Adrien-Marie Legendre | |
|---|---|
 Watercolor caricature by Julien-Léopold Boilly (see§ Mistaken portrait), the only Authenticated portrait of Legendre[2] | |
| Born | (1752-09-18)18 September 1752 |
| Died | 9 January 1833(1833-01-09) (aged 80) |
| Alma mater | Collège Mazarin |
| Known for | Associated Legendre polynomials Legendre transformation Legendre polynomials Elliptic functions Introducing the character∂[1] |
| Scientific career | |
| Fields | Mathematician |
| Institutions | École Militaire École Normale École Polytechnique |
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Adrien-Marie Legendre (/ləˈʒɑːndər,-ˈʒɑːnd/;[3]French:[adʁiɛ̃maʁiləʒɑ̃dʁ]; 18 September 1752 – 9 January 1833) was aFrenchmathematician who made numerous contributions tomathematics. Well-known and important concepts such as theLegendre polynomials andLegendre transformation are named after him. He is also known for his contributions to themethod of least squares, and was the first to officially publish on it, thoughCarl Friedrich Gauss had discovered it before him.[4][5]
Adrien-Marie Legendre was born inParis on 18 September 1752 to a wealthy family. He received his education at theCollège Mazarin in Paris, and defended his thesis in physics and mathematics in 1770. He taught at theÉcole Militaire in Paris from 1775 to 1780 and at theÉcole Normale from 1795. At the same time, he was associated with theBureau des Longitudes. In 1782, theBerlin Academy awarded Legendre a prize for his treatise on projectiles in resistant media. This treatise also brought him to the attention ofLagrange.[6]
TheAcadémie des sciences made Legendre an adjoint member in 1783 and an associate in 1785. In 1789, he was elected aFellow of the Royal Society.[7]
He assisted with theAnglo-French Survey (1784–1790) to calculate the precise distance between theParis Observatory and theRoyal Greenwich Observatory by means oftrigonometry. To this end in 1787 he visited Dover and London together withDominique, comte de Cassini andPierre Méchain. The three also visitedWilliam Herschel, the discoverer of the planetUranus.
Legendre lost his private fortune in 1793 during theFrench Revolution. That year, he also married Marguerite-Claudine Couhin, who helped him put his affairs in order. In 1795, Legendre became one of six members of the mathematics section of the reconstituted Académie des Sciences, renamed the Institut National des Sciences et des Arts. Later, in 1803, Napoleon reorganized the Institut National, and Legendre became a member of the Geometry section. From 1799 to 1812, Legendre served as mathematics examiner for graduating artillery students at the École Militaire and from 1799 to 1815 he served as permanent mathematics examiner for theÉcole Polytechnique.[8] In 1824, Legendre's pension from the École Militaire was stopped because he refused to vote for the government candidate at the Institut National. In 1831, he was made an officer of theLégion d'Honneur.[6]
Legendre died in Paris on 9 January 1833, after a long and painful illness, and Legendre's widow carefully preserved his belongings to memorialize him. Upon her death in 1856, she was buried next to her husband in the village ofAuteuil, where the couple had lived, and left their last country house to the village. Legendre's name is one of the72 names inscribed on the Eiffel Tower.
Abel's work onelliptic functions was built on Legendre's, and some ofGauss's work in statistics andnumber theory completed that of Legendre. He developed, and first communicated to his contemporaries before Gauss, theleast squares method[9] which has broad application inlinear regression,signal processing, statistics, andcurve fitting; this was published in 1806 as an appendix to his book on the paths of comets. Today, the term "least squares method" is used as a direct translation from the French "méthode des moindres carrés".
His major work isExercices de Calcul Intégral, published in three volumes in 1811, 1817 and 1819. In the first volume he introduced the basic properties of elliptic integrals,beta functions andgamma functions, introducing the symbol Γ and normalizing it to Γ(n+1) = n!. Further results on the beta and gamma functions along with their applications to mechanics – such as the rotation of the earth, and the attraction of ellipsoids – appeared in the second volume.[10] In 1830, he gave a proof ofFermat's Last Theorem for exponentn = 5, which was also proven byLejeune Dirichlet in 1828.[10]
Innumber theory, he conjectured thequadratic reciprocity law, subsequently proved by Gauss; in connection to this, theLegendre symbol is named after him. He also did pioneering work on the distribution ofprimes, and on the application of analysis to number theory. His 1798 conjecture of theprime number theorem was rigorously proved byHadamard andde la Vallée-Poussin in 1896.
Legendre did an impressive amount of work onelliptic functions, including the classification ofelliptic integrals, but it tookAbel's study of the inverses ofJacobi'sfunctions to solve the problem completely.
He is known for theLegendre transformation, which is used to go from theLagrangian to theHamiltonian formulation ofclassical mechanics. Inthermodynamics it is also used to obtain theenthalpy and theHelmholtz andGibbs(free) energies from theinternal energy. He is also the namesake of theLegendre polynomials, solutions to Legendre's differential equation, which occur frequently in physics and engineering applications, such aselectrostatics.
Legendre is best known as the author ofÉléments de géométrie, which was published in 1794 and was the leading elementary text on the topic for around 100 years. This text greatly rearranged and simplified many of the propositions fromEuclid'sElements to create a more effective textbook.
For two centuries, until the recent discovery of the error in 2005, books, paintings and articles have incorrectly shown a profile portrait of the obscure French politicianLouis Legendre (1752–1797) as a portrait of the mathematician. The error arose from the fact that the sketch was labelled simply "Legendre" and appeared in a book along with contemporary mathematicians such as Lagrange. One of only two known portraits of Legendre, rediscovered in 2008, is found in the 1820 bookAlbum de 73 portraits-charge aquarellés des membres de I'Institut, a book of caricatures of seventy-three members of the Institut de France in Paris by the French artistJulien-Léopold Boilly as shown below.[13][2] The other portrait is from the bookLe Panthéon scientifique de la tour Eiffel.[14]
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Media related toAdrien-Marie Legendre at Wikimedia Commons
