Spherical Distribution of 5 Points with Maximal Distance Sum
Discrete Mathematics
2009-06-05 v1 Symbolic Computation
Abstract
In this paper, we mainly consider the problem of spherical distribution of 5 points, that is, how to configure 5 points on a sphere such that the mutual distance sum attains the maximum. It is conjectured that the sum of distances is maximal if 5 points form a bipyramid configuration in which case two points are positioned at two poles of the sphere and the other three are positioned uniformly on the equator. We study this problem using interval methods and related technics, and give a proof for the conjecture through computers in finite time.
Keywords
Cite
@article{arxiv.0906.0937,
title = {Spherical Distribution of 5 Points with Maximal Distance Sum},
author = {Xiaorong Hou and Junwei Shao},
journal= {arXiv preprint arXiv:0906.0937},
year = {2009}
}
Comments
45 pages, 3 figures