Gabriel Lamé

Gabriel Lamé (July 22, 1795 - May 1, 1870) was a French mathematician.

Biography

Lamé was born in Tours, in today's "département" of Indre-et-Loire.

He became well known for his general theory of curvilinear coordinates and his notation and study of classes of ellipse-like curves, now known as Lamé curves, and defined by the equation:

: $left|,\{xover\; a\},\; ight|^n\; +\; left|,\{yover\; b\},\; ight|^n\; =1$

where "n" is any positive real number.

He is also known for his running time analysis of the Euclidean algorithm. Using Fibonacci numbers, he proved that when finding the greatest common divisor of integers "a" and "b", the algorithm runs in no more than 5"k" steps, where "k" is the number of (decimal) digits of "b". He also proved a special case of Fermat's last theorem. He actually thought that he found a complete proof for the theorem, but his proof was flawed.The Lamé functions are part of the theory of ellipsoidal harmonics.

He worked on a wide variety of different topics. Often problems in the engineering tasks he undertook led him to study mathematical questions. For example his work on the stability of vaults and on the design of suspension bridges led him to work on elasticity theory. In fact this was not a passing interest, for Lamé made substantial contributions to this topic. Another example is his work on the conduction of heat which led him to his theory of curvilinear coordinates.

Curvilinear coordinates proved a very powerful tool in Lamé's hands. He used them to transform Laplace's equation into ellipsoidal coordinates and so separate the variables and solve the resulting equation.

The general Cartesian notation of the super–ellipse form comes from Gabriel Lamé, who generalized the equation for the ellipse.

His most significant contribution to engineering was to accurately define the stresses and capabilities of a press fit joint, such as that seen in a dowel pin in a housing.

Lamé died in Paris in 1870.

Books by G. Lamé

* [http://gallica.bnf.fr/notice?N=FRBNF37268127 Leçons sur les coordonnées curvilignes et leurs diverses applications] (Mallet-Bachelier, 1859)
* [http://gallica.bnf.fr/notice?N=FRBNF37259502 Leçons sur les fonctions inverses des transcendantes et les surfaces isothermes ] (Mallet-Bachelier, 1857)
* [http://gallica.bnf.fr/notice?N=FRBNF38827934 Leçons sur la théorie analytique de la chaleur] (Mallet-Bachelier, 1861)
* [http://gallica.bnf.fr/notice?N=FRBNF37259227 Examen des différentes méthodes employées pour résoudre les problèmes de géométrie ] ( Vve Courcier, 1818)
* [http://gallica.bnf.fr/notice?N=FRBNF37277624 Cours de physique de l'Ecole Polytechnique. Tome premier, Propriétés générales des corps-Théorie physique de la chaleur] (Bachelier, 1840)
* [http://gallica.bnf.fr/notice?N=FRBNF37284136 Cours de physique de l'Ecole Polytechnique. Tome deuxième, Acoustique-Théorie physique de la lumière] (Bachelier, 1840)
* [http://gallica.bnf.fr/notice?N=FRBNF37284138 Cours de physique de l'Ecole Polytechnique. Tome troisième, Electricité-Magnétisme-Courants électriques-Radiations] (Bachelier, 1840)
* [http://books.google.com/books?id=rat4N6-k_QcC&pg=RA1-PR10&dq=Gabriel+Lam%C3%A9&hl=fr#PRA1-PR3,M1 Leçons sur la théorie mathématique de l'élasticité des corps solides] (Bachelier, 1852)

ee also

* Piet Hein
* Lamé's special quartic
* Julius Plücker
* Stefan problem
* Super ellipse
* Lamé parameters

External links

* [http://mathworld.wolfram.com/Superellipse.html Superellipse (MathWorld)]
* [http://www.activeart.de/dim-shops/training/SuperEllipse Lamé's Oval / Superellipse (Java-Applet)]
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