Kissing number

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  • The kissing number problem asks for the maximal number k(n) of equal size nonoverlapping spheres in n-dimensional space that can touch another sphere of the same size. This problem in dimension three was the subject of a famous discussion between Isaac Newton and David Gregory in 1694. In three dimensions the problem was finally solved only in 1953 by Sch¨tte and van der u Waerden. In this paper we present a solution of a long-standing problem about the kissing number in four dimensions. Namely, the equality k(4) = 24 is proved. The proof is based on a modification of...

    pdf33p dontetvui 17-01-2013 17 6   Download

  • Tuyển tập các báo cáo nghiên cứu khoa học hay nhất của tạp chí toán học quốc tế đề tài: On Kissing Numbers in Dimensions 32 to 128...

    pdf5p thulanh4 11-09-2011 19 1   Download

  • Sphere packings is one of the most fascinating and challenging subjects in mathematics. Almost four centuries ago, Kepler studied the densities of sphere packings and made his famous conjecture. Several decades later, Gregory and Newton discussed the kissing numbers of spheres and proposed the Gregory-Newton problem. Since then, these problems and related ones have attracted the attention of many prominent mathematicians such as Blichfeldt, Dirichlet, Gauss, Hermite, Korkin, Lagrange, Minkowski, Thue, Voronoi, Watson, and Zolotarev, as well as many active today....

    pdf256p maket1311 16-10-2012 17 1   Download

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