Louis Poinsot

Background

Louis Poinsot was born on January 3, 1777, in Paris, France.

Education

Poinsot attended the school of Lycée Louis-le-Grand for secondary preparatory education for entrance to the famous École Polytechnique. In October 1794, at age 17, he took the École Polytechnique entrance exam and failed the algebra section but was still accepted. He left in 1797 in order to enter the Ecole des Ponts et Chaussees, where he remained for three years.

Career

Neglecting his technical studies - which held little attraction for him - in favor of mathematics, Poinsot eventually gave up the idea of becoming an engineer. From 1804 to 1809 he taught mathematics at the Lycee Bonaparte in Paris; he was then appointed inspector general of the Imperial University.

Despite the frequent travels to the provinces necessitated by this new post, on 1 November 1809 Poinsot was named assistant professor of analysis and mechanics at the Ecole Polytechnique, substituting for Labey. Although he held this position until the school was reorganized in September 1816, he actually taught there for only three years, after which time he arranged for A. A. L. Reynaud and later for Cauchy to substitute for him. He owed his appointment at the Polytechnique to the favorable reception given to his Elements de statique (1803) and to three subsequent memoirs that dealt with the composition of momenta and the composition of areas (1806), the general theory of equilibrium and of movement in systems (1806), and polygons and polyhedra (1809). His reputation also resulted in his election on 31 May 1813 to the mathematics section of the Academie des Sciences, replacing Lagrange.

From 1816 to 1826 Poinsot served as admissions examiner at the Ecole Polytechnique, and on several occasions, after 1830 he worked with the school’s Conseil de Perfectionnement. Although in 1824 he gave up his duties as inspector general, his nomination in 1840 to the Conseil Royal de l’lnstruction Publique kept him informed of university problems.

Meanwhile, he continued research on number theory and on mechanics, publishing a small number of original and carefully executed memoirs. Named to the Bureau des Longitudes in 1843, he displayed a certain interest in celestial mechanics. Moderately liberal in his political opinions, he protested against the clericalism of the Restoration but later accepted a nomination to the Chambre des Pairs (1846) and to the Senate (1852).

Poinsot was determined to publish only fully developed results and to present them with clarity and elegance. Consequently, he left a rather limited body of work, which was devoted mainly to mechanics, geometry, and number theory. He showed almost no interest in algebra except for his early investigations concerning the fifth-degree equation and his remarkable analysis of Lagrange’s Traite de la resolution des equal ions numeriques de tons les degres (1808). Similarly, the infinitesimal calculus appears in his work only in the form of extracts (published in 1815) from his course in analysis at the Ecole Polytechnique.

Poinsot’s contributions to number theory (1818 -1849) have been analyzed by L. E. Dickson. They deal primarily with primitive roots, certain Diophantine equations, and the expression of a number as a difference of two squares.

A fervent disciple of Monge, Poinsot was one of the principal leaders of the revival of geometry in France during the first half of the nineteenth century. In particular, he was responsible for the creation in 1846 of a chair of advanced geometry at the Sorbonne, which was intended for Chasles. Poinsot, who had a presentiment of the importance of the geometry of position, established the theory of regular star polygons and discovered several types of regular star polyhedra (1809), a general study of which was carried out by Cauchy shortly afterward.

Yet it was in mechanics that Poinsot most effectively displayed his gift for geometry. Although Elements de statique (1803) was merely a manual designed for candidates to the Ecole Polytechnique, the work possessed the great merit of applying geometric methods to the study of elementary problems of mechanics and of introducing the concept of the couple. The latter notion, moreover, held a central place in two more highly developed memoirs that Poinsot presented to the Academie des Sciences in 1804 and published in the Journal de T Ecole Polytechnique in 1806. The second of these memoirs inspired an interesting debate between Poinsot and Lagrange concerning the principles of mechanics.

Among Poinsot’s other writings on mechanics, the most important is Theorie nouvelle de la rotation des corps (1834). Pursuing the theoretical study undertaken in the eighteenth century by Euler, d’Alembert, and Lagrange, Poinsot established in a purely geometric fashion the existence of the axes of permanent rotation and worked out a very elegant representation of rotary motion by the rolling of the ellipsoid of inertia of a body on a fixed plane (Poinsot motion). This theory was developed by Sylvester and was applied by Foucault to the discovery of the gyroscope. Poinsot’s remarkable geometric intuition also enabled him to elaborate a purely geometric theory of the precession of the equinoxes (1858).

In frequent opposition to the French analytic school of the first half of the nineteenth century, Poinsot produced an original body of work by successfully submitting to geometric treatment a certain number of fundamental questions in the mechanics of solids.

Achievements

• Louis Poinsot's major achievement was in his invention of geometrical mechanics, investigating how a system of forces acting on a rigid body can be resolved into a single force and a couple. Also, he wrote an important work on polyhedra in 1809, discovering four new regular polyhedra, which are now known as the Kepler-Poinsot solids. Poinsot also worked in number theory, studying Diophantine equations with a view to expressing numbers as the difference of two squares and primitive roots.
  
  In 1846 he was made an officer of the Legion of Honour.

Works

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  • Questions dynamiques sur la percussion des corps 1857
  • Éléments De Statique: Suivis De Quatre Mémoires Sur La Composition Des Moments Et Des Aires; Sur Le Plan Invariable Du Système Du Monde 1848
  • Mémoire sur les atmosphères liquides, et leur influence sur l'action mutuelle des molécules solides qu'elles enveloppent 1824
  • Aléments de statique, a l'usage des lycées, par L. Poinsot, inspecteurgénéral de l'Université impériale 1811
  • Précession des équinoxes 1857
  • Theorie nouvelle de la rotation des corps 1834
  • Trait De La Rsolution Des quations Numriques De Tous Les Degrs: Avec Des Notes Sur Plusieurs Points De La Thorie Des quations Algbriques, Issue 2 (Spanish Edition) 1844

Views

Quotations: "Everyone makes for himself a clear idea of the motion of a point, that is to say, of the motion of a corpuscle which one supposes to be infinitely small, and which one reduces by thought in some way to a mathematical point." — Louis Poinsot, Théorie nouvelle de la rotation des corps (1834).

Membership

Poinsot was elected Fellow of the Royal Society of London in 1858.

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  Royal Society , United Kingdom

  1858 - 1859

Connections

collaborator:

Gaspard Monge

References

• Dictionary of Scientific Biography
  1975