Spherical Distribution of 5 Points with Maximal Distance Sum |
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Authors: | Xiaorong Hou Junwei Shao |
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Institution: | 1.School of Automation Engineering,University of Electronic Science and Technology of China,Sichuan,P.R. China |
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Abstract: | In this paper, we consider the problem of spherical distribution of 5 points, that is, how to configure 5 points on the unit
sphere such that the mutual distance sum is maximal. It is conjectured that the sum of distances is maximal if the 5 points
form a bipyramid distribution with two points positioned at opposite poles of the sphere and the other three positioned uniformly
on the equator. We study this problem using interval methods and related techniques, and give a computer-assisted proof. |
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