Riemann sentence example
- His father, Friedrich Bernhard Riemann, came from Mecklenburg, had served in the war of freedom, and had finally settled as pastor in Quickborn.
- Here with his five brothers and sisters Riemann spent his boyhood and received, chiefly from his father, the elements of his education.
- The 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.
- In 1846 Riemann entered himself as a student of philology and theology in the university of GÃ¶ttingen.
- This 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.Advertisement
- The 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.
- In 1855 Gauss died and was succeeded by Dirichlet, who along with others made an effort to obtain Riemann's nomination as extraordinary professor.
- Riemann's health had never been strong.
- Negative 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'.
- Riemann, Geschichte des Jeverlandes (Jever, 1896).Advertisement
- See 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).
- Riemann 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.
- Riemann, Recherches archeologiques sur les lies Ioniennes (Paris, 1879-1880); Partsch, Kephallenia and Ithaka (1890); see also CORFU; IONIAN ISLANDS.
- He 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.
- The 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.Advertisement
- In fact, there are areas of mathematics that have been developed by mathematicians on the assumption that the Riemann Hypothesis is true.
- In 1846 Riemann entered himself as a student of philology and theology in the university of GÃƒ¶ttingen.