Optimizing the arrangement of points on the unit sphere-Reference-Cited by-同舟云学术

Optimizing the arrangement of points on the unit sphere

Published:1977 Issue:140 Volume:31 Page:1006-1008
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Berman Joel,Hanes Kit

Abstract

This paper is concerned with the problem of placing N points on the unit sphere in E 3 {E^3} so as to maximize the sum of their mutual distances. A necessary condition is proved which led to a computer algorithm. This in turn led to the apparent best arrangements for values of N from 5 to 10 inclusive.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1977-31-140/S0025-5718-1977-0478006-1/S0025-5718-1977-0478006-1.pdf

Reference12 articles.

1. On the sum of distances between 𝑛 points on a sphere;Alexander, R.;Acta Math. Acad. Sci. Hungar.,1972

2. Extremal problems of distance geometry related to energy integrals;Alexander, Ralph;Trans. Amer. Math. Soc.,1974

3. Volumes of polyhedra inscribed in the unit sphere 𝐸³;Berman, Joel D.;Math. Ann.,1970

4. Inequalities for sums of distances;Chakerian, G. D.;Amer. Math. Monthly,1973

5. Stability configurations of electrons on a sphere;Cohn, Harvey;Math. Tables Aids Comput.,1956

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