Article
J.j. Sylvester’s Two Convex Sets Theorem and G.-L. Lesage’s Theory of Gravity
Authors
, and
Abstract
Given two convex sets \(K_1\) and \(K_2\) in the plane, J.J. Sylvester
computes the measure \(m(K_1, K_2)\) of the family of straight lines which
meet both \(K_1\) and \(K_2\). As their distance \(d = d(K_1, K_2)\) increases
to infinity
\[
m(K_1, K_2) = \frac{h(K_1)h(K_2)}{d} + O\!\left(\frac{1}{d^2}\right)
\]
for some \(h(K_i) > 0\) and \(h(K_2) \ge 0\), suggesting Newton's law of
attraction in the plane. We discuss the analogy in the spirit of G.-L. Lesage.
Keywords
Geometric Probability - Gravitation.
Citation
Chabanol, M., France, M. M., & Ruch, J. (2012). J.j. sylvester’s two convex sets theorem and G.-L. lesage’s theory of gravity. Uniform Distribution Theory, 7(1), 135–145.
M. Chabanol, M. M. France and J. Ruch, “J.j. sylvester’s two convex sets theorem and G.-L. lesage’s theory of gravity,” Uniform Distribution Theory, vol. 7, no. 1, pp. 135–145, 2012.
Chabanol M, France MM, Ruch J. J.j. sylvester’s two convex sets theorem and G.-L. lesage’s theory of gravity. Uniform Distribution Theory. 2012;7(1):135–145.
Chabanol, M., France, M. M. and Ruch, J. (2012), ‘J.j. sylvester’s two convex sets theorem and G.-L. lesage’s theory of gravity’, Uniform Distribution Theory, 7(1), pp. 135–145.
Chabanol, Marie-Line, et al. “J.j. Sylvester’s Two Convex Sets Theorem and G.-L. Lesage’s Theory of Gravity.” Uniform Distribution Theory, vol. 7, no. 1, 2012, pp. 135–145.
Chabanol, Marie-Line, Michel Mendes France, and Jean-Jacques Ruch. “J.j. Sylvester’s Two Convex Sets Theorem and G.-L. Lesage’s Theory of Gravity.” Uniform Distribution Theory 7, no. 1 (2012): 135–145.
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Published by: Engineering Journals
