• Corpus ID: 81326

Partitioning Regular Polygons into Circular Pieces I: Convex Partitions

  title={Partitioning Regular Polygons into Circular Pieces I: Convex Partitions},
  author={Mirela Damian and Joseph O'Rourke},
We explore an instance of the question of partitioning a polygon into pieces, each of which is as “circular” as possible, in the sense of having an aspect ratio close to 1. The aspect ratio of a polygon is the ratio of the diameters of the smallest circumscribing circle to the largest inscribed disk. The problem is rich even for partitioning regular polygons into convex pieces, the focus of this paper. We show that the optimal (most circular) partition for an equilateral triangle has an… 
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