Jacques Philippe Marie Binet (; 2 February 1786 – 12 May 1856) 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 O ...

physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate caus ...

and

astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, moons, comets and galaxies – in either obse ...

born in

Rennes Rennes (; br, Roazhon ; Gallo: ''Resnn''; ) is a city in the east of Brittany in northwestern France at the confluence of the Ille and the Vilaine. Rennes is the prefecture of the region of Brittany, as well as the Ille-et-Vilaine departmen ...

; he 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. S ...

, France, in 1856. He made significant contributions to

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathe ...

, and the mathematical foundations of

matrix algebra In abstract algebra, a matrix ring is a set of matrices with entries in a ring ''R'' that form a ring under matrix addition and matrix multiplication . The set of all matrices with entries in ''R'' is a matrix ring denoted M''n''(''R'')Lang, '' ...

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 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 in closed form is named in his honour, although the same result was known to

Abraham de Moivre Abraham de Moivre FRS (; 26 May 166727 November 1754) was a French mathematician known for de Moivre's formula, a formula that links complex numbers and trigonometry, and for his work on the normal distribution and probability theory. He move ...

a century earlier.

Career

Binet graduated from l'

École Polytechnique École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savo ...

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 13 November 1830, when he was dismissed by the recently sworn in

King Louis-Philippe Louis Philippe (6 October 1773 – 26 August 1850) was King of the French from 1830 to 1848, and the penultimate monarch of France. As Louis Philippe, Duke of Chartres, he distinguished himself commanding troops during the Revolutionary War ...

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 Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, galax ...

at the ''

Collège de France The Collège de France (), formerly known as the ''Collège Royal'' or as the ''Collège impérial'' founded in 1530 by François I, is a higher education and research establishment ('' grand établissement'') in France. It is located in Paris ...

''. He was made a

Chevalier Chevalier may refer to: Honours Belgium * a rank in the Belgian Order of the Crown * a rank in the Belgian Order of Leopold * a rank in the Belgian Order of Leopold II * a title in the Belgian nobility France * a rank in the French Legion d' ...

in the

Légion d'Honneur The National Order of the Legion of Honour (french: Ordre national de la Légion d'honneur), formerly the Royal Order of the Legion of Honour ('), is the highest French order of merit, both military and civil. Established in 1802 by Napoleon ...

in 1821, and was elected to the

Académie des Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at the ...

in 1843.

Binet's Fibonacci number formula

The

Fibonacci sequence 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 ...

is defined by *

u_0 = 0

u_1 = 1

u_n = u_ + u_,\textn > 1

Binet's formula provides a

closed-form expression In mathematics, a closed-form expression is a mathematical expression that uses a finite number of standard operations. It may contain constants, variables, certain well-known operations (e.g., + − × ÷), and functions (e.g., ''n''th r ...

for the

n^\text

term in this sequence: :

u_n = \frac

Notes

References

* John J O'Connor and Edmund F Robertson, 2005
Jacques Philippe Marie Binet
Retrieved November 21, 2005. * William A. McWorter Jr., 2005
When the Counting Gets Tough, the Tough Count on Mathematics
Retrieved November 21, 2005. {{DEFAULTSORT:Binet, Jacques Philippe Marie 19th-century French mathematicians 1786 births 1856 deaths École Polytechnique alumni Collège de France faculty French Roman Catholics Linear algebraists Members of the French Academy of Sciences

Career

Binet's Fibonacci number formula

See also

Notes

References