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The problem of ellipsoide and harmonic analysis: The controversy between Legendre and Laplace. (Le problème de l’ellipsoïde et l’analyse harmonique: La controverse entre Legendre et Laplace.) (French) Zbl 0799.01015

Chabert, Jean-Luc (ed.) et al., Analyse diophantienne et géométrie algébrique. Exposés du Séminaire d’Histoire des Mathématiques de l’Institut Henri Poincaré. Paris: Université Pierre et Marie Curie, Lab. de Mathématiques Fondamentales, Cah. Sémin. Hist. Math., 2. Sér. 3, 113-157 (1993).
This paper is based on a dissertation, “Histoire des relations d’orthogonalité en analyse”, written by the author under the direction of Jean Dhombres. He describes the controversy between Legendre and Laplace in the 1780s; they used various techniques of harmonic analysis to determine the possible forms of equilibrium of a fluid planet rotating uniformly about an axis. The paper begins with a brief history of the previous research, and also considers the work of the successors of Legendre and Laplace.
For the entire collection see [Zbl 0782.00054].

MSC:

01A50 History of mathematics in the 18th century
76U05 General theory of rotating fluids

Biographic References:

Legendre, A.-M.; Laplace, P.-S.
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