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'Albert Girard' (1595–1632) was a French-born mathematician. He studied at the University of Leiden. According to the MacTutor Archive, "he had early thoughts on the fundamental theorem of algebra" and gave the inductive definition for the Fibonacci numbers.
He was the first to use the Trigonometry abbreviations 'sin', 'cos' and 'tan' in a treatise. According to Ivan M. Niven, Girard was the first to state, in 1632, that each prime of form 1 mod 4 was the sum of two squares in exactly one way. (See Fermat's theorem on sums of two squares.)
In the opinion of Charles Hutton, as quoted in Funkhouser (1930), Girard was
In his paper, Funkhouser locates the work of Girard in the history of the study of equations using symmetric functions. In his work on theory of equations, Lagrange cited Girard. Still later, in the 19th century, this work eventuated in the creation of group theory by Cauchy, Galois and others.
Girard also made precise a theorem relating the area of a spherical triangle to its interior angles, the result is called "[Girard's Theorem]."
Girard began as a lute player, not a mathematician.
★
★ An introduction to the theory of numbers, Fifth Edition, Nivan, Iven; Herbert S. Zuckerman and Hugh L. Montgomery, , , , , ISBN 0-471-62546-9
★ A short account of the history of symmetric functions of roots of equations, H. Gray Funkhouser, , , American Mathematical Monthly,
He was the first to use the Trigonometry abbreviations 'sin', 'cos' and 'tan' in a treatise. According to Ivan M. Niven, Girard was the first to state, in 1632, that each prime of form 1 mod 4 was the sum of two squares in exactly one way. (See Fermat's theorem on sums of two squares.)
In the opinion of Charles Hutton, as quoted in Funkhouser (1930), 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.
In his paper, Funkhouser locates the work of Girard in the history of the study of equations using symmetric functions. In his work on theory of equations, Lagrange cited Girard. Still later, in the 19th century, this work eventuated in the creation of group theory by Cauchy, Galois and others.
Girard also made precise a theorem relating the area of a spherical triangle to its interior angles, the result is called "[Girard's Theorem]."
Girard began as a lute player, not a mathematician.
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References
★ An introduction to the theory of numbers, Fifth Edition, Nivan, Iven; Herbert S. Zuckerman and Hugh L. Montgomery, , , , , ISBN 0-471-62546-9
★ A short account of the history of symmetric functions of roots of equations, H. Gray Funkhouser, , , American Mathematical Monthly,
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