• Medientyp: E-Artikel
  • Titel: Covering a sphere by equal circles, and the rigidity of its graph
  • Beteiligte: Tarnai, T.; Gáspár, Zs.
  • Erschienen: Cambridge University Press (CUP), 1991
  • Erschienen in: Mathematical Proceedings of the Cambridge Philosophical Society, 110 (1991) 1, Seite 71-89
  • Sprache: Englisch
  • DOI: 10.1017/s0305004100070134
  • ISSN: 0305-0041; 1469-8064
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  • Beschreibung: 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.