Adrien-Marie Legendre
From Wikipedia, the free encyclopedia
| Adrien-Marie Legendre | |
| Born | September 18, 1752 Paris, France |
|---|---|
| Died | January 10, 1833 (aged 80) Paris, France |
| Residence |  France |
| Nationality |  French |
| Fields | Mathematician |
| Institutions | École Militaire |
| Alma mater | Collège Mazarin |
| Known for | Lagrangian and elliptic functions |
Adrien-Marie Legendre (September 18, 1752 – January 10, 1833) was a French mathematician. He made important contributions to statistics, number theory, abstract algebra and mathematical analysis.
The Moon crater Legendre is named after him.
[edit] 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, which has broad application in linear regression, signal processing, statistics, and curve fitting. Today, the term "least squares method" is used as a direct translation from the French "méthode des moindres carrés".
In 1830 he gave a proof of Fermat's last theorem for exponent n = 5, which was also proven by 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 1796 conjecture of the Prime number theorem was rigorously proved by Hadamard and de la Vallée-Poussin in 1898.
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 transform, 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.
He also wrote the influential Éléments de géométrie in 1794.
Adrien-Marie was born September 18, 1752. He was raised by his parents who were very wealthy and lived in Paris. He went to college at the Collège Mazarin and was given a top quality education in mathematics and physics. Later on he taught at a military academy out of interest, not because of financial need. Although he did lose his money during the French Revolution.
Adrien-Marie 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. Legendre died in Paris on January 9, 1833, after a long, painful illness. He and his wife had never had children. Legendre's widow made a cult of his memory, carefully preserving his belongings. Upon her death in 1856, she left to the village of Auteuil the last country house where the couple had lived.
[edit] See also
- Gauss-Legendre algorithm
- Legendre's constant
- Legendre's equation
- Legendre polynomials
- Legendre's conjecture
- Legendre transformation
- Legendre symbol
[edit] External links
- The True Face of Adrien-Marie Legendre (Portrait of Legendre)
- O'Connor, John J.; Robertson, Edmund F., "Adrien-Marie Legendre", MacTutor History of Mathematics archive.
- Biography at Fermat's Last Theorem Blog
- References for Adrien-Marie 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 : Firmin-Didot, 1830)
- Traité des fonctions elliptiques et des intégrales eulériennes (Paris : Huzard-Courcier, 1825-1828)
This article incorporates material from Adrien-Marie Legendre on PlanetMath, which is licensed under the GFDL.
