and enrolled at the University of Gottingen.
		Georg was enrolled in some mathematics courses at Gottingen, and soon asked his father if he could change majors from theology to philosphy so that he could focus more on mathematics.
	www.chester.k12.sc.us /lewisvillehigh/honors/riemann.htm (823 words)

	Georg Friedrich Bernhard Riemann (Site not responding. Last check: 2007-10-29)
		Georg Friedrich Bernhard Riemann was born in Breselenz, Germany, on September 17th 1826.
		He was the second of 6 children of a Protestant minister and received his elementary education from his father, later assisted by a local teacher.
		Riemann could not be made an extraordinary professor and so he got a stipend of the government.
	math.berkeley.edu /~robin/Riemann (634 words)

	Riemann, Bernhard on Encyclopedia.com (Site not responding. Last check: 2007-10-29)
		He laid the foundations of a non-Euclidean system of geometry (Riemannian geometry) representing elliptic space and generalized to n dimensions the work of C. Gauss in differential geometry, thus creating the basic tools for the mathematical expression of the general theory of relativity.
		Riemann also was interested in mathematical physics, particularly optics and electromagnetic theory.
		The so called “Riemann hypothesis,” concerning the instances in which the function's value is zero, is one of the great unsolved problems in mathematics.
	www.encyclopedia.com /html/R/Riemann.asp (359 words)

	Johanneum Lüneburg Bernhard Riemann Jugend und Schulzeit am Johanneum
		Zu Riemanns Jugendzeit in der Elbmarsch und in Lüneburg haben A. und D. Laugwitz [Lau] einen bebilderten Artikel auf Englisch verfasst.
		Riemann sollte nach den Vorstellungen seines Vaters Pastor werden und besuchte daher nicht diese Klassen.
		Bernhard Riemann ging nun nach Göttingen und studierte ein Semester Theologie, wie der Vater es wollte, konnte aber dann -sicher unter Verweis auf diese Abiturbemerkung- sich ganz der Mathematik widmen.
	www.fh-lueneburg.de /u1/gym03/homepage/chronik/riemann/jugend/jugend.htm (2598 words)

	Bernhard Riemann (Site not responding. Last check: 2007-10-29)
		His father Friedrich Bernhard Riemann was pastor in Breselenz.
		In 1840 Bernhard went to Hanover to live with his grandmother and the Lyceum.
		Bernhard Riemann, 1826-1866: Wendepunkte in der Auffassung der Mathematik (Vita mathematica)
	www.freeglossary.com /Bernhard_Riemann (500 words)

	GEORG FRIEDRICH BERNHARD RIEMANN (Site not responding. Last check: 2007-10-29)
		Nejznámějším příkladem takové zakřivené plochy je povrch koule.) V neeuklidovské geometrii měla přijít ještě jedna revoluce - a tu provedl právě Bernhard Riemann.
		Tam, kde Gauss, Lobačevskij a Bolyai položili základy, Riemann vystavěl celou budovu.
		Riemann šel pěšky, ale cesta byla vyčerpávající a na kraji Itálie v červenci 1866 zemřel.
	vedci.wz.cz /Osobnosti/Riemann_G_F_B.htm (486 words)

	Bernhard Riemann - Wikipedia, den fria encyklopedin
		Georg Friedrich Bernhard Riemann föddes i Breselenz, Tyskland den 17 september 1826 och dog den 20 juni 1866 i Italien.
		1846 började Riemann studera teologi och filosofi vid universitetet i Göttingen där han närvarade vid Gauss föreläsningar om minsta-kvadrat-metoden varvid hans far sedan tillät honom avbryta sina teologistudier 1847 och börja studera matematik.
		1854 höll Riemann sina första föreläsningar (Habilitationsvortrag) som lade grunden till Riemanngeometri och möjliggjorde Einsteins relativitetsteori.
	sv.wikipedia.org /wiki/Bernhard_Riemann (115 words)

	Georg Friedrich Bernhard Riemann (Site not responding. Last check: 2007-10-29)
		Riemann did a lot of work in the theory of complex functions in his PhD thesis.
		So he derived the Cauchy-Riemann equations ([Werke, p.6]) and the Riemann mapping theorem and developed the idea of a Riemann surface and multiple planes.
		He also constructed the Riemann integral and found a necessary and a sufficient condition for a function to be integrable.
	math.berkeley.edu /~robin/Riemann/work.html (129 words)

	Bernhard Riemann -- Encyclopædia Britannica
		in full Georg Friedrich Bernhard Riemann German mathematician whose profound and novel approaches to the study of geometry laid the mathematical foundation for Albert Einstein's theory of relativity.
		The real significance of Lobachevsky's geometry was not fully understood and appreciated until the work of the great German mathematician Bernhard Riemann on the foundations of geometry (1868) and the proof of the consistency of non-Euclidean geometry by his compatriot Felix Klein in 1871.
		German journalist and writer Bernhard Kellermann is best known for his novel Der Tunnel (The Tunnel), a sensational utopian work about an attempt to build a transatlantic tunnel.
	www.britannica.com /eb/article-9063646 (769 words)

	Rieman - Biography of Bernhard Riemann (1826-1866).
		Riemann Hypothesis -- from MathWorld Riemann Hypothesis -- from MathWorld First published by Riemann (1859), the Riemann hypothesis states that the nontrivial Riemann zeta function zeros, i.
		Riemann Zeta Function -- from MathWorld Riemann Zeta Function -- from MathWorld The Riemann zeta function is an extremely important special function of mathematics and physics that arises in definite integration and is intimately related with.
		The Riemann Hypothesis is currently the most famous unsolved problem in mathematics I did some playing around with the Riemann Hypothesis, and I'm convinced it is true.
	www.destarter.com /Riemann/Rieman.html (546 words)

	Biografía de Georg Friedrich Bernhard Riemann (Site not responding. Last check: 2007-10-29)
		Riemann se trasladó de Gottingen en Berlín el año 1846 para estudiar bajo la enseñanza de Jacobi, Dirichlet y Eisenstein.
		Los escritos de Riemann de 1854 llegaron a ser un clásico en las matemáticas y estos resultados fueron incorporados dentro de la teoría de la relatividad y gravitación de Einstein.
		Las ideas de Riemann concernientes a la geometría del espacio tuvo un profundo efecto en el desarrollo de la teoría física moderna y proveía los conceptos y métodos usados después en la Teoría de la Relatividad.
	www.astrocosmo.cl /biografi/b-b_riemann.htm (248 words)

	Bernhard Riemann
		Georg Friedrich Bernhard Riemann wurde 1826 bei Hannover geboren.
		Diese berühmte Vermutung findet sich in seinem Werk 'Über die Anzahl der Primzahlen unter einer gegebenen Grösse' das Riemann 1849 als Dreiundzwanzigjähriger veröffentlichte.
		Riemann zeigte auf, dass es in gleicher Weise, wie es verschiedene Arten von Kurven und Flächen gibt, auch verschiedene Arten von dreidimensionalen Räumen gibt.
	www.mathematik.ch /mathematiker/riemann.php (216 words)

	Georg Friedrich Bernhard Riemann Biography / Biography of Georg Friedrich Bernhard Riemann 1800 To 1899: Mathematics ...
		Georg Friedrich Bernhard Riemann Biography / Biography of Georg Friedrich Bernhard Riemann 1800 To 1899: Mathematics Biography
		Georg Friedrich Bernhard Riemann was a brilliant German mathematician who recognized the application of his work in non-Euclidean geometry to physics, including the shape of space itself.
		Riemann was born on September 17, 1826, in Breselenz, Germany, the second child of a Lutheran pastor.
	www.bookrags.com /biography-georg-friedrich-bernhard-riemann-scit-05123 (246 words)

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