Albert Girard (1595, Saint-Mihiel –8 December 1632, Leiden) 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 abbreviations 'sin', 'cos' and 'tan' for the trigonometric functions 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.
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 functions. In his work on the 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 showed how the area of a spherical triangle depends on its interior angles. The result is called Girard's theorem.
Girard began as a lute player, not a mathematician.[citation needed]
External links
References
- Niven, Ivan; Herbert S. Zuckerman and Hugh L. Montgomery (1991). An introduction to the theory of numbers, Fifth Edition. New York: Wiley. ISBN 0-471-62546-9.
- Funkhouser, H. Gray (1930). "A short account of the history of symmetric functions of roots of equations". American Mathematical Monthly 37 (7): 357–365. doi:.
This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)
