Jacques Philippe Marie Binet

Jacques Binet

Jacques Philippe Marie Binet (born February 2, 1786 in Rennes , † May 12, 1856 in Paris ) was a French mathematician .

Binet was from November 22, 1804 until his graduation in 1806 at the École polytechnique and then worked at the École Nationale des Ponts et Chaussées . From 1807 he taught at the École Polytechnique and in 1823 became professor of astronomy at the Collège de France . In 1843 he was elected a member of the Académie des Sciences .

Binet is promised the basics of matrix theory , such as the definition of matrix multiplication . According to him, are Cauchy-Binet formula named, and a non-recursive formula for the nth term of the Fibonacci sequence , which he found in 1843: ${\ displaystyle u_ {n}}$

{\ displaystyle u_ {n} = {\ frac {1} {\ sqrt {5}}} \ left (\ left ({\ frac {1 + {\ sqrt {5}}} {2}} \ right) ^ {n} - \ left ({\ frac {1 - {\ sqrt {5}}} {2}} \ right) ^ {n} \ right)}

However, this formula was already known to Leonhard Euler , Daniel Bernoulli and Abraham de Moivre .

According to Binet, the sum of two main moments of inertia of a body is always greater than its other moments of inertia. Furthermore, all main moments of inertia are always sums of two Binet moments of inertia .

Web links

John J. O'Connor, Edmund F. Robertson : Jacques Philippe Marie Binet. In: MacTutor History of Mathematics archive .

Individual evidence

^ Weisstein, Eric W: Binet's Fibonacci Number Formula . MathWorld. Retrieved January 10, 2011.
↑ Richard Gammel: The top . Its theory and its applications. 2nd Edition. tape 2 . Springer, Berlin, Göttingen, Heidelberg 1950, DNB 451641280 , p. 26-29 .

personal data
SURNAME	Binet, Jacques Philippe Marie
BRIEF DESCRIPTION	French mathematician
DATE OF BIRTH	February 2, 1786
PLACE OF BIRTH	Rennes
DATE OF DEATH	May 12, 1856
Place of death	Paris

[1] Weisstein, Eric W: Binet's Fibonacci Number Formula . MathWorld. Retrieved January 10, 2011.

[2] Richard Gammel: The top . Its theory and its applications. 2nd Edition. tape 2 . Springer, Berlin, Göttingen, Heidelberg 1950, DNB 451641280 , p. 26-29 .