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Finding equal-diameter triangulations in polygons

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Abstract

In this paper we show that every simple polygon can be triangulated with equal-diameter triangles. Our constructive proof does not give bounds for the number of triangles needed. We also show that every simple polygon can be partitioned into an infinite number of equal-perimeter triangles.

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Authors and Affiliations

  1. MTA Rényi Institute, Budapest, Hungary

    András Bezdek

  2. Department of Mathematics and Statistics, Auburn University, Auburn, AL, USA

    András Bezdek

  3. Mathematics and Statistics, University of Calgary, Calgary, Canada

    Ted Bisztriczky

Authors
  1. András Bezdek
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  2. Ted Bisztriczky
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Correspondence to András Bezdek.

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Bezdek, A., Bisztriczky, T. Finding equal-diameter triangulations in polygons. Beitr Algebra Geom 56, 541–549 (2015). https://doi.org/10.1007/s13366-014-0206-6

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  • DOI: https://doi.org/10.1007/s13366-014-0206-6

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