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, structure, space, models, and change. History On ...

, and

social reformer A reform movement or reformism is a type of social movement that aims to bring a social or also a political system closer to the community's ideal. A reform movement is distinguished from more radical social movements such as revolutionary move ...

. In mathematics Rodrigues is remembered for

Rodrigues' rotation formula In the theory of three-dimensional rotation, Rodrigues' rotation formula, named after Olinde Rodrigues, is an efficient algorithm for rotating a vector in space, given an axis and angle of rotation. By extension, this can be used to transform al ...

for vectors, the

Rodrigues formula In mathematics, Rodrigues' formula (formerly called the Ivory–Jacobi formula) is a formula for the Legendre polynomials independently introduced by , and . The name "Rodrigues formula" was introduced by Heine in 1878, after Hermite pointed out ...

about series of

orthogonal polynomials In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonality, orthogonal to each other under some inner product. The most widely used orthogonal polynomial ...

and the Euler–Rodrigues parameters.

Biography

Rodrigues was born into a well-to-do Sephardi Jewish family in

Bordeaux Bordeaux ( , ; Gascon oc, Bordèu ; eu, Bordele; it, Bordò; es, Burdeos) is a port city on the river Garonne in the Gironde department, Southwestern France. It is the capital of the Nouvelle-Aquitaine region, as well as the prefectur ...

. He was awarded a

doctorate A doctorate (from Latin ''docere'', "to teach"), doctor's degree (from Latin ''doctor'', "teacher"), or doctoral degree is an academic degree awarded by universities and some other educational institutions, derived from the ancient formalism ''l ...

in mathematics on 28 June 1815 by the

University of Paris , image_name = Coat of arms of the University of Paris.svg , image_size = 150px , caption = Coat of Arms , latin_name = Universitas magistrorum et scholarium Parisiensis , motto = ''Hic et ubique terrarum'' (Latin) , mottoeng = Here and a ...

. His dissertation contains the result now called

Rodrigues' formula In mathematics, Rodrigues' formula (formerly called the Ivory–Jacobi formula) is a formula for the Legendre polynomials independently introduced by , and . The name "Rodrigues formula" was introduced by Heine in 1878, after Hermite pointed out ...

. After graduation, Rodrigues became a banker. A close associate of the

Comte de Saint-Simon Claude Henri de Rouvroy, comte de Saint-Simon (17 October 1760 – 19 May 1825), often referred to as Henri de Saint-Simon (), was a French political, economic and socialist theorist and businessman whose thought had a substantial influence on p ...

, Rodrigues continued, after Saint-Simon's death in 1825, to champion the older man's

socialist Socialism is a left-wing economic philosophy and movement encompassing a range of economic systems characterized by the dominance of social ownership of the means of production as opposed to private ownership. As a term, it describes the e ...

ideals, a school of thought that came to be known as

Saint-Simonianism Saint-Simonianism was a French political, religious and social movement of the first half of the 19th century, inspired by the ideas of Claude Henri de Rouvroy, comte de Saint-Simon (1760–1825). Saint-Simon's ideas, expressed largely through a ...

. During this period, Rodrigues published writings on politics, social reform, and banking. In 1840 he published a result on

transformation group In mathematics, the automorphism group of an object ''X'' is the group consisting of automorphisms of ''X'' under composition of morphisms. For example, if ''X'' is a finite-dimensional vector space, then the automorphism group of ''X'' is the g ...

s, which applied

Leonhard Euler Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ...

four squares formula In mathematics, Euler's four-square identity says that the product of two numbers, each of which is a sum of four square (algebra), squares, is itself a sum of four squares. Algebraic identity For any pair of quadruples from a commutative ring, th ...

, a precursor to the

quaternions 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. Hamilton defined a quatern ...

William Rowan Hamilton Sir William Rowan Hamilton Doctor of Law, LL.D, Doctor of Civil Law, DCL, Royal Irish Academy, MRIA, Royal Astronomical Society#Fellow, FRAS (3/4 August 1805 – 2 September 1865) was an Irish mathematician, astronomer, and physicist. He was the ...

, to the problem of representing rotations in space. In 1846

Arthur Cayley Arthur Cayley (; 16 August 1821 – 26 January 1895) was a prolific United Kingdom of Great Britain and Ireland, British mathematician who worked mostly on algebra. He helped found the modern British school of pure mathematics. As a child, C ...

acknowledged

(1846) "Sur Quelques Proprietes des Determinants Gauches",

Crelle's Journal ''Crelle's Journal'', or just ''Crelle'', is the common name for a mathematics journal, the ''Journal für die reine und angewandte Mathematik'' (in English: ''Journal for Pure and Applied Mathematics''). History The journal was founded by Augus ...

32: 119–23, and ''Collected Mathematical Papers of Arthur Cayley'', volume 1, page 335 Euler's and Rodrigues' priority describing

orthogonal transformation In linear algebra, an orthogonal transformation is a linear transformation ''T'' : ''V'' → ''V'' on a real inner product space ''V'', that preserves the inner product. That is, for each pair of elements of ''V'', we h ...

s. Rodrigues is credited as originating the idea of the artist as an

avant-garde The avant-garde (; In 'advance guard' or ' vanguard', literally 'fore-guard') is a person or work that is experimental, radical, or unorthodox with respect to art, culture, or society.John Picchione, The New Avant-garde in Italy: Theoretical ...

Publications

* ''Mouvement de rotation d'un corps de révolution pesant'', Paris, 1815
Read online
*''De l'attraction des sphéroïdes'', 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 * ''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'', 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 * ''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

References

External links

Olinde Rodrigues sur Le Maitron

Olinde Rodrigues sur Jewish Encyclopedia

Bibliography

* *

Louis Gabriel Michaud Louis-Gabriel Michaud (19 January 1773, Castle Richemont – 8 March 1858) was a French writer, historian, printer, and bookseller. He was notable as the compiler of ''Biographie Universelle'' (1811–). Life He became a lieutenant on 15 July ...

(1863) ''Biographie universelle ancienne et moderne'' * * * Jeremy J. Gray (1980) ''Olinde Rodrigues' paper of 1840 on Transformation Groups'',

Archive for History of Exact Sciences ''Archive for History of Exact Sciences'' is a peer-reviewed academic journal currently published bimonthly by Springer Science+Business Media, covering the history of mathematics and of astronomy observations and techniques, epistemology of scienc ...

21(4): 375–385, . {{DEFAULTSORT:Rodrigues, Olinde 1795 births 1851 deaths Businesspeople from Bordeaux Lycée Louis-le-Grand alumni French bankers 19th-century French Sephardi Jews Scientists from Bordeaux Historical treatment of quaternions 19th-century French mathematicians Saint-Simonists Burials at Père Lachaise Cemetery British social reformers Jewish socialists French people of Portuguese descent

Biography

Publications

See also

References

External links

Bibliography