Editing Gabriel Lamé (section)

==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 curve]]s or superellipses, and defined by the equation:

: <math>\left|\,{x\over a}\,\right|^n + \left|\,{y\over b}\,\right|^n = 1</math>

where ''n'' is any positive [[real number]].

He is also known for his [[running time]] analysis of the [[Euclidean algorithm]], marking the beginning of [[computational complexity theory]]. In 1844, using [[Fibonacci number]]s, he [[mathematical proof|proved]] that when finding the [[greatest common divisor]] of [[integer]]s ''a'' and ''b'', the algorithm runs in no more than 5''k'' steps, where ''k'' is the number of (decimal) [[numerical digit|digit]]s 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 function]]s are part of the theory of [[ellipsoidal harmonic]]s.

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.

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.

In 1854, he was elected a foreign member of the [[Royal Swedish Academy of Sciences]].

Lamé died in [[Paris]] in 1870.  His name is one of the [[List of the 72 names on the Eiffel Tower|72 names inscribed on the Eiffel Tower]].