Legendre, Adrien-Marie

(1752-1833)

   mathematician

   Born in Paris, Adrien-Marie Legendre was commissioned by the Convention at the time of the revolution of 1789 to work on geodesics and, in doing so, enriched the study of trigonometry, developing a method, for instance, of calculating the area of a spherical triangle and studying geodesic lines. His Éléments de géométrie (1794) has historical interest because of his return to the mathematical principles of antiquity. He demonstrated in particular the incommensurability of pi (already known) and that of pi squared. His Théorie des nombres (1798) remains a classic, containing remarkable results of the law of reciprocity of quadratic residuals. in 1806, he showed the method of least squares (without being aware of the work of C. F. Gauss). in his most important work, Traité des fonctions élliptiques et des intégrals eulériennes (1825), Legendre demonstrated that elliptical integrals can always be reduced to three forms, and he calculated the extended numerical tables. Also, in Figure des planètes (1782), he introduced the polynomials that bear his name. Legendre was named to the Academy of Sciences in 1783.