Shapes of stars

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10 Citations (Scopus)

Abstract

In this paper we construct a natural geometric structure for the space of shapesof a star-shaped polygon. Roughly speaking we find: The set ofsimilarity classes of marked stars forms a hyperbolic right angle pentagon bundle over the space of external angle sets ofinscribed pentagons.The assignment of the shape of its fiber to each angle setforms a hyperbolic plane bundle over the Teichmiiller space of hyperbolic right angle pentagons. Any automorphism induced by renumbering is compatible with these geometric structures.

Original languageEnglish
Pages (from-to)845-851
Number of pages7
JournalProceedings of the American Mathematical Society
Volume117
Issue number3
DOIs
Publication statusPublished - 1993 Mar

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Keywords

  • Geometric structure
  • Hyperbolic geometry
  • Moduli space
  • Similarity class

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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