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Adrien-Marie Legendre
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Adrien-Marie Legendre
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Life
Adrien-Marie Legendre was born in Paris on 18 September 1752 to a wealthy family. He received his education at the CollÃ¨ge Mazarin in Paris, and defended his thesis in physics and mathematics in 1770. He taught at the Ã‰cole Militaire in Paris from 1775 to 1780 and at the Ã‰cole Normale from 1795. At the same time, he was associated with the Bureau des Longitudes. In 1782, the Berlin Academy awarded Legendre a prize for his treatise on projectiles in resistant media. This treatise also brought him to the attention of Lagrange.{{MacTutor Biography|id=Legendre}}The AcadÃ©mie des sciences made Legendre an adjoint member in 1783 and an associate in 1785. In 1789, he was elected a Fellow of the Royal Society.WEB,weblink Library and Archive, Royal Society, 6 August 2012, He assisted with the Anglo-French Survey (1784â€“1790) to calculate the precise distance between the Paris Observatory and the Royal Greenwich Observatory by means of trigonometry. To this end in 1787 he visited Dover and London together with Dominique, comte de Cassini and Pierre MÃ©chain. The three also visited William Herschel, the discoverer of the planet Uranus.Legendre lost his private fortune in 1793 during the French 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 AcadÃ©mie 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 Ã‰cole Militaire and from 1799 to 1815 he served as permanent mathematics examiner for the Ã‰cole Polytechnique.AndrÃ© Weil, Number Theory: An approach through history From Hammurapi to Legendre, Springer Science & Business Media2006, p. 325. In 1824, Legendre's pension from the Ã‰cole Militaire was stopped because he refused to vote for the government candidate at the Institut National. His pension was partially reinstated with the change in government in 1828. In 1831, he was made an officer of the LÃ©gion d'Honneur.{{Citation needed|date=October 2018}}Legendre died in Paris on 10 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 of Auteuil, where the couple had lived, and left their last country house to the village. Legendre's name is one of the 72 names inscribed on the Eiffel Tower.Mathematical work
Abel's work on elliptic functions was built on Legendre's and some of Gauss' work in statistics and number theory completed that of Legendre. He developed the least squares method and firstly communicated it to his contemporaries before Gauss,JOURNAL, Stephen M. Stigler, 1981, Gauss and the Invention of Least Squares,weblink Ann. Stat., 9, 3, 465â€“474, 10.1214/aos/1176345451, which has broad application in linear regression, signal processing, statistics, and curve 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 "mÃ©thode des moindres carrÃ©s".His major work is Exercices de Calcul IntÃ©gral, published in three volumes in 1811, 1817 and 1819. In the first volume he introduced the basic properties of elliptic integrals, beta functions and gamma functions, introducing the symbol Î“ normalizing it to Î“(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.BOOK,weblink Creators of mathematical and computational sciences, Agarwal, Ravi P., Sen, Syamal K., Springer, 2014, 9783319108704, 218â€“19, 895161901, In 1830, he gave a proof of Fermat's last theorem for exponent n = 5, which was also proven by Lejeune Dirichlet in 1828.In number theory, he conjectured the quadratic reciprocity law, subsequently proved by Gauss; in connection to this, the Legendre symbol is named after him. He also did pioneering work on the distribution of primes, and on the application of analysis to number theory. His 1798 conjecture of the prime number theorem was rigorously proved by Hadamard and de la VallÃ©e-Poussin in 1896.Legendre did an impressive amount of work on elliptic functions, including the classification of elliptic integrals, but it took Abel's stroke of genius to study the inverses of Jacobi's functions and solve the problem completely.He is known for the Legendre transformation, which is used to go from the Lagrangian to the Hamiltonian formulation of classical mechanics. In thermodynamics it is also used to obtain the enthalpy and the Helmholtz and Gibbs (free) energies from the internal energy. He is also the namesake of the Legendre polynomials, solutions to Legendre's differential equation, which occur frequently in physics and engineering applications, e.g. electrostatics.Legendre is best known as the author of Ã‰lÃ©ments de gÃ©omÃ©trie, 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 from Euclid's Elements to create a more effective textbook.Honors
- Foreign Honorary Member of the American Academy of Arts and Sciences (1832)WEB, Book of Members, 1780â€“2010: Chapter L,weblink American Academy of Arts and Sciences, 28 July 2014,
- The Moon crater Legendre is named after him.
- Main-belt asteroid 26950 Legendre is named after him.
- Legendre is one of the 72 prominent French scientists who were commemorated on plaques at the first stage of the Eiffel Tower when it first opened.
Publications
- Essays
- 1782 Recherches sur la trajectoire des projectiles dans les milieux rÃ©sistants (prize on projectiles offered by the Berlin Academy)
- Books
- ElÃ©ments de gÃ©omÃ©trie, textbook 1794
- Essai sur la ThÃ©orie des Nombres 1797-8 ("An VI"), 2nd ed. 1808, 3rd ed. in 2 vol. 1830
- Nouvelles MÃ©thodes pour la DÃ©termination des Orbites des ComÃ¨tes, 1805
- Exercices de Calcul IntÃ©gral, book in three volumes 1811, 1817, and 1819
- TraitÃ© des Fonctions Elliptiques, book in three volumes 1825, 1826, and 1830
- Memoires in Histoire de l'AcadÃ©mie Royale des Sciences
- 1783 Sur l'attraction des SphÃ©roÃ¯des homogÃ¨nes (work on Legendre polynomials)
- 1784 Recherches sur la figure des PlanÃ¨tes p. 370
- 1785 Recherches d'analyse indÃ©terminÃ©e p. 465 (work on number theory)
- 1786 MÃ©moire sur la maniÃ¨re de distinguer les Maxima des Minima dans le Calcul des Variations p. 7 (as Legendre)
- 1786 MÃ©moire sur les IntÃ©grations par arcs d'ellipse p. 616 (as le Gendre)
- 1786 Second MÃ©moire sur les IntÃ©grations par arcs d'ellipse p. 644
- 1787 L'intÃ©gration de quelques Ã©quations aux diffÃ©rences Partielles (Legendre transform)
- In Memoires prÃ©sentÃ©s par divers Savants Ã la l'AcadÃ©mie des Sciences de l'Institut de France
- 1806 Nouvelle formula pour rÃ©duire en distances vraies les distances apparentes de la Lune au Soleil ou Ã une Ã©toile (30â€“54)
- 1807 Analyse des triangles tracÃ©s sur la surface d'un sphÃ©roide (130â€“161)
- Tome 10 Recherches sur diverses sortes d'intÃ©grales dÃ©fines (416â€“509)
- 1819 MÃ©thode des moindres carrÃ©s pour trouver le milieu le plus probable entre les rÃ©sultats de diffÃ©rentes observations (149â€“154), MÃ©moire sur l'attraction des ellipsoÃ¯des homogÃ¨nes (155â€“183)
- 1823 Recherches sur quelques objets d'Analyse indÃ©terminÃ©e et particuliÃ¨rement sur le thÃ©orÃ¨me de Fermat (1â€“60)
- 1828 MÃ©moire sur la dÃ©termination des fonctions Y et Z que satisfont Ã l'Ã©quation 4(X^n-1) = (X-1)(Y^2+-nZ^2), n Ã©tant un nombre premier 4i-+1 (81â€“100)
- 1833 RÃ©flexions sur diffÃ©rentes maniÃ¨res de dÃ©montrer la thÃ©orie des paralÃ¨les ou le thÃ©orÃ¨me sur la somme des trois angles du triangle, avec 1 planche (367â€“412)
Mistaken portrait
For two centuries, until the recent discovery of the error in 2005, books, paintings and articles have incorrectly shown a (:File:Louis Legendre.jpg|side-view portrait) of the obscure French politician Louis Legendre (1752â€“1797) as that of the mathematician Legendre. 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. The only known portrait of Legendre, recently unearthed, is found in the 1820 book Album de 73 portraits-charge aquarellÃ©s des membres de I'Institut, a book of caricatures of seventy-three members of the Institut de France in Paris by the French artist Julien-Leopold Boilly as shown below:Boilly, Julien-Leopold. (1820). Album de 73 portraits-charge aquarellÃ©s des membres de I'Institut (watercolor portrait #29). Biliotheque de l'Institut de France.{| class="wikitable"center1820 watercolor caricatures of the French mathematicians Adrien-Marie Legendre (left) and Joseph Fourier (right) by French artist Julien-Leopold BoillyJulien-Leopold Boilly File:Louis Legendre.jpgthumb|Side view sketching of French politician Louis LegendreLouis LegendreSee also
- List of things named after Adrien-Marie Legendre
- Associated Legendre polynomials
- Gaussâ€“Legendre algorithm
- Legendre's constant
- Legendre duplication formula
- Legendre's equation in number theory
- Legendre functions
- Legendre's functional relation for elliptic integrals
- Legendre's differential equation
- Legendre's conjecture
- Legendre sieve
- Legendrian submanifold
- Legendre symbol
- Legendre's theorem on spherical triangles
- Saccheriâ€“Legendre theorem
- Gamma function
- Least squares
- Seconds pendulum
Notes
{{reflist|30em}}External links
{{EB1911 poster|Legendre, Adrien Marie}}- {{PlanetMath|urlname=adrienmarielegendre}}
- The True Face of Adrien-Marie Legendre (Portrait of Legendre)
- Biography at Fermat's Last Theorem Blog
- References for Adrien-Marie Legendre
- {{fr icon}} ElÃ©ments de gÃ©omÃ©trie (Paris : F. Didot, 1817)
- Elements of geometry and trigonometry, from the works of A. M. Legendre. Revised and adapted to the course of mathematical instruction in the United States, by Charles Davies. (New York: A. S. Barnes & co., 1858) : English translation of the above text
- MÃ©moires sur la mÃ©thode des moindres quarrÃ©s, et sur l'attraction des ellipsoÃ¯des homogÃ¨nes (1830)
- ThÃ©orie des nombres (Paris : Firmin-Didot, 1830)
- TraitÃ© des fonctions elliptiques et des intÃ©grales eulÃ©riennes (Paris : Huzard-Courcier, 1825â€“1828)
- Nouvelles MÃ©thodes pour la DÃ©termination des Orbites des ComÃ¨tes (Paris : Courcier, 1806)
- Essai sur la ThÃ©orie des Nombres (Paris : Duprat, 1798)
- Exercices de Calcul IntÃ©gral V.3 (Paris : Courcier, 1816)
- Correspondance mathÃ©matique avec Legendre in C. G. J. Jacobis gesammelte Werke (Berlin: 1852)
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