Groemer–Wallen measure of asymmetry for Reuleaux polygons

Abstract

In this paper, we consider the Groemer–Wallen measure of asymmetry for Reuleaux polygons, and show that the n-th (\(n \ge 5, n \;\text {odd}\)) regular Reuleaux polygons are the most symmetric among all n-th Reuleaux polygons.

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Correspondence to Hai Lin Jin.

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The authors declare that we have no conflict of interest.

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Project supported by national NSF of China No. 11671293.

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Guo, P.Z., Jin, H.L. Groemer–Wallen measure of asymmetry for Reuleaux polygons. J. Geom. 108, 879–884 (2017). https://doi.org/10.1007/s00022-017-0382-2

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Mathematics Subject Classification

  • 52A38

Keywords

  • Measure of asymmetry
  • Reuleaux triangle
  • Reuleaux polygons
  • Constant width