Research ArticleOpen AccessGoogle Scholar indexed
A Small Correction to a Paper of Vandermonde
Department of Mathematics, West Chester University of Pennsylvania, West Chester, PA 19383, USA
Department of Mathematics, West Chester University of Pennsylvania, West Chester, PA 19383, USA
- 1 Department of Mathematics, West Chester University of Pennsylvania, West Chester, PA 19383, USA
- 2 Department of Mathematics, West Chester University of Pennsylvania, West Chester, PA 19383, USA
Open Journal of Discrete Mathematics·Volume 11 (2021)·Pages 43–53·Published 15 April 2021·DOI10.4236/ojdm.2021.112004
Copy link · social · email
Abstract
In this paper using elementary Galois Theory, we give a detailed explanation of the calculation of the radical expression for which was first discussed by Vandermonde decades before Galois and we point out and correct a minor correction in his work which was also observed by Lagrange.
KeywordsCyclotomyGaloisGalois GroupGaussLagrangeTignolVandermonde
- Vandermonde, A.T. (1771) Mémoire sur la résolution des équations, Histoire de l'Acad. Royale des Sciences (avec les mémoires de Math. & Phys. pour la même année, tirés des registres de cette Acad.), 365-416.
- Tignol, J.-P. (2001) Galois’ Theory of Algebraic Equations. World Scientific, Singapore, 348 p. https://doi.org/10.1142/4628
- Jones, P.S. (1976) Vandermonde, Alexandre-Théophile, Dictionary of Scientific Biography, Vol. 8, Charles Scribner’s Sons, New York, 571-572.
- Neumann, O. (2007) Cyclotomy: From Euler through Vandermonde to Gauss. In: Bradley, R.E. and Sandifer, C.E., Eds., Leonhard Euler: Life, Work and Legacy, Elsevier, Amsterdam, 323-361. https://doi.org/10.1016/S0928-2017(07)80018-1
- Hamburg, R.R. (1976) The Theory of Equations in the 18th Century: The Work of Joseph Lagrange. Archive for the History of Exact Sciences, 16, 17-36.
- Lagrange, J. (1869) Oeuvres. Notes sur la théorie des équations, Note XIV (Où l’on donne la résolution générale des équations à deux termes), Gauthier-Villars, Paris, 354-355.