Editing Gabriel Lamé

{{Short description|French mathematician (1795–1870)}}
{{Use dmy dates|date=May 2021}}
{{Expand French|Gabriel Lamé|topic=bio|date=December 2012}}
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| name        = Gabriel Lamé
| image       = Gabriel-Lamé.jpeg
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| birth_date  = {{birth date |df=y|1795|7|22}}
| birth_place = [[Tours]], France
| death_date  = {{death date and age |df=y|1870|5|1 |1795|7|22}}
| death_place = [[Paris]], France
| fields      = [[Mathematics]]
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| known_for   = [[Euclidean algorithm]]<br>[[Curvilinear_coordinates#Coordinates,_basis,_and_vectors|Lamé coefficients]]<br>[[Superellipse|Lamé curve]]<br>[[Lamé function]]<br>[[Lamé parameters]]<br>[[Lamé's special quartic]]
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'''Gabriel Lamé''' (22 July 1795 – 1 May 1870) was a French [[mathematician]] who contributed to the theory of [[partial differential equation]]s by the use of [[curvilinear coordinates]], and the mathematical theory of [[elasticity (physics)|elasticity]] (for which [[linear elasticity]] and [[finite strain theory]] elaborate the mathematical abstractions).

==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]].

==Books==

* 1818: [http://gallica.bnf.fr/notice?N=FRBNF37259227 Examen des différentes méthodes employées pour résoudre les problèmes de géométrie ] ( Vve Courcier)
* 1840: [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)
* 1852: [https://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)
* 1857: [http://gallica.bnf.fr/notice?N=FRBNF37259502   Leçons sur les fonctions inverses des transcendantes et les surfaces isothermes ]  (Mallet-Bachelier)
* 1859: [http://gallica.bnf.fr/notice?N=FRBNF37268127 Leçons sur les coordonnées curvilignes et leurs diverses applications] (Mallet-Bachelier)
* 1861: [http://gallica.bnf.fr/notice?N=FRBNF38827934 Leçons sur la théorie analytique de la chaleur] (Mallet-Bachelier)

==See also==
* [[Lamé’s Theorem]]
* [[Euclidean algorithm#Algorithmic efficiency|Euclidean algorithm (Algorithmic efficiency)]]
* [[Lamé crater]]
* [[Piet Hein (Denmark)|Piet Hein]]
* [[Julius Plücker]]
* [[Helmholtz equation]]
* [[Proof of Fermat's Last Theorem for specific exponents]]
* [[Stefan problem]]

==External links==
* [http://mathworld.wolfram.com/Superellipse.html Superellipse (MathWorld)]
* [https://web.archive.org/web/20090227141121/http://www.activeart.de/dim-shops/training/SuperEllipse/ Lamé's Oval / Superellipse (Java-applet)]
* {{MacTutor Biography|id=Lame}}

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{{DEFAULTSORT:Lame, Gabriel}}
[[Category:École Polytechnique alumni]]
[[Category:Mines Paris - PSL alumni]]
[[Category:Corps des mines]]
[[Category:1795 births]]
[[Category:1870 deaths]]
[[Category:Scientists from Tours, France]]
[[Category:Members of the French Academy of Sciences]]
[[Category:Members of the Royal Swedish Academy of Sciences]]
[[Category:19th-century French mathematicians]]