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J.J. Sylvester's two convex sets theorem and G.-L. Lesage's theory of gravity

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorCHABANOL, Marie-Line
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorRUCH, Jean-Jacques
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorMENDES-FRANCE, Michel
dc.date.accessioned2024-04-04T03:22:04Z
dc.date.available2024-04-04T03:22:04Z
dc.date.issued2012
dc.identifier.issn2309-5377
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194719
dc.description.abstractEnGiven 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.isoen
dc.publisherMathematical Institute of the Slovak Academy of Sciences
dc.subject.enGeometric probability
dc.subject.enGravitation
dc.title.enJ.J. Sylvester's two convex sets theorem and G.-L. Lesage's theory of gravity
dc.typeArticle de revue
dc.subject.halPhysique [physics]/Physique mathématique [math-ph]
dc.subject.halMathématiques [math]/Physique mathématique [math-ph]
dc.subject.halMathématiques [math]/Probabilités [math.PR]
dc.subject.halMathématiques [math]/Géométrie métrique [math.MG]
bordeaux.journalUniform Distribution Theory
bordeaux.page135
bordeaux.volume7
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue1
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01018133
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01018133v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Uniform%20Distribution%20Theory&rft.date=2012&rft.volume=7&rft.issue=1&rft.spage=135&rft.epage=135&rft.eissn=2309-5377&rft.issn=2309-5377&rft.au=CHABANOL,%20Marie-Line&RUCH,%20Jean-Jacques&MENDES-FRANCE,%20Michel&rft.genre=article


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