Finding equal-diameter triangulations in polygons

Original Paper

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.

Keywords

Triangulation Diameter Perimeter 

Mathematics Subject Classification (2010)

52C15 

Copyright information

© The Managing Editors 2014

Authors and Affiliations

  1. 1.MTA Rényi InstituteBudapestHungary
  2. 2.Department of Mathematics and StatisticsAuburn UniversityAuburnUSA
  3. 3.Mathematics and StatisticsUniversity of CalgaryCalgaryCanada

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