%0 Journal Article
%T J.J. Sylvester's two convex sets theorem and G.-L. Lesage's theory of gravity
%A Marie-Line Chabanol
%A Michel Mend¨¨s France
%A Jean-Jacques Ruch
%J Uniform Distribution Theory
%D 2012
%I Mathematical Institute of the Slovak Academy of Sciences
%X 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 $$displaystyle{m(K_1,K_2)=h(K_1)h(K_2)/d+O(1/d^2)}$$ for some $h(K_1)ge 0$ 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.
%K Geometric Probability - Gravitation
%U http://www.boku.ac.at/MATH/udt/vol07/no1/06ChabMendRuch23-11.pdf