J.J. Sylvester's two convex sets theorem and G.-L. Lesage's theory of gravity
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | CHABANOL, Marie-Line | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | RUCH, Jean-Jacques | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | MENDES-FRANCE, Michel | |
| dc.date.accessioned | 2024-04-04T03:22:04Z | |
| dc.date.available | 2024-04-04T03:22:04Z | |
| dc.date.issued | 2012 | |
| dc.identifier.issn | 2309-5377 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194719 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.publisher | Mathematical Institute of the Slovak Academy of Sciences | |
| dc.subject.en | Geometric probability | |
| dc.subject.en | Gravitation | |
| dc.title.en | J.J. Sylvester's two convex sets theorem and G.-L. Lesage's theory of gravity | |
| dc.type | Article de revue | |
| dc.subject.hal | Physique [physics]/Physique mathématique [math-ph] | |
| dc.subject.hal | Mathématiques [math]/Physique mathématique [math-ph] | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.subject.hal | Mathématiques [math]/Géométrie métrique [math.MG] | |
| bordeaux.journal | Uniform Distribution Theory | |
| bordeaux.page | 135 | |
| bordeaux.volume | 7 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 1 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01018133 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01018133v1 | |
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