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arXiv:math/0611451math.MG

Experimental study of energy-minimizing point configurations on spheres

Brandon Ballinger, Grigoriy Blekherman, Henry Cohn, Noah Giansiracusa, Elizabeth Kelly, Achill Schuermann

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Abstract

In this paper we report on massive computer experiments aimed at finding spherical point configurations that minimize potential energy. We present experimental evidence for two new universal optima (consisting of 40 points in 10 dimensions and 64 points in 14 dimensions), as well as evidence that there are no others with at most 64 points. We also describe several other new polytopes, and we present new geometrical descriptions of some of the known universal optima.

arXiv comments
41 pages, 12 figures, to appear in Experimental Mathematics
Journal reference
Experimental Mathematics 18 (2009), 257-283
DOI
doi:10.1080/10586458.2009.10129052
Subjects
math.MGMetric Geometry

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  1. Mathematicians discover new way for spheres to 'kiss' 1 comment

    • Here is an example of that sort of thing, using gradient descent as a starting point: https://arxiv.org/abs/math/0611451. It is technically about spherical codes rather than the kissing problem specifically, but they are closely related…

      awanderingmindView on HNParent context

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