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Faculty Sponsor

Dr. Peter Dragnev

University Affiliation

Indiana University – Purdue University Fort Wayne

Abstract

Optimal configurations on the sphere have various applications in physics, chemistry, biology, and computer science. The Generalized Thomson Problems is to place N points on the unit sphere so that their energy (sum of all weighted reciprocal distances) will be minimized. This paper investigates the case for N=5. We show that among all configurations with two antipodal points the best one is the triangular bipyramid. Computational comparison with the square pyramid is provided and open problems discussed.

Disciplines

Mathematics | Physical Sciences and Mathematics

Generalized Thomson Problem for 5 points

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Mathematics Commons

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