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, mathematical structure, structure, space, Mathematica ...
who contributed to the theory of
partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.
The function is often thought of as an "unknown" that solves the equation, similar to ho ...
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 invertible, l ...
, 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 by prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mechani ...
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 str ...
elaborate the mathematical abstractions).
Biography
Lamé was born in
Tours
Tours ( ; ) is the largest city in the region of Centre-Val de Loire, France. It is the Prefectures in France, prefecture of the Departments of France, department of Indre-et-Loire. The Communes of France, commune of Tours had 136,463 inhabita ...
, 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 invertible, l ...]
and his notation and study of classes of ellipse-like curves, now known as
Lamé curves 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 duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every re ...
.
He is also known for his
running time 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 a ...
, 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 explores the relationships between these classifications. A computational problem ...
. In 1844, using
Fibonacci number
In mathematics, the Fibonacci sequence is a Integer sequence, sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted . Many w ...
s, he
proved that when finding the
greatest common divisor
In mathematics, the greatest common divisor (GCD), also known as greatest common factor (GCF), of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers , , the greatest co ...
of
integer
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...
s ''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 number, positive integers , , and satisfy the equation for any integer value of greater than . The cases ...
. 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
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 invertible, l ...
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 in 1786. This is often written as
\nabla^2\! f = 0 or \Delta f = 0,
where \Delt ...
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
The Royal Swedish Academy of Sciences () is one of the Swedish Royal Academies, royal academies of Sweden. Founded on 2 June 1739, it is an independent, non-governmental scientific organization that takes special responsibility for promoting nat ...
.
Lamé died in
Paris
Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...
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’s Theorem
*
Euclidean algorithm (Algorithmic efficiency)
*
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 di ...
*
Helmholtz equation
In mathematics, the Helmholtz equation is the eigenvalue problem for the Laplace operator. It corresponds to the elliptic partial differential equation:
\nabla^2 f = -k^2 f,
where is the Laplace operator, is the eigenvalue, and is the (eigen)fun ...
*
Proof of Fermat's Last Theorem for specific exponents
*
Stefan problem
External links
Superellipse (MathWorld)Lamé's Oval / Superellipse (Java-applet)*
{{DEFAULTSORT:Lame, Gabriel
École Polytechnique alumni
Mines Paris - PSL 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