Historical Overview of the Kepler Conjecture
نویسندگان
چکیده
منابع مشابه
An Overview of the Kepler Conjecture
A packing of spheres is an arrangement of nonoverlapping spheres of radius 1 in Euclidean space. Each sphere is determined by its center, so equivalently it is a collection of points in Euclidean space separated by distances of at least 2. The density of a packing is defined as the lim sup of the densities of the partial packings formed by spheres inside a ball with fixed center of radius R. (B...
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The Kepler conjecture asserts that the density of a packing of congruent balls in three dimensions is never greater than π/ √ 18. A computer assisted verification confirmed this conjecture in 1998. This article gives a historical introduction to the problem. It describes the procedure that converts this problem into an optimization problem in a finite number of variables and the strategies used...
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The Kepler conjecture asserts that no packing of congruent balls in three-dimensional Euclidean space has density greater than that of the face-centered cubic packing. The original proof, announced in 1998 and published in 2006, is long and complex. The process of revision and review did not end with the publication of the proof. This article summarizes the current status of a long-term initiat...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2006
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-005-1210-2