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Media type:
E-Article
Title:
Covering a sphere by equal circles, and the rigidity of its graph
Contributor:
Tarnai, T.;
Gáspár, Zs.
Published:
Cambridge University Press (CUP), 1991
Published in:
Mathematical Proceedings of the Cambridge Philosophical Society, 110 (1991) 1, Seite 71-89
Language:
English
DOI:
10.1017/s0305004100070134
ISSN:
0305-0041;
1469-8064
Origination:
Footnote:
Description:
AbstractHow must a sphere be covered by n equal circles so that the angular radius of the circles will be as small as possible? In this paper, conjectured solutions of this problem for n = 15 to 20 are given and some sporadic results for n > 20 (n = 22, 26, 38, 42, 50) are presented. The local optima are obtained by using a ‘cooling technique’ based on the theory of bar-and-joint structures. Thus the graph of the coverings by circles is considered as a spherical cable net in which the edge lengths are uniformly decreased, e.g. due to a uniform decrease in the temperature, until the graph becomes rigid and tensile stresses appear in the cables.