Gabriel Lamé
Encyclopedia
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
.
Biography
Lamé was born in ToursTours
Tours is a city in central France, the capital of the Indre-et-Loire department.It is located on the lower reaches of the river Loire, between Orléans and the Atlantic coast. Touraine, the region around Tours, is known for its wines, the alleged perfection of its local spoken French, and for the...
, in today's département of Indre-et-Loire
Indre-et-Loire
Indre-et-Loire is a department in west-central France named after the Indre and the Loire rivers.-History:Indre-et-Loire is one of the original 83 départements created during the French Revolution on 4 March 1790...
.
He became well known for his general theory of curvilinear coordinates
Curvilinear coordinates
Curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. These coordinates may be derived from a set of Cartesian coordinates by using a transformation that is locally invertible at each point. This means that one can convert a point given...
and his notation and study of classes of ellipse-like curves, now known as Lamé curves, and defined by the equation:
where n is any positive real number
Real number
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...
.
He is also known for his running time
Running Time
Running Time may refer to:* Running Time * see Analysis of algorithms...
analysis of the Euclidean algorithm
Euclidean algorithm
In mathematics, the Euclidean algorithm is an efficient method for computing the greatest common divisor of two integers, also known as the greatest common factor or highest common factor...
. Using Fibonacci number
Fibonacci number
In mathematics, the Fibonacci numbers are the numbers in the following integer sequence:0,\;1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\; \ldots\; ....
s, he proved that when finding the greatest common divisor
Greatest common divisor
In mathematics, the greatest common divisor , also known as the greatest common factor , or highest common factor , of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder.For example, the GCD of 8 and 12 is 4.This notion can be extended to...
of integers a and b, the algorithm runs in no more than 5k steps, where k is the number of (decimal) digit
Numerical digit
A digit is a symbol used in combinations to represent numbers in positional numeral systems. The name "digit" comes from the fact that the 10 digits of the hands correspond to the 10 symbols of the common base 10 number system, i.e...
s of b. He also proved a special case of Fermat's last theorem
Fermat's Last Theorem
In number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two....
. He actually thought that he found a complete proof for the theorem, but his proof was flawed.
The Lamé function
Lamé function
In mathematics, a Lamé function is a solution of Lamé's equation, a second-order ordinary differential equation. It was introduced in the paper . Lamé's equation appears in the method of separation of variables applied to the Laplace equation in elliptic coordinates...
s 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 superellipse 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.
In 1854, he was elected a foreign member of the Royal Swedish Academy of Sciences
Royal Swedish Academy of Sciences
The Royal Swedish Academy of Sciences or Kungliga Vetenskapsakademien is one of the Royal Academies of Sweden. The Academy is an independent, non-governmental scientific organization which acts to promote the sciences, primarily the natural sciences and mathematics.The Academy was founded on 2...
.
Lamé died in Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
in 1870. His name is one of the 72 names inscribed on the Eiffel Tower.
Books by G. Lamé
- Leçons sur les coordonnées curvilignes et leurs diverses applications (Mallet-Bachelier, 1859)
- Leçons sur les fonctions inverses des transcendantes et les surfaces isothermes (Mallet-Bachelier, 1857)
- Leçons sur la théorie analytique de la chaleur (Mallet-Bachelier, 1861)
- Examen des différentes méthodes employées pour résoudre les problèmes de géométrie ( Vve Courcier, 1818)
- Cours de physique de l'Ecole Polytechnique. Tome premier, Propriétés générales des corps—Théorie physique de la chaleur (Bachelier, 1840)
- Cours de physique de l'Ecole Polytechnique. Tome deuxième, Acoustique—Théorie physique de la lumière (Bachelier, 1840)
- Cours de physique de l'Ecole Polytechnique. Tome troisième, Electricité-Magnétisme-Courants électriques-Radiations (Bachelier, 1840)
- Leçons sur la théorie mathématique de l'élasticité des corps solides (Bachelier, 1852)
See also
- Lamé crater
- Piet HeinPiet Hein (Denmark)Piet Hein was a Danish scientist, mathematician, inventor, designer, author, and poet, often writing under the Old Norse pseudonym "Kumbel" meaning "tombstone"...
- Lamé's special quartic
- Julius PlückerJulius PlückerJulius Plücker was a German mathematician and physicist. He made fundamental contributions to the field of analytical geometry and was a pioneer in the investigations of cathode rays that led eventually to the discovery of the electron. He also vastly extended the study of Lamé curves.- Early...
- Stefan problemStefan problemIn mathematics and its applications, particularly to phase transitions in matter, a Stefan problem is a particular kind of boundary value problem for a partial differential equation , adapted to the case in which a phase boundary can move with time...
- Super ellipse
- Lamé parameters