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Jean-Robert Argand

From Wikipedia, the free encyclopedia
Genevan mathematician
Jean-Robert Argand
BornJuly 18, 1768
Geneva, Republic of Geneva
DiedAugust 13, 1822 (1822-08-14) (aged 54)
NationalityRepublic of Geneva, and thenSwitzerland (since 1815)
Known forArgand diagram and Proof ofFundamental Theorem of Algebra
Scientific career
FieldsMathematics

Jean-Robert Argand (UK:/ˈɑːrɡænd/,US:/ˌɑːrˈɡɑːn(d)/,[1][2]French:[ʒɑ̃ʁɔbɛʁaʁɡɑ̃]; July 18, 1768 – August 13, 1822) was a Genevanamateur mathematician. In 1806, while managing abookstore inParis, he published the idea of geometrical interpretation ofcomplex numbers known as theArgand diagram and is known for the first rigorousproof of theFundamental Theorem of Algebra.

Life

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Jean-Robert Argand was born inGeneva, thenRepublic of Geneva, to Jacques Argand and Eve Carnac. His background and education are mostly unknown. Since his knowledge of mathematics was self-taught and he did not belong to any mathematical organizations, he likely pursued mathematics as a hobby rather than a profession.

Argand moved to Paris in 1806 with his family and, when managing a bookshop there, privately published hisEssai sur une manière de représenter les quantités imaginaires dans les constructions géométriques (Essay on a method of representingimaginary quantities). In 1813, it was republished in the French journalAnnales de Mathématiques. The Essay discussed a method of graphing complex numbers via analytical geometry. It proposed the interpretation of the valuei as a rotation of 90 degrees in the Argand plane. In this essay he was also the first to propose the idea ofmodulus to indicate the magnitude ofvectors andcomplex numbers, as well as the notation for vectorsab{\displaystyle {\overrightarrow {ab}}}. The topic of complex numbers was also being studied by other mathematicians, notablyCarl Friedrich Gauss andCaspar Wessel. Wessel's 1799 paper on a similar graphing technique did not attract attention.

Argand is also renowned for delivering a proof of thefundamental theorem of algebra in his 1814 workRéflexions sur la nouvelle théorie d'analyse (Reflections on the new theory ofanalysis). It was the first complete andrigorous proof of the theorem, and was also the first proof to generalize the fundamental theorem of algebra to includepolynomials with complexcoefficients.

The first textbook containing a proof of the theorem wasCauchy'sCours d'analyse de l'École Royale Polytechnique (1821). It contained Argand's proof, although Argand is not credited for it. And the proof was later referenced inChrystal's influential textbookAlgebra.

Argand died of an unknown cause on August 13, 1822, in Paris. In 1978 his proof of the fundamental theorem of algebra was called by The Mathematical Intelligencer “both ingenious and profound.”

See also

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References

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  1. ^Wells, John C. (2008).Longman Pronunciation Dictionary (3rd ed.). Longman.ISBN 978-1-4058-8118-0.
  2. ^Jones, Daniel (2011).Roach, Peter;Setter, Jane;Esling, John (eds.).Cambridge English Pronouncing Dictionary (18th ed.). Cambridge University Press.ISBN 978-0-521-15255-6.

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