FORUM, Forum Discussion, Forum Gratuit, Nom de domaine, Nom de domaine gratuit, Redirection gratuite,

Forum Physiks Causali Administrators :saucer, Iseason, us2u
Forum Physiks Causali
Not logged | Login
Online:There are 5 online. Click here to see more
Register Register | Profile Profile | Private messages Private messages | Search Search | Online Online | Help Help | Create a free blog

forum Forum index forumLegendre forumLegendre

forumEmail Notification | forumWarn moderators
Pages : Prec. 1 2
Author : Topic: Legendre  Bottom
 saucer
 admin
 Posts : 673
 A Good Tautology is Hard to Find!
 saucer
  Posted 19/11/2007 02:53:09 PM
Profile Edit this message Quote this message /!\ Delete the topicSent a email to saucerSend a private message to saucer
-



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 also wrote the influential Éléments de géométrie in 1794.





-

 saucer
 admin
 Posts : 673
 A Good Tautology is Hard to Find!
 saucer
  Posted 20/01/2008 06:11:39 AM
Profile Edit this message Quote this message /!\ Delete the topicSent a email to saucerSend a private message to saucer

 saucer
 admin
 Posts : 673
 A Good Tautology is Hard to Find!
 saucer
  Posted 20/02/2008 06:32:24 AM
Profile Edit this message Quote this message /!\ Delete the topicSent a email to saucerSend a private message to saucer

 zee
 Posts : 115
  Posted 20/04/2008 09:19:07 AM
Profile Edit this message Quote this message /!\ Delete the topicSend a private message to zee
Elliptic Functions

This is the subject with which Legendre's name will always be most closely connected, and his researches upon it extend over a period of more than forty years. His first published writings upon the subject consist of two papers in the Memoires de l'Academie Francaise for 1786 upon elliptic arcs. In 1792 he presented to the Academy a memoir on elliptic transcendents. The contents of these memoirs are included in the first volume of his Exercices de calcul integral (1811). The third volume (1816) contains the very elaborate and now well-known tables of the elliptic integrals which were calculated by Legendre himself, with an account of the mode of their construction. In 1827 appeared the Traite des fonctions elliptiques (2 vols., the first dated 1825, the second 1826); a great part of the first volume agrees very closely with the contents of the Exercices; the tables, &c., are given in the second volume. Three supplements, relating to the researches of N. H. Abel and C. G. J. Jacobi, were published in 1828-1832, and form a third volume. Legendre had pursued the subject which would now be called elliptic integrals alone from 1786 to 1827, the results of his labours having been almost entirely neglected by his contemporaries, but his work had scarcely appeared in 1827 when the discoveries which were independently made by the two young and as yet unknown mathematicians Abel and Jacobi placed the subject on a new basis, and revolutionized it completely. The readiness with which Legendre, who was then seventy-six years of age, welcomed these important researches, that quite overshadowed his own, and included them in successive supplements to his work, does the highest honour to him.  

--Last edited by zee on 2008-04-20 09:23:52 --

 saucer
 admin
 Posts : 673
 A Good Tautology is Hard to Find!
 saucer
  Posted 28/03/2009 03:25:26 PM
Profile Edit this message Quote this message /!\ Delete the topicSent a email to saucerSend a private message to saucer

Pages : Prec. 1 2

forum Forum index forumLegendre forumLegendre
top
Go to :
  Add a quick reply

Add a quick reply

Get a free forum!
AceBoard Free Forum v 5.3
Download Premium Web Templates!