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Olinde Rodrigues

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Template:Short description Template:Use dmy dates Template:Infobox scientist Benjamin Olinde Rodrigues (6 October 1795 – 17 December 1851), more commonly known as Olinde Rodrigues, was a French banker, mathematician, and social reformer. In mathematics Rodrigues is remembered for Rodrigues' rotation formula for vectors, the Rodrigues formula for the Legendre polynomials, and the Euler–Rodrigues parameters.

BiographyEdit

Rodrigues was born into a well-to-do Sephardi Jewish family in Bordeaux. His family was of Portuguese-Jewish descent.<ref>Simon Altmann, "Rotations, Quaternions and Double Groups"(Clarendon Press, Oxford, 1986, Template:ISBN): "The family is often said to have been of Spanish origin, but the spelling of the family name rather suggests Portuguese descent (as indeed asserted by the 'Enciclopedia Universal Illustrada Espasa-Calpe')". For more information on the Rodrigues as Portuguese Jews in Bordeaux see also the Jewish Encyclopedia Template:Cite encyclopedia</ref><ref>Template:Cite journal</ref><ref>Template:Cite journal</ref><ref>Template:Cite journal</ref><ref>Template:Cite book</ref><ref>Template:Cite journal</ref> He was awarded a doctorate in mathematics on 28 June 1815 by the University of Paris.<ref>Altmann and Ortiz(2005), p. 12</ref> His dissertation contains the result now called Rodrigues' formula.<ref>Template:Cite journal</ref>

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 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.<ref>Olinde Rodrigues (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" (On the geometrical laws that govern the displacements of a solid system in space, and on the change of coordinates resulting from these displacements considered independently of the causes that can produce them), Journal de Mathématiques Pures et Appliquées, vol. 5, pages 380-440.</ref> 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 to relate changes in rotation axis and angle due to the composition of two rotations. This formula is a precursor to the quaternion product of William Rowan Hamilton.<ref>Template:Cite arxiv</ref><ref>John H. Conway, Derek A. Smith (2003) On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry, AK Peters Template:ISBN, p. 9</ref> In 1846, Arthur Cayley acknowledged<ref>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</ref> Euler's and Rodrigues' priority describing orthogonal transformations.

Rodrigues is credited as originating the idea of the artist as an avant-garde.<ref name="Margolin">Template:Cite book</ref>

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