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riemann

GEORG FRIEDRICH BERNHARD RIEMANN (1826-1866), German mathematician, was born on the 17th of September [[Xxiii.

00His father, Friedrich Bernhard Riemann, came from Mecklenburg, had served in the war of freedom, and had finally settled as pastor in Quickborn.

00Here with his five brothers and sisters Riemann spent his boyhood and received, chiefly from his father, the elements of his education.

00The director, Schmalfuss, encouraged him in his mathematical studies by lending him books (among them Leonhard Euler's works and Adrien Marie Legendre's Theory of Numbers), which Riemann read, mastered and returned within a few days.

00In 1846 Riemann entered himself as a student of philology and theology in the university of GÃ¶ttingen.

00This double cultivation of his scientific powers had the happiest effect on his subsequent work; for the greatest achievements of Riemann were effected by the application in pure mathematics generally of a method (theory of potential) which had up to this time been used solely in the solution of certain problems that arise in mathematical physics.

00The fundamental method of research which Riemann employed has just been alluded to; the results will be best indicated in his own words: "The methods in use hitherto for treating functions of a complex variable always started from an expression for the function as its definition, whereby its value was given for every value of the argument; by our investigation it has been shown that, in consequence of the general character of a function of a complex variable, in a definition of this sort one part of the determining conditions is a consequence of the rest, and the extent of the determining conditions has been reduced to what is necessary to effect the determination.

00It was fortunate, no doubt, for Riemann that he had the kind advice and encouragement of Dirichlet himself, who was then on a visit at GÃ¶ttingen during the preparation of his essay; but the result was a memoir of such originality and refinement as showed that the pupil was fully the equal of the master.

00In 1855 Gauss died and was succeeded by Dirichlet, who along with others made an effort to obtain Riemann's nomination as extraordinary professor.

00Riemann's health had never been strong.

00The collected works of Riemann were published by H.

00Negative values of n must be interpreted by a streaming motion on a parallel plane at a level slightly different, as on a double Riemann sheet, the stream passing from one sheet to the other across a cut SS' joining the foci S, S'.

00Riemann, Geschichte des Jeverlandes (Jever, 1896).

00Riemann and C. Graux; (in archaeology) A.

00Riemann and S.

00See Riemann, Geschichte der Stadt Kolberg (Kolberg, 1873); Stoewer, Geschichte der Stadt Kolberg (Kolberg, 1897); Schonlein, Geschichte der Belagerungen Kolbergs in den Jahren 1758, 1760, 1761 and 1807 (Kolberg, 1878); and Kempin, Fi hrer durch Bad Kolberg (Kolberg, 1899).

00Ansted, The Ionian Islands in the Year 1863 (London, 1863); Riemann, Recherches archeologiques sur les lies ioniennes (Paris, 1879-1880); J.

00Riemann and H.

009-12 (Athens, 1877); Riemann, "Recherches archeologiques sur les Iles ioniennes" in Bibliotheque des Ecoles francaises d'Athenes et de Rome (Paris, 1879-1880); Gregorovius, Corfu: eine ionische Idylle (Leipzig, 1882); J.

00Riemann, Goethes Romantechnik (1901); R.

00Riemann on the same subject; these are to be found in the Journal of the Ecole Polytechnique from 1813 to 1823, and in the Memoirs de l'academie for 1823.

00Riemann, R.

00Riemann, Recherches archeologiques sur les lies Ioniennes (Paris, 1879-1880); Partsch, Kephallenia and Ithaka (1890); see also CORFU; IONIAN ISLANDS.

00See Riemann, Geschichte der Stadt Greifenberg (1862).

00He was much interested, too, in universal algebra, non-Euclidean geometry and elliptic functions, his papers "Preliminary Sketch of Bi-quaternions" (1873) and "On the Canonical Form and Dissection of a Riemann's Surface" (1877) ranking as classics.

00Riemann, the rational transformation of a plane curve; Luigi Cremona, the rational transformation of a plane; and Chasles, correspondence of points on the same curve, and united points.

00Riemann's results are contained in the memoirs on " Abelian Integrals," &c. (Crelle, t.

00The transformation may be applied to any curve u=o, which is thus rationally transformed into a curve u =o, by a rational transformation such as is considered in Riemann's theory: hence the two curves have the same deficiency.

00In fact, there are areas of mathematics that have been developed by mathematicians on the assumption that the Riemann Hypothesis is true.

00GEORG FRIEDRICH BERNHARD RIEMANN (1826-1866), German mathematician, was born on the 17th of September [[Xxiii.

00His father, Friedrich Bernhard Riemann, came from Mecklenburg, had served in the war of freedom, and had finally settled as pastor in Quickborn.

00Here with his five brothers and sisters Riemann spent his boyhood and received, chiefly from his father, the elements of his education.

00The director, Schmalfuss, encouraged him in his mathematical studies by lending him books (among them Leonhard Euler's works and Adrien Marie Legendre's Theory of Numbers), which Riemann read, mastered and returned within a few days.

00In 1846 Riemann entered himself as a student of philology and theology in the university of GÃƒ¶ttingen.

00This double cultivation of his scientific powers had the happiest effect on his subsequent work; for the greatest achievements of Riemann were effected by the application in pure mathematics generally of a method (theory of potential) which had up to this time been used solely in the solution of certain problems that arise in mathematical physics.

00The fundamental method of research which Riemann employed has just been alluded to; the results will be best indicated in his own words: "The methods in use hitherto for treating functions of a complex variable always started from an expression for the function as its definition, whereby its value was given for every value of the argument; by our investigation it has been shown that, in consequence of the general character of a function of a complex variable, in a definition of this sort one part of the determining conditions is a consequence of the rest, and the extent of the determining conditions has been reduced to what is necessary to effect the determination.

00It was fortunate, no doubt, for Riemann that he had the kind advice and encouragement of Dirichlet himself, who was then on a visit at GÃƒ¶ttingen during the preparation of his essay; but the result was a memoir of such originality and refinement as showed that the pupil was fully the equal of the master.

00In 1855 Gauss died and was succeeded by Dirichlet, who along with others made an effort to obtain Riemann's nomination as extraordinary professor.

00Riemann's health had never been strong.

00The collected works of Riemann were published by H.

00Negative values of n must be interpreted by a streaming motion on a parallel plane at a level slightly different, as on a double Riemann sheet, the stream passing from one sheet to the other across a cut SS' joining the foci S, S'.

00Riemann, Geschichte des Jeverlandes (Jever, 1896).

00Riemann and C. Graux; (in archaeology) A.

00Riemann and S.

00See Riemann, Geschichte der Stadt Kolberg (Kolberg, 1873); Stoewer, Geschichte der Stadt Kolberg (Kolberg, 1897); Schonlein, Geschichte der Belagerungen Kolbergs in den Jahren 1758, 1760, 1761 and 1807 (Kolberg, 1878); and Kempin, Fi hrer durch Bad Kolberg (Kolberg, 1899).

00Ansted, The Ionian Islands in the Year 1863 (London, 1863); Riemann, Recherches archeologiques sur les lies ioniennes (Paris, 1879-1880); J.

00Riemann and H.

009-12 (Athens, 1877); Riemann, "Recherches archeologiques sur les Iles ioniennes" in Bibliotheque des Ecoles francaises d'Athenes et de Rome (Paris, 1879-1880); Gregorovius, Corfu: eine ionische Idylle (Leipzig, 1882); J.

00Riemann, Goethes Romantechnik (1901); R.

00Riemann on the same subject; these are to be found in the Journal of the Ecole Polytechnique from 1813 to 1823, and in the Memoirs de l'academie for 1823.

00Riemann, R.

00Riemann, Recherches archeologiques sur les lies Ioniennes (Paris, 1879-1880); Partsch, Kephallenia and Ithaka (1890); see also CORFU; IONIAN ISLANDS.

00See Riemann, Geschichte der Stadt Greifenberg (1862).

00He was much interested, too, in universal algebra, non-Euclidean geometry and elliptic functions, his papers "Preliminary Sketch of Bi-quaternions" (1873) and "On the Canonical Form and Dissection of a Riemann's Surface" (1877) ranking as classics.

00Riemann, the rational transformation of a plane curve; Luigi Cremona, the rational transformation of a plane; and Chasles, correspondence of points on the same curve, and united points.

00Riemann's results are contained in the memoirs on " Abelian Integrals," &c. (Crelle, t.

00The transformation may be applied to any curve u=o, which is thus rationally transformed into a curve u =o, by a rational transformation such as is considered in Riemann's theory: hence the two curves have the same deficiency.

00

The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.