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Dr. Peter Dragnev
Indiana University – Purdue University Fort Wayne
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.
Mathematics | Physical Sciences and Mathematics
Shukurlu, Altun, "Generalized Thomson Problem for 5 points" (2013). 2013 IPFW Student Research and Creative Endeavor Symposium. 50.