Gaston Darboux

This article is about the mathematician Gaston Darboux . For the Art Nouveau artist of almost the same name , see also Gaston Darbour .

Gaston Darboux

Jean Gaston Darboux , called Gaston Darboux , (born August 14, 1842 in Nîmes / Languedoc , † February 23, 1917 in Paris ) was a French mathematician .

Life

Darboux attended school in Nimes and the Lyceum in Montpellier , studied from 1861 at the École polytechnique and then at the École normal supérieure in Paris, where he received his doctorate under Michel Chasles in 1866 (Sur les surfaces orthogonales). He was one of the best students to ever attend these elite schools and it came as a surprise to many that he chose mathematics. In 1873 Darboux became professor at the Sorbonne and assisted Joseph Liouville .

Darboux contributed significantly to the development of differential geometry of his time and wrote a standard three-volume work on it. He applied the methods of analysis to curves and surfaces ( Darboux sums ). His Darboux integral provided a new way of looking at the Riemann integral . He also contributed to the theory of analytical functions .

In differential geometry, the Darboux vector describes the angular velocity of the accompanying tripod of a space curve. It is calculated in curves as follows: . The scalars that appear in this formula mean twist (torsion, ) and curvature ( ), and the (unit) vectors mean tangent (T) and binormal (B) (see Frenet's formulas ). The curvature indicates the angular velocity around B and the torson around T. The following applies: and analogously for T and N (the normal vector). ${\displaystyle {\boldsymbol {\omega }}=\tau \mathbf {T} +\kappa \mathbf {B} }$ ${\displaystyle \tau }$ ${\displaystyle \kappa }$ ${\displaystyle {\frac {d}{ds}}\mathbf {B} ={\boldsymbol {\omega }}\times \mathbf {B} }$

Darboux was co-editor of the works of Jean Baptiste Joseph Fourier and Joseph-Louis Lagrange .

Honors

In 1884 he became a member of the Académie des Sciences in Paris. In 1902 Darboux was accepted as a Foreign Member in the Royal Society , which in 1916 awarded him the New Year's Eve Medal . From 1902 he was also an elected member of the American Philosophical Society and Honorary Fellow of the Royal Society of Edinburgh . In 1908 he gave a plenary lecture at the International Congress of Mathematicians in Rome (Les origines, les méthodes et les problemèmes de la géométrie infinitésimale). Also in 1908 he was elected a member of the Leopoldina Scholars' Academy . Since 1895 he was a corresponding member of the Russian Academy of Sciences in Saint Petersburg , since 1897 of the Prussian and since 1899 of the Bavarian Academy of Sciences . In 1878 he was president of the Société Mathématique de France . The Darboux Island in Antarctica bears his name. In 1913 Darboux was elected to the National Academy of Sciences .

See also

• Christoffel – Darboux formula, see Orthogonal Polynomials
• Darboux's theorem (Darboux theorems), see Symplectic manifold
• Darboux transformation

Works

• Leçons sur la theory des surfaces . 3 volumes, Paris: Gauthier-Villars, 1887 to 1893
• Cours de géometrie de la Faculté des sciences , 2 volumes, Paris, 1887, 1888

Web links

• John J. O'Connor, Edmund F. Robertson :  Gaston Darboux. In: MacTutor History of Mathematics archive .
• Entry to Darboux; Jean Gaston (1842–1917) in the Archives of the Royal Society , London
• Gaston Darboux in the Mathematics Genealogy Project (English)

Individual evidence

1. ^ Darboux Vector, Mathworld
2. ^ Fellows Directory. Biographical Index: Former RSE Fellows 1783–2002. Royal Society of Edinburgh, accessed October 19, 2019 . 
3. ^ Foreign members of the Russian Academy of Sciences since 1724. Jean-Gaston Darboux. Russian Academy of Sciences, accessed August 24, 2015 . 
4. ^ Members of the previous academies. Jean-Gaston Darboux. Berlin-Brandenburg Academy of Sciences and Humanities , accessed on March 11, 2015 . 
5. ↑ Member entry by Gaston Darboux (with a link to an obituary) at the Bavarian Academy of Sciences , accessed on January 22, 2017.