Gromov-Hausdorff distance between vertex sets of regular polygons inscribed in a given circle
Talant Talipov
TL;DR
This paper computes the Gromov-Hausdorff distance between vertex sets of regular polygons inscribed in a circle, providing explicit formulas for certain cases and distances to small polygons.
Contribution
It offers a complete calculation of the Gromov-Hausdorff distance for regular polygons with specific divisibility conditions and for small polygons, filling gaps in geometric metric theory.
Findings
Explicit formulas for distances between n- and m-gons when m is divisible by n
Distances from polygons to 2-gons and 3-gons are fully determined
Provides a comprehensive analysis of the metric space of polygon vertex sets
Abstract
We calculate the Gromov-Hausdorff distance between vertex sets of regular polygons endowed with the round metric. We give a full answer for the case of n- and m-gons with m divisible by n. Also, we calculate all distances to 2-gons and 3-gons
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Taxonomy
TopicsPoint processes and geometric inequalities · Mathematics and Applications · Computational Geometry and Mesh Generation