Packing Spheres in High Dimensions

IF 1.5 Q2 PHYSICS, MULTIDISCIPLINARY
Physics Pub Date : 2023-09-21 DOI:10.1103/physics.16.s131
Charles Day
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引用次数: 0

Abstract

V eit Elser of Cornell University has just described a new way to elucidate a problem that has baffled mathematicians for over a century: How densely can identical spheres be packed as the dimension of the spheres and of the space they occupy grow ever larger [1]? Schemes for densely packing spheres have been worked out in low dimensions and for two special cases: 8 and 24 dimensions. (A sphere in n-dimensional space is a set of points that are the same fixed distance away from a given center point.) Surprisingly, some schemes in high dimensions are little better than a random approach. What’s more, a century of research has failed to improve on the result from Hermann Minkowski, a Germanmathematician who came up with the concept of four-dimensional spacetime, that with each additional dimension, the highest fraction of space that can be occupied by spheres falls by a factor of 2. Intuitively, the rate of decrease should be slower.
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来源期刊
Physics
Physics PHYSICS, MULTIDISCIPLINARY-
CiteScore
3.00
自引率
6.20%
发文量
0
审稿时长
10 weeks
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