Olinde Rodrigues
   HOME

TheInfoList



OR:

Benjamin Olinde Rodrigues (6 October 1795 – 17 December 1851), more commonly known as Olinde Rodrigues, was a French banker,
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
, and social reformer. In mathematics Rodrigues is remembered for Rodrigues' rotation formula for vectors, the Rodrigues formula for the
Legendre polynomials In mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a wide number of mathematical properties and numerous applications. They can be defined in many ways, and t ...
, and the Euler–Rodrigues parameters.


Biography

Rodrigues was born into a well-to-do Sephardi Jewish family in
Bordeaux Bordeaux ( ; ; Gascon language, Gascon ; ) is a city on the river Garonne in the Gironde Departments of France, department, southwestern France. A port city, it is the capital of the Nouvelle-Aquitaine region, as well as the Prefectures in F ...
. His family was of Portuguese-Jewish descent. He was awarded a
doctorate A doctorate (from Latin ''doctor'', meaning "teacher") or doctoral degree is a postgraduate academic degree awarded by universities and some other educational institutions, derived from the ancient formalism '' licentia docendi'' ("licence to teach ...
in mathematics on 28 June 1815 by the
University of Paris The University of Paris (), known Metonymy, metonymically as the Sorbonne (), was the leading university in Paris, France, from 1150 to 1970, except for 1793–1806 during the French Revolution. Emerging around 1150 as a corporation associated wit ...
. His dissertation contains the result now called Rodrigues' formula. After graduation, Rodrigues became a banker. A close associate of the Comte de Saint-Simon, Rodrigues continued, after Saint-Simon's death in 1825, to champion the older man's
socialist Socialism is an economic ideology, economic and political philosophy encompassing diverse Economic system, economic and social systems characterised by social ownership of the means of production, as opposed to private ownership. It describes ...
ideals, a school of thought that came to be known as Saint-Simonianism. During this period, Rodrigues published writings on politics, social reform, and banking. Rodrigues' 1840 paper developed new results on transformation groups. It uses three numbers to parameterize the entries of a rotation matrix using only rational functions. When converted to four parameters, this representation is equivalent to a unit quaternion, and describes the axis and angle of a rotation. In addition, he applied
spherical trigonometry Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the edge (geometry), sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, ge ...
to relate changes in rotation axis and angle due to the composition of two rotations. This formula is a precursor to the
quaternion In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. The algebra of quater ...
product of William Rowan Hamilton. In 1846, Arthur Cayley acknowledged Arthur Cayley (1846) "Sur Quelques Proprietes des Determinants Gauches", Crelle's Journal 32: 119–23, and ''Collected Mathematical Papers of Arthur Cayley'', volume 1, page 335 Euler's and Rodrigues' priority describing orthogonal transformations. Rodrigues is credited as originating the idea of the artist as an
avant-garde In the arts and literature, the term ''avant-garde'' ( meaning or ) identifies an experimental genre or work of art, and the artist who created it, which usually is aesthetically innovative, whilst initially being ideologically unacceptable ...
.


Publications


''Mouvement de rotation d'un corps de révolution pesant''
Paris, 1815
"Mémoire sur l'attraction des sphéroïdes"
''Correspondence Sur l'École Impériale Polytechnique'', vol. 3, pp. 361–385, 1815 * ''Théorie de la caisse hypothécaire, ou Examen du sort des emprunteurs, des porteurs d'obligations et des actionnaires de cet établissement'', 1820 * ''Appel : religion saint-simonienne'', 1831 * ''L'artiste, le savant et l'industriel: Dialogue'', 1825 * ''Réunion générale de la famille : séances des 19 et 21 novembre'', 1831 * ''Son premier écrit / Saint-Simon'', 1832 * ''Le disciple de Saint-Simon aux Saint-Simoniens et au public'', 1832 * ''Aux saint-simoniens, 13 février 1832 : bases de la loi morale proposées à l'acceptation des femmes'', 1832 * ''Olinde Rodrigues à M. Michel Chevalier, rédacteur du "Globe" : religion saint-simonienne'', 1832
"Sur le nombre de manière de décomposer un Polygone en triangles au moyen de diagonales"
''Journal de Mathématiques Pures et Appliquées'', vol. 3, pp. 547–548, 1838
"Sur le nombre de manière de d'effectuer un produit de n facteurs"
''Journal de Mathématiques Pures et Appliquées'', vol. 3, p. 549, 1838
"Démonstration élémentaire et purement algébrique du développement d'un binome élevé à une puissance négative ou fractionnaire"
''Journal de Mathématiques Pures et Appliquées'', vol. 3, pp. 550–551, 1838
"Note sur les inversions, ou dérangements produits dans les permutations"
''Journal de Mathématiques Pures et Appliquées'', vol. 4, pp. 236–240, 1839 * ''De l'organisation des banques à propos du projet de loi sur la Banque de France'', 1840
"Des lois géométriques qui régissent les déplacements d'un système solide dans l'espace: et de la variation des coordonnées provenant de ces déplacements considérés indépendamment des causes qui peuvent les produire"
''Journal de Mathématiques Pures et Appliquées'', vol. 5, pp. 380–440, 1840 * ''Les Peuples et les diplomates. La Paix ou la guerre'', 1840 * ''Œuvres de Saint-Simon'', 1841 * ''Poésies sociales des ouvriers, réunies et publiées par Olinde Rodrigues'', 1841
"Du devéloppement des fonctions trigonométriques en produits de facteurs binomes"
''Journal de Mathématiques Pures et Appliquées'', vol. 8, pp. 217–224, 1843
"Note sur l’évaluation des arcs de cercle, en fonction linéaire des sinus ou des tangentes de fractions de ces arcs, décroissant en progression géométrique"
''Journal de Mathématiques Pures et Appliquées'', vol. 8, pp. 225–234, 1843 * ''Théorie des banques'', 1848 * ''De l'Organisation du suffrage universel, proposition d'un nouveau mode électoral par Olinde Rodrigues'', 1848 * ''Organisation du travail, association du travail et du capital'', 1848 * ''Organisation du travail, bases de l'organisation des banques'', 1848


See also

* Euler–Rodrigues formula *
Orthogonal polynomials In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal In mathematics, orthogonality (mathematics), orthogonality is the generalization of the geom ...
* Spherical harmonics


References


External links


Olinde Rodrigues sur Le Maitron

Olinde Rodrigues sur Jewish Encyclopedia



Bibliography

* * Louis Gabriel Michaud (1863) ''Biographie universelle ancienne et moderne'' * * * Jeremy J. Gray (1980) ''Olinde Rodrigues' paper of 1840 on Transformation Groups'', Archive for History of Exact Sciences 21(4): 375–385, . {{DEFAULTSORT:Rodrigues, Olinde 1795 births 1851 deaths 19th-century French mathematicians 19th-century French Sephardi Jews British social reformers Burials at Père Lachaise Cemetery Businesspeople from Bordeaux French bankers French people of Portuguese-Jewish descent Historical treatment of quaternions Jewish socialists Lycée Louis-le-Grand alumni Saint-Simonists Scientists from Bordeaux