Gabriel Lamé (22 July 1795 – 1 May 1870) was a French
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
who contributed to the theory of
partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function.
The function is often thought of as an "unknown" to be solved for, similarly to h ...
s by the use of
curvilinear coordinates
In geometry, 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 inve ...
, and the mathematical theory of
elasticity (for which
linear elasticity
Linear elasticity is a mathematical model of how solid objects deform and become internally stressed due to prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mec ...
and
finite strain theory
In continuum mechanics, the finite strain theory—also called large strain theory, or large deformation theory—deals with deformations in which strains and/or rotations are large enough to invalidate assumptions inherent in infinitesimal strai ...
elaborate the mathematical abstractions).
Biography
Lamé was born in
Tours
Tours ( , ) is one of the largest cities in the region of Centre-Val de Loire, France. It is the prefecture of the department of Indre-et-Loire. The commune of Tours had 136,463 inhabitants as of 2018 while the population of the whole metro ...
, in today's ''département'' of
Indre-et-Loire
Indre-et-Loire () is a department in west-central France named after the Indre River and Loire River. In 2019, it had a population of 610,079.[curvilinear coordinates
In geometry, 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 inve ...]
and his notation and study of classes of ellipse-like curves, now known as
Lamé curve
A superellipse, also known as a Lamé curve after Gabriel Lamé, is a closed curve resembling the ellipse, retaining the geometric features of semi-major axis and semi-minor axis, and symmetry about them, but a different overall shape.
In the C ...
s or superellipses, and defined by the equation:
:
where ''n'' is any positive
real number
In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every ...
.
He is also known for his
running time
In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by t ...
analysis of the
Euclidean algorithm
In mathematics, the Euclidean algorithm,Some widely used textbooks, such as I. N. Herstein's ''Topics in Algebra'' and Serge Lang's ''Algebra'', use the term "Euclidean algorithm" to refer to Euclidean division or Euclid's algorithm, is an e ...
, marking the beginning of
computational complexity theory
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved ...
. Using
Fibonacci number
In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from ...
s, he proved that when finding the
greatest common divisor
In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers ''x'', ''y'', the greatest common divisor of ''x'' and ''y'' is ...
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
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers , , and satisfy the equation for any integer value of greater than 2. The cases and have been ...
. He actually thought that he found a complete proof for the theorem, but his proof was flawed.
The
Lamé function
In mathematics, a Lamé function, or ellipsoidal harmonic 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 variable ...
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
In geometry, 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 inve ...
proved a very powerful tool in Lamé's hands. He used them to transform
Laplace's equation
In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties. This is often written as
\nabla^2\! f = 0 or \Delta f = 0,
where \Delta = \na ...
into
ellipsoidal coordinates
Ellipsoidal coordinates are a three-dimensional orthogonal coordinate system (\lambda, \mu, \nu) that generalizes the two-dimensional elliptic coordinate system. Unlike most three-dimensional orthogonal coordinate systems that feature quadratic ...
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
The Royal Swedish Academy of Sciences ( sv, Kungliga Vetenskapsakademien) is one of the royal academies of Sweden. Founded on 2 June 1739, it is an independent, non-governmental scientific organization that takes special responsibility for prom ...
.
Lamé died in
Paris
Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. Si ...
in 1870. His name is one of the
72 names inscribed on the Eiffel Tower.
Books
* 1818
Examen des différentes méthodes employées pour résoudre les problèmes de géométrie ( Vve Courcier)
* 1840
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)
* 1852
Leçons sur la théorie mathématique de l'élasticité des corps solides(Bachelier)
* 1857
Leçons sur les fonctions inverses des transcendantes et les surfaces isothermes (Mallet-Bachelier)
* 1859
Leçons sur les coordonnées curvilignes et leurs diverses applications(Mallet-Bachelier)
* 1861
Leçons sur la théorie analytique de la chaleur(Mallet-Bachelier)
See also
*
Lamé crater
*
Piet Hein
*
Julius Plücker
Julius Plücker (16 June 1801 – 22 May 1868) 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 dis ...
*
Helmholtz equation
In mathematics, the eigenvalue problem for the Laplace operator is known as the Helmholtz equation. It corresponds to the linear partial differential equation
\nabla^2 f = -k^2 f,
where is the Laplace operator (or "Laplacian"), is the eigenvalu ...
*
Proof of Fermat's Last Theorem for specific exponents
*
Stefan problem
In mathematics and its applications, particularly to phase transitions in matter, a Stefan problem is a particular kind of boundary value problem for a system of partial differential equations (PDE), in which the boundary between the phases can m ...
External links
Superellipse (MathWorld)Lamé's Oval / Superellipse (Java-applet)*
{{DEFAULTSORT:Lame, Gabriel
École Polytechnique alumni
Mines ParisTech alumni
Corps des mines
1795 births
1870 deaths
Scientists from Tours, France
Members of the French Academy of Sciences
Members of the Royal Swedish Academy of Sciences
19th-century French mathematicians