Jacques Philippe Marie Binet
Encyclopedia
Jacques Philippe Marie Binet (February 2, 1786 – May 12, 1856) was a French
mathematician, physicist and astronomer born in Rennes
; he died in Paris
, France
, in 1856. He made significant contributions to number theory
, and the mathematical foundations of matrix algebra
which would later lead to important contributions by Cayley
and others. In his memoir on the theory of the conjugate axis and of the moment of inertia of bodies he enumerated the principle now known as Binet's theorem. He is also recognized as the first to describe the rule for multiplying matrices
in 1812, and Binet's formula expressing Fibonacci number
s in closed form is named in his honour, although the same result was known to Abraham de Moivre
a century earlier.
Binet graduated from l'École Polytechnique
in 1806, and returned as a teacher in 1807. He advanced in position until 1816 when he became an inspector of studies at l'École. He held this post until November 13, 1830, when he was dismissed by the recently crowned King Louis-Philippe of France, probably because of Binet's strong support of the previous King, Charles X
. In 1823 Binet succeeded Delambre in the chair of astronomy
at the Collège de France
. He was made a Chevalier
in the Légion d'Honneur
in 1821, and was elected to the Académie des Sciences in 1843.
term in the Fibonacci Series, and is defined using the recurrence formula:
where
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, physicist and astronomer born in Rennes
Rennes
Rennes is a city in the east of Brittany in northwestern France. Rennes is the capital of the region of Brittany, as well as the Ille-et-Vilaine department.-History:...
; he 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...
, France
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...
, in 1856. He made significant contributions to number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, and the mathematical foundations of matrix algebra
Matrix algebra
Matrix algebra may refer to:*Matrix theory, is the branch of mathematics that studies matrices*Matrix ring, thought of as an algebra over a field or a commutative ring...
which would later lead to important contributions by Cayley
Arthur Cayley
Arthur Cayley F.R.S. was a British mathematician. He helped found the modern British school of pure mathematics....
and others. In his memoir on the theory of the conjugate axis and of the moment of inertia of bodies he enumerated the principle now known as Binet's theorem. He is also recognized as the first to describe the rule for multiplying matrices
Matrix multiplication
In mathematics, matrix multiplication is a binary operation that takes a pair of matrices, and produces another matrix. If A is an n-by-m matrix and B is an m-by-p matrix, the result AB of their multiplication is an n-by-p matrix defined only if the number of columns m of the left matrix A is the...
in 1812, and Binet's formula expressing 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 in closed form is named in his honour, although the same result was known to Abraham de Moivre
Abraham de Moivre
Abraham de Moivre was a French mathematician famous for de Moivre's formula, which links complex numbers and trigonometry, and for his work on the normal distribution and probability theory. He was a friend of Isaac Newton, Edmund Halley, and James Stirling...
a century earlier.
Binet graduated from l'École Polytechnique
École Polytechnique
The École Polytechnique is a state-run institution of higher education and research in Palaiseau, Essonne, France, near Paris. Polytechnique is renowned for its four year undergraduate/graduate Master's program...
in 1806, and returned as a teacher in 1807. He advanced in position until 1816 when he became an inspector of studies at l'École. He held this post until November 13, 1830, when he was dismissed by the recently crowned King Louis-Philippe of France, probably because of Binet's strong support of the previous King, Charles X
Charles X of France
Charles X was known for most of his life as the Comte d'Artois before he reigned as King of France and of Navarre from 16 September 1824 until 2 August 1830. A younger brother to Kings Louis XVI and Louis XVIII, he supported the latter in exile and eventually succeeded him...
. In 1823 Binet succeeded Delambre in the chair of astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
at the Collège de France
Collège de France
The Collège de France is a higher education and research establishment located in Paris, France, in the 5th arrondissement, or Latin Quarter, across the street from the historical campus of La Sorbonne at the intersection of Rue Saint-Jacques and Rue des Écoles...
. He was made a Chevalier
Knight
A knight was a member of a class of lower nobility in the High Middle Ages.By the Late Middle Ages, the rank had become associated with the ideals of chivalry, a code of conduct for the perfect courtly Christian warrior....
in the Légion d'Honneur
Légion d'honneur
The Legion of Honour, or in full the National Order of the Legion of Honour is a French order established by Napoleon Bonaparte, First Consul of the Consulat which succeeded to the First Republic, on 19 May 1802...
in 1821, and was elected to the Académie des Sciences in 1843.
- Portions from the 1910 New Catholic Dictionary
Binet's Fibonacci Number Formula
This formula provides the term in the Fibonacci Series, and is defined using the recurrence formula:
, for 
,
where
