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Asymmetry of Reuleaux polygons

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Abstract

In this paper, we consider a measure of asymmetry for Reuleaux polygons, and show that the n-th (\(n \ge 3, n \;\text {odd}\)) regular Reuleaux polygons are the most symmetric ones among all n-th Reuleaux polygons. As a byproduct, we show that the Reuleaux triangles are the most asymmetric planar convex bodies of constant width.

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Authors and Affiliations

  1. Department of Mathematics, Suzhou University of Science and Technology, Suzhou, 215009, China

    HaiLin Jin

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  1. HaiLin Jin
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Correspondence to HaiLin Jin.

Additional information

Project supported by NSF of Suzhou University of Science and Technology No. 341410004.

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Jin, H. Asymmetry of Reuleaux polygons. Beitr Algebra Geom 58, 311–317 (2017). https://doi.org/10.1007/s13366-016-0318-2

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  • DOI: https://doi.org/10.1007/s13366-016-0318-2

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