J.J. Sylvester's two convex sets theorem and G.-L. Lesage's theory of gravity
Language
en
Article de revue
This item was published in
Uniform Distribution Theory. 2012, vol. 7, n° 1, p. 135
Mathematical Institute of the Slovak Academy of Sciences
English 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 ...Read more >
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.Read less <
English Keywords
Geometric probability
Gravitation
Origin
Hal imported