Abstract
How must n equal circles (spherical caps) of given angular radius r be arranged on the surface of a sphere so that the area covered by the circles will be as large as possible? In this paper, conjectured solutions of this problem for n = 5, 7, 8, 9, 10, 11 are given when r varies from the maximum packing radius to the minimum covering radius. The relation of the results of this problem to the extremal configurations of n mutually repulsive equal point charges on the surface of a sphere is discussed. Variation of the solution polyhedra with r gives an abstract model of chemical isomerization processes, for example for n = 5 where the packing → covering transition models the Berry pseudo-rotation of a trigonal bipyramid.
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Schedule a callMore From: Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
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