Albert Girard
Encyclopedia
Albert Girard was a French
-born mathematician
. He studied at the University of Leiden. He "had early thoughts on the fundamental theorem of algebra
" and gave the inductive definition for the Fibonacci number
s.
He was the first to use the abbreviations 'sin', 'cos' and 'tan' for the trigonometric functions in a treatise. Girard was the first to state, in 1632, that each prime of the form 1 mod 4 was the sum of two squares. (See Fermat's theorem on sums of two squares.)
In the opinion of Charles Hutton
, Girard was
This had previously been given by François Viète
for positive roots, and is today called Viète's formulas, but Viète did not give these for general roots.
In his paper, Funkhouser locates the work of Girard in the history of the study of equations using symmetric function
s. In his work on the theory of equations
, Lagrange
cited Girard. Still later, in the nineteenth century, this work eventuated in the creation of group theory
by Cauchy, Galois and others.
Girard also showed how the area of a spherical triangle depends on its interior angles. The result is called Girard's theorem.
Girard was a lute
nist and mentioned having written a treatise on music, though this was never published.
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...
-born mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He studied at the University of Leiden. He "had early thoughts on the fundamental theorem of algebra
Fundamental theorem of algebra
The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root...
" and gave the inductive definition for the 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.
He was the first to use the abbreviations 'sin', 'cos' and 'tan' for the trigonometric functions in a treatise. Girard was the first to state, in 1632, that each prime of the form 1 mod 4 was the sum of two squares. (See Fermat's theorem on sums of two squares.)
In the opinion of Charles Hutton
Charles Hutton
Charles Hutton was an English mathematician.Hutton was born at Newcastle-on-Tyne. He was educated in a school at Jesmond, kept by Mr Ivison, a clergyman of the Church of England...
, Girard was
...the first person who understood the general doctrine of the formation of the coefficients of the powers from the sum of the roots and their products. He was the first who discovered the rules for summing the powers of the roots of any equation.
This had previously been given by François Viète
François Viète
François Viète , Seigneur de la Bigotière, was a French mathematician whose work on new algebra was an important step towards modern algebra, due to its innovative use of letters as parameters in equations...
for positive roots, and is today called Viète's formulas, but Viète did not give these for general roots.
In his paper, Funkhouser locates the work of Girard in the history of the study of equations using symmetric function
Symmetric function
In algebra and in particular in algebraic combinatorics, the ring of symmetric functions, is a specific limit of the rings of symmetric polynomials in n indeterminates, as n goes to infinity...
s. In his work on the theory of equations
Theory of equations
In mathematics, the theory of equations comprises a major part of traditional algebra. Topics include polynomials, algebraic equations, separation of roots including Sturm's theorem, approximation of roots, and the application of matrices and determinants to the solving of equations.From the point...
, Lagrange
Joseph Louis Lagrange
Joseph-Louis Lagrange , born Giuseppe Lodovico Lagrangia, was a mathematician and astronomer, who was born in Turin, Piedmont, lived part of his life in Prussia and part in France, making significant contributions to all fields of analysis, to number theory, and to classical and celestial mechanics...
cited Girard. Still later, in the nineteenth century, this work eventuated in the creation of group theory
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...
by Cauchy, Galois and others.
Girard also showed how the area of a spherical triangle depends on its interior angles. The result is called Girard's theorem.
Girard was a lute
Lute
Lute can refer generally to any plucked string instrument with a neck and a deep round back, or more specifically to an instrument from the family of European lutes....
nist and mentioned having written a treatise on music, though this was never published.