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| [[Image:Jacques Binet.jpg|thumb|right|Jacques Binet]]
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| '''Jacques Philippe Marie Binet''' (February 2, 1786 – May 12, 1856) was a [[France|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 [[Arthur Cayley|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 [[matrix multiplication|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.
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| 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 of France|Charles X]]. In 1823 Binet succeeded [[Delambre]] in the chair of [[astronomy]] at the ''[[Collège de France]]''.<ref>{{cite web |url=http://saints.sqpn.com/ncd01283.htm |title=Jacques Philippe Marie Binet |publisher=New Catholic Dictionary |accessdate=8 June 2013}}</ref> He was made a [[knight|Chevalier]] in the [[Légion d'Honneur]] in 1821, and was elected to the [[Académie des Sciences]] in 1843.
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| ==Binet's Fibonacci number formula==
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| This formula provides the <math>n^\text{th}</math> term in the [[Fibonacci sequence]], and is defined using the recurrence formula:
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| *<math>u_n = u_{n-1} + u_{n-2},\text{ for }n > 1, \,</math>
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| where
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| *<math>u_0 = 0 \, </math>
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| *<math>u_1 = 1 \, </math>
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| : <math>u_n = \frac{(1 + \sqrt{5})^n - (1 - \sqrt{5})^n}{2^n \sqrt{5}}</math> <ref>{{cite web |url=http://mathworld.wolfram.com/BinetsFibonacciNumberFormula.html |title=Binet's Fibonacci Number Formula |author=Weisstein, Eric W |publisher=From MathWorld—A Wolfram Web Resource |accessdate=10 January 2011}}</ref>
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| ==See also==
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| *[[Binet–Cauchy identity]]
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| *[[Binet equation]]
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| *[[Cauchy-Binet formula]]
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| == References ==
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| {{reflist}}
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| * John J O'Connor and Edmund F Robertson, 2005. [http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Binet.html Jacques Philippe Marie Binet]. Retrieved November 21, 2005.
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| * William A. McWorter Jr., 2005. [http://www.cut-the-knot.org/arithmetic/Fibonacci.shtml When the Counting Gets Tough, the Tough Count on Mathematics]. Retrieved November 21, 2005.
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| {{Authority control|VIAF=73844274}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Binet, Jacques Philippe Marie
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = French mathematician
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| | DATE OF BIRTH = February 2, 1786
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| | PLACE OF BIRTH =
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| | DATE OF DEATH = May 12, 1856
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| | PLACE OF DEATH =
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| }}
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| {{DEFAULTSORT:Binet, Jacques Philippe Marie}}
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| [[Category:19th-century French mathematicians]]
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| [[Category:1786 births]]
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| [[Category:1856 deaths]]
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| [[Category:École Polytechnique alumni]]
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| [[Category:Collège de France faculty]]
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Art Director (Video, Television or Period ) Anton from Sussex, usually spends time with interests which includes beachcombing, property developers in singapore and badge collecting. Always loves going to spots like and its Po Delta.
Here is my weblog ... http://www.jugi-zollikon.ch/?author=262419