Olinde Rodrigues

Benjamin Olinde Rodrigues
Born(1795-10-06)6 October 1795
Bordeaux, France
Died17 December 1851(1851-12-17) (aged 56)
Paris, France
Alma materUniversity of Paris

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.

Biography

Rodrigues was born into a well-to-do Sephardi Jewish family in Bordeaux. His family was of Portuguese-Jewish descent.[1][2][3][4][5][6] He was awarded a doctorate in mathematics on 28 June 1815 by the University of Paris.[7] His dissertation contains the result now called Rodrigues' formula.[8]

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.[9] 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-norm 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 combined effect of two rotations. This formula is a precursor to the quaternion product of William Rowan Hamilton.[10][11] In 1846, Arthur Cayley acknowledged[12] Euler's and Rodrigues' priority describing orthogonal transformations.

Rodrigues is credited as originating the idea of the artist as an avant-garde.[13]

Publications

See also

References

  1. ^ Simon Altmann, "Rotations, Quaternions and Double Groups"(Clarendon Press, Oxford, 1986, ISBN 0-19-855372-2): "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 "?". Jewish Encyclopedia.
  2. ^ Marbach, Christian (1 June 2016). "Olinde Rodrigues vu par Emmanuel Grison". Bulletin de la Sabix. Société des amis de la Bibliothèque et de l'Histoire de l'École polytechnique (in French) (59): 129–142. doi:10.4000/sabix.1803. ISSN 0989-3059. S2CID 165403093.
  3. ^ Eckalbar, John C. (1979). "The Saint-Simonians in Industry and Economic Development". The American Journal of Economics and Sociology. 38 (1): 83–96. doi:10.1111/j.1536-7150.1979.tb02866.x. ISSN 0002-9246. JSTOR 3486307.
  4. ^ Pilbeam, Pamela (2013). "Saint-Simonians in Nineteenth-Century France". SpringerLink. doi:10.1057/9781137313966. ISBN 978-1-349-36549-4.
  5. ^ Saint-Simon, Henri (1 August 2013). Œuvres complètes (4 volumes sous coffret): Introduction, notes et commentaires sous la direction de Pierre Musso (in French). Humensis. ISBN 978-2-13-062090-7.
  6. ^ Bernon, Thomas (13 December 2018). "La science des races : la Société Ethnologique de Paris et le tournant colonial (1839-1848)". La Révolution française. Cahiers de l'Institut d'histoire de la Révolution française (in French) (15). doi:10.4000/lrf.2448. ISSN 2105-2557. S2CID 192381639.
  7. ^ Altmann and Ortiz(2005), p. 12
  8. ^ Rodrigues, Olinde (1816). "Mémoire sur l'attraction des sphéroïdes". Correspondence Sur l'École Impériale Polytechnique. 3 (3): 361–385.
  9. ^ 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.
  10. ^ Friedberg, Richard M. (2022). "Rodrigues, Olinde: "Des lois géométriques qui régissent les déplacements d'un système solide...", translation and commentary". arXiv:2211.07787.
  11. ^ John H. Conway, Derek A. Smith, On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry. AK Peters, 2003, ISBN 1-56881-134-9, p. 9
  12. ^ 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
  13. ^ Margolin, Victor (1997). The struggle for utopia: Rodchenko, Lissitzky, Moholy-Nagy, 1917-1946. Chicago: University of Chicago Press. ISBN 978-0-226-50516-9.

Bibliography