منابع مشابه
The Kissing Number in Four Dimensions
The kissing number τn is the maximal number of equal size nonoverlapping spheres in n dimensions that can touch another sphere of the same size. The number τ3 was the subject of a famous discussion between Isaac Newton and David Gregory in 1694. The Delsarte method gives an estimate τ4 ≤ 25. In this paper we present an extension of the Delsarte method and use it to prove that τ4 = 24. We also p...
متن کاملThe one-sided kissing number in four dimensions
Let H be a closed half-space of n-dimensional Euclidean space. Suppose S is a unit sphere in H that touches the supporting hyperplane of H . The one-sided kissing number B(n) is the maximal number of unit nonoverlapping spheres in H that can touch S. Clearly, B(2) = 4. It was proved that B(3) = 9. Recently, K. Bezdek proved that B(4) = 18 or 19, and conjectured that B(4) = 18. We present a proo...
متن کاملThe Kissing Problem in Three Dimensions
The kissing number k(3) is the maximal number of equal size nonoverlapping spheres in three dimensions that can touch another sphere of the same size. This number was the subject of a famous discussion between Isaac Newton and David Gregory in 1694. The first proof that k(3) = 12 was given by Schütte and van der Waerden only in 1953. We present a new solution of this problem.
متن کاملAn Extension of Delsarte’s Method. the Kissing Problem in Three and Four Dimensions
The kissing number k(n) is the highest number of equal nonoverlapping spheres in R that can touch another sphere of the same size. In three dimensions the kissing number problem is asking how many white billiard balls can kiss (touch) a black ball. The most symmetrical configuration, 12 billiard balls around another, is if the 12 balls are placed at positions corresponding to the vertices of a ...
متن کاملNew formulations for the Kissing Number Problem
Determining the maximum number of D-dimensional spheres of radius r that can be adjacent to a central sphere of radius r is known as the Kissing Number Problem (KNP). The problem has been solved for 2, 3 and very recently for 4 dimensions. We present two nonlinear (nonconvex) mathematical programming models for the solution of the KNP. We solve the problem by using two stochastic global optimiz...
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2008
ISSN: 0003-486X
DOI: 10.4007/annals.2008.168.1