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Improved packing of equal circles on a sphere and rigidity of its graph

Published online by Cambridge University Press:  24 October 2008

T. Tarnai  and
Zs. Gáspár
T. Tarnai
Affiliation:
Hungarian Institute for Building Science, Budapest, Dávid F.u.6., H-1113, Hungary
Zs. Gáspár
Affiliation:
Technical University of Budapest, Department of Civil Engineering Mechanics, Budapest, Müegyetem rkp. 3. H-1111, Hungary
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Abstract

How must n equal non-overlapping circles be packed on a sphere so that the angular diameter of the circles will be as great as possible? In the paper, the conjectured solutions of this problem for n = 18, 27, 34, 35, 40 are improved on the basis of an idea of Danzer. Using the theory of bar structures it is ascertained that, in these cases, the edge-length of the graphs of the circle-packings can be increased till, in the graphs, additional edges appear which prevent further motions apart from rigid motions. The cases of n = 17 and 32 are also dealt with and there are references to the possibilities of further applications of the method applied in this paper (n = 59, 80, 110, 122).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 2 , March 1983 , pp. 191 - 218
Copyright
Copyright © Cambridge Philosophical Society 1983

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