Optimizing the arrangement of points on the unit sphere
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- by Joel Berman and Kit Hanes PDF
- Math. Comp. 31 (1977), 1006-1008 Request permission
Abstract:
This paper is concerned with the problem of placing N points on the unit sphere in ${E^3}$ 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.References
- R. Alexander, On the sum of distances between $n$ points on a sphere, Acta Math. Acad. Sci. Hungar. 23 (1972), 443β448. MR 312395, DOI 10.1007/BF01896964
- Ralph Alexander and Kenneth B. Stolarsky, Extremal problems of distance geometry related to energy integrals, Trans. Amer. Math. Soc. 193 (1974), 1β31. MR 350629, DOI 10.1090/S0002-9947-1974-0350629-3
- Joel D. Berman and Kit Hanes, Volumes of polyhedra inscribed in the unit sphere $E^{3}$, Math. Ann. 188 (1970), 78β84. MR 266052, DOI 10.1007/BF01435416
- G. D. Chakerian and M. S. Klamkin, Inequalities for sums of distances, Amer. Math. Monthly 80 (1973), 1009β1017. MR 331224, DOI 10.2307/2318775
- Harvey Cohn, Stability configurations of electrons on a sphere, Math. Tables Aids Comput. 10 (1956), 117β120. MR 81133, DOI 10.1090/S0025-5718-1956-0081133-0
- L. Fejes TΓ³th, On the sum of distances determined by a pointset, Acta Math. Acad. Sci. Hungar. 7 (1956), 397β401 (English, with Russian summary). MR 107212, DOI 10.1007/BF02020534 M. GOLDBERG, "Stability configurations of electrons on a sphere," Math. Comp., v. 23, 1969, pp. 785-786. D. W. GRACE, "Search for largest polyhedra," Math. Comp., v. 17, 1963, pp. 197-199.
- Einar Hille, Some geometric extremal problems, J. Austral. Math. Soc. 6 (1966), 122β128. MR 0198349
- Theodor William Melnyk, Osvald Knop, and William Robert Smith, Extremal arrangements of points and unit charges on a sphere: equilibrium configurations revisited, Canad. J. Chem. 55 (1977), no.Β 10, 1745β1761 (English, with French summary). MR 0444497
- Kenneth B. Stolarsky, The sum of the distances to $N$ points on a sphere, Pacific J. Math. 57 (1975), no.Β 2, 563β573. MR 396417
- Kenneth B. Stolarsky, Sums of distances between points on a sphere. II, Proc. Amer. Math. Soc. 41 (1973), 575β582. MR 333995, DOI 10.1090/S0002-9939-1973-0333995-9
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Math. Comp. 31 (1977), 1006-1008
- MSC: Primary 52-04; Secondary 52A15, 90C30
- DOI: https://doi.org/10.1090/S0025-5718-1977-0478006-1
- MathSciNet review: 0478006