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{{Short description|French banker and mathematician (1795–1851)}}
'''Benjamin Olinde Rodrigues''' (] - ]), more commonly known as '''Olinde Rodrigues''', was a ] ] and ].
{{Use dmy dates|date=April 2022}}
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'''Benjamin Olinde Rodrigues''' (6 October 1795 – 17 December 1851), more commonly known as '''Olinde Rodrigues''', was a French banker, ], and ]. In mathematics Rodrigues is remembered for ] for vectors, the ] for the ], and the ].


==Biography== ==Biography==
Rodrigues was born into a well-to-do ]ish family in ]. His family was of Portuguese-Jewish descent.<ref>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 {{cite encyclopedia |url=http://www.jewishencyclopedia.com/view.jsp?artid=1332&letter=B |title=? |encyclopedia=] }}</ref><ref>{{Cite journal |last=Marbach |first=Christian |date=2016-06-01 |title=Olinde Rodrigues vu par Emmanuel Grison |url=https://journals.openedition.org/sabix/1803 |journal=Bulletin de la Sabix. Société des amis de la Bibliothèque et de l'Histoire de l'École polytechnique |language=fr |issue=59 |pages=129–142 |doi=10.4000/sabix.1803 |s2cid=165403093 |issn=0989-3059}}</ref><ref>{{Cite journal |last=Eckalbar |first=John C. |date=1979 |title=The Saint-Simonians in Industry and Economic Development |url=https://www.jstor.org/stable/3486307 |journal=The American Journal of Economics and Sociology |volume=38 |issue=1 |pages=83–96 |doi=10.1111/j.1536-7150.1979.tb02866.x |jstor=3486307 |issn=0002-9246}}</ref><ref>{{Cite journal |last=Pilbeam |first=Pamela |date=2013 |title=Saint-Simonians in Nineteenth-Century France |url=https://link.springer.com/book/10.1057/9781137313966 |journal=SpringerLink |language=en |doi=10.1057/9781137313966|isbn=978-1-349-36549-4 }}</ref><ref>{{Cite book |last=Saint-Simon |first=Henri |url=https://books.google.com/books?id=XMoICwAAQBAJ&pg=PT1810 |title=Œuvres complètes (4 volumes sous coffret): Introduction, notes et commentaires sous la direction de Pierre Musso |date=2013-08-01 |publisher=Humensis |isbn=978-2-13-062090-7 |language=fr}}</ref><ref>{{Cite journal |last=Bernon |first=Thomas |date=2018-12-13 |title=La science des races : la Société Ethnologique de Paris et le tournant colonial (1839-1848) |url=https://journals.openedition.org/lrf/2448?lang=en |journal=La Révolution française. Cahiers de l'Institut d'histoire de la Révolution française |language=fr |issue=15 |doi=10.4000/lrf.2448 |s2cid=192381639 |issn=2105-2557|doi-access=free }}</ref> He was awarded a ] in mathematics on 28 June 1815 by the ].<ref>Altmann and Ortiz(2005), p. 12</ref> His dissertation contains the result now called ].<ref>{{cite journal |title=Mémoire sur l'attraction des sphéroïdes |last=Rodrigues |first=Olinde |journal=Correspondence Sur l'École Impériale Polytechnique |volume=3 |issue=3 |year=1816 |pages=361–385 |url=https://archive.org/details/correspondancesu03hach/page/361/mode/1up }}</ref>
Rodrigues was born into a well-to-do ] ]ish family in ], ]. Jews were prohibited from enrolling at the '']'', the most prestigious school in ], and it is still unknown how he learned his advanced mathematics. Rodrigues was awarded a ] in mathematics in 1816. His dissertation contains the result now called ].


After graduation, Rodrigues became a banker. A close associate of the ], after the latter's death in ], he continued to champion his ] ideals ('']''). Rodrigues published writings on politics, social reform, and banking. After graduation, Rodrigues became a banker. A close associate of the ], Rodrigues continued, after Saint-Simon's death in 1825, to champion the older man's ] ideals, a school of thought that came to be known as ]. During this period, Rodrigues published writings on politics, social reform, and banking.


Rodrigues' 1840 paper developed new results on ]s.<ref>Olinde Rodrigues (1840) (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-norm ], 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 ] product of ].<ref>{{cite arxiv | arxiv=2211.07787 | title=Rodrigues, Olinde: "Des lois géométriques qui régissent les déplacements d'un système solide...", translation and commentary | first=Richard M. | last=Friedberg | year=2022}}</ref><ref>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</ref> In 1846, ] acknowledged<ref>] (1846) "Sur Quelques Proprietes des Determinants Gauches", ] 32: 119–23, and ''Collected Mathematical Papers of Arthur Cayley'', volume 1, page 335</ref> Euler's and Rodrigues' priority describing ]s.
In ], he published a result on ]s. However, his work on mathematics was largely ignored, and has only relatively recently been rediscovered. He died in Paris.


Rodrigues is credited as originating the idea of the artist as an ].<ref name="Margolin">{{cite book |last1=Margolin |first1=Victor |title=The struggle for utopia: Rodchenko, Lissitzky, Moholy-Nagy, 1917-1946 |date=1997 |publisher=University of Chicago Press |location=Chicago |isbn=978-0-226-50516-9}}</ref>
==Why we call it the Rodrigues formula ==


== Publications ==
In the MacTutor biography of Rodrigues, J.J.O'Connor and E.F.Robertson provide this information:
* , Paris, 1815
:"The fact that we know it today as the Rodrigues formula is due to Heine . Heine was an expert on Legendre polynomials, Lamé functions and Bessel functions and he wrote a book in which he proposed that, since Hermite had shown that Rodrigues had priority in discovering the formula, then it should be known as the Rodrigues formula."
* , ''Correspondence Sur l'École Impériale Polytechnique'', vol. 3, pp. 361–385, 1815
==See also==
* ''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
* ] which discusses Rodrigues' formula
* ''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
* , ''Journal de Mathématiques Pures et Appliquées'', vol. 3, pp. 547–548, 1838
* , ''Journal de Mathématiques Pures et Appliquées'', vol. 3, p. 549, 1838
* , ''Journal de Mathématiques Pures et Appliquées'', vol. 3, pp. 550–551, 1838
* , ''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
* , ''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
* , ''Journal de Mathématiques Pures et Appliquées'', vol. 8, pp. 217–224, 1843
* , ''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


==External links== == See also ==
{{Portal|Biographies|Mathematics}}
*]
* ]
* ]


== References ==
* {{cite journal | author = Simon L. Altmann | title = Hamilton, Rodrigues and the quaternion scandal | journal = Mathematics Magazine | date = 1989 | volume = 62 | pages = 291-308 | id = ISSN 0025-570X }}
{{reflist}}


== External links ==
* {{cite book | author=Simon L. Altmann | title= Rotations, Quaternions and Double Groups | publisher= Dover Publications | year=2005 | id = ISBN 0-486-44518-6}}
*
* {{cite book | author=Simon L. Altmann; & Eduardo L.Ortiz (eds.) | title=Mathematics and social utopias in France: Olinde Rodrigues and his times | publisher = American Mathematical Society, Providence, RI | date=2005 | id=ISBN 0-8218-3860-1 }} Corrects some of the traditional thinking about Rodrigues as a mathematician
*
* {{MacTutor Biography|id=Rodrigues}}
*


== Bibliography ==
]
* {{Cite book|language=en|first1=Simon|last1=Altmann|first2=Eduardo L.|last2=Ortiz|title=Mathematics and Social Utopias in France: Olinde Rodrigues and His Times|publisher=AMS|location=Providence RI|year=2005|isbn=978-0-821-83860-0|url=https://books.google.com/books?id=oTyJYUx8Jr4C}}
]
* ] (1863) ''Biographie universelle ancienne et moderne''
]
* {{cite magazine | author = Simon L. Altmann | title = Hamilton, Rodrigues and the quaternion scandal |magazine=] | year = 1989 | volume = 62 | pages = 291–308 | doi = 10.2307/2689481 | jstor = 2689481 | issue = 5 }}
]
* {{cite book | author=Simon L. Altmann | title= Rotations, Quaternions and Double Groups | publisher= Dover Publications | year=2005 | isbn = 978-0-486-44518-2}}
]
* ] (1980) ''Olinde Rodrigues' paper of 1840 on Transformation Groups'', ] 21(4): 375–385, {{doi|10.1007/BF00595376}}.
]
]
]


{{Authority control}}
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{{portal bar|mathematics|Business and economics|France}}


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Latest revision as of 02:25, 10 December 2024

French banker and mathematician (1795–1851)

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. He was awarded a doctorate in mathematics on 28 June 1815 by the University of Paris. 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 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-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. In 1846, Arthur Cayley acknowledged Euler's and Rodrigues' priority describing orthogonal transformations.

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

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.

External links

Bibliography

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