AdrienMarie Legendre (French pronunciation: ) (18 September 1752 – 10 January 1833) was a French mathematician. Legendre made numerous contributions to mathematics. Wellknown and important concepts such as the Legendre polynomials and Legendre transformation are named after him.
Contents

Life 1

Scientific activity 2

Portrait debacle 3

Honors 4

Publications 5

Essay 5.1

Books 5.2

Memoires in Histoire de l'Académie Royale des Sciences 5.3

In Memoires présentés par divers Savants à la l'Académie des Sciences de l'Institut de France 5.4

See also 6

Notes 7

External links 8
Life
AdrienMarie Legendre was born in Paris on 18 September 1752 to a wealthy family. He received his education at the Collège Mazarin in Paris, and defended his thesis in physics and mathematics in 1770. He taught at the École Militaire in Paris from 1775 to 1780 and at the École 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.
The Académie des Sciences made Legendre an adjoint member in 1783 and an associé in 1785. In 1789 he was elected a Fellow of the Royal Society.^{[2]}
Legendre lost his private fortune in 1793 during the French Revolution. That year, he also married MargueriteClaudine 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 1815, Legendre served as mathematics examiner for graduating artillery students at the École Militaire. In 1824, Legendre was denied his pension from the École Militaire because he refused to vote for the government candidate at the Institut National—the comte de Corbière, Ministre de L'Intérieur of the ultraroyalist government. His pension was partially reinstated with the change in government in 1828. In 1831 he was made an officer of the Légion d'Honneur.
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.
Scientific activity
Most of his work was brought to perfection by others: his work on roots of polynomials inspired Galois theory; Abel's work on elliptic functions was built on Legendre's; 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,^{[3]} 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 "méthode des moindres carrés".
Around 1811 he named the gamma function and introduced the symbol Γ normalizing it to Γ(n+1) = n!.
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 ValléePoussin 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 namegiver 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 Éléments 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 from Euclid's Elements to create a more effective textbook.
Portrait debacle
For two centuries, until the recent discovery of the error in 2005, books, paintings and articles have incorrectly shown a sideview portrait of the obscure French politician Louis Legendre (1752–1797) as that of the mathematician Legendre. The error arose from the fact that the sketch was labelled simply "Legendre". The only known portrait of Legendre, recently unearthed, is found in the 1820 book Album de 73 portraitscharge aquarellés des membres de I’Institut, a book of caricatures of seventythree members of the Institut de France in Paris by the French artist JulienLeopold Boilly as shown below:^{[4]}
1820 watercolor caricatures of the French mathematicians AdrienMarie Legendre (left) and Joseph Fourier (right) by French artist JulienLeopold Boilly, watercolor portrait numbers 29 and 30 of Album de 73 portraitscharge aquarellés des membres de I’Institut. ^{[4]}

Side view sketching of French politician Louis Legendre (1752–1797), whose portrait has been mistakenly used, for nearly 200 years, to represent French mathematician AdrienMarie Legendre, i.e. up until 2005 when the mistake was discovered. ^{[1]}

Honors
Publications
Essay

1782 Recherches sur la trajectoire des projectiles dans les milieux résistants (prize on projectiles offered by the Berlin Academy)
Books

Eléments de géométrie, textbook 1794

Essai sur la Théorie des Nombres 17978 ("An VI"), 2nd ed. in two vol. 1808, 3rd ed. in 2 vol. 1830

Nouvelles Méthodes pour la Détermination des Orbites des Comètes, 1805

Exercices de Calcul Intégral, book in three volumes 1811, 1817, and 1819

Traité des Fonctions Elliptiques, book in three volumes 1825, 1826, and 1830
Memoires in Histoire de l'Académie Royale des Sciences

1783 Sur l'attraction des Sphéroïdes homogènes (said to contain Legendre polys)

1784 Recherches sur la figure des Planètes p. 370

1785 Recherches d'analyse indéterminée p. 465 (number theory)

1786 Mémoire sur la manière de distinguer les Maxima des Minima dans le Calcul des Variations p. 7 (as Legendre)

1786 Mémoire sur les Intégrations par arcs d'ellipse p. 616 (as le Gendre)

1786 Second Mémoire sur les Intégrations par arcs d'ellipse p. 644

1787 L’intégration de quelques équations aux différences Partielles (Legendre transform)
In Memoires présentés par divers Savants à la l'Académie des Sciences de l'Institut de France

1806 Nouvelle formula pour réduire en distances vraies les distances apparentes de la Lune au Soleil ou à une étoile (3054)

1807 Analyse des triangles tracés sur la surface d'un sphéroide (130161)

Tome 10 Recherches sur diverses sortes d'intégrales défines (416509)

1819 Méthode des moindres carrés pour trouver le milieu le plus probable entre les résultats de différentes observations (149154), Mémoire sur l'attraction des ellipsoïdes homogènes (155183)

1823 Recherches sur quelques objets d'Analyse indéterminée et particulièrement sur le théorème de Fermat (160)

1828 Mémoire sur la détermination des fonctions Y et Z que satisfont à l'équation 4(X^n1) = (X1)(Y^2+nZ^2), n étant un nombre premier 4i+1 (81100)

1833 Réflexions sur différentes manières de démontrer la théorie des paralèles ou le théorème sur la somme des trois angles du triangle, avec 1 planche (367412)
See also
Notes

^ ^{a} ^{b} Duren, Peter (December 2009). "Changing Faces: The Mistaken Portrait of Legendre".

^ "Library and Archive". Royal Society. Retrieved 20120806.

^ Stephen M. Stigler (1981). "Gauss and the Invention of Least Squares". Ann. Statist. 9 (3): 465–474.

^ ^{a} ^{b} Boilly, JulienLeopold. (1820). Album de 73 portraitscharge aquarellés des membres de I’Institut (watercolor portrait #29). Biliotheque de l’Institut de France.

^ "Book of Members, 1780–2010: Chapter L". American Academy of Arts and Sciences. Retrieved 28 July 2014.
External links

The True Face of AdrienMarie Legendre (Portrait of Legendre)

.

Biography at Fermat's Last Theorem Blog

References for AdrienMarie Legendre

(French) Eléments de géométrie (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

Mémoires sur la méthode des moindres quarrés, et sur l'attraction des ellipsoïdes homogènes (1830)

Théorie des nombres (Paris : FirminDidot, 1830)

Traité des fonctions elliptiques et des intégrales eulériennes (Paris : HuzardCourcier, 1825–1828)

Nouvelles Méthodes pour la Détermination des Orbites des Comètes (Paris : Courcier, 1806)

Essai sur la Théorie des Nombres (Paris : Duprat, 1798)

Exercices de Calcul Intégral V.3 (Paris : Courcier, 1816)

Correspondance mathématique avec Legendre in C. G. J. Jacobis gesammelte Werke (Berlin: 1852)
This article incorporates material from AdrienMarie Legendre on PlanetMath, which is licensed under the Creative Commons Attribution/ShareAlike License.
This article was sourced from Creative Commons AttributionShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, EGovernment Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a nonprofit organization.