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Measures of axial symmetry for ovals

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Abstract

A measure of axial symmetry for ovals is defined, and eleven particular measures are studied. Lower bounds for these measures are determined on the classes of arbitrary ovals, centrally symmetric ovals, and ovals of constant breadth. The proofs of these results make use only of elementary geometry and the properties of convexity.

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Authors and Affiliations

  1. College of Santa Fe, Santa Fe, New Mexico

    B. Abel Devalcourt

Authors
  1. B. Abel Devalcourt
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Additional information

This paper represents part of the author’s Ph. D. thesis presented to the University of Minnesota, advisor Professor H. W. Guggenheimer. Its preparation was partially supported by grant AF-AFOSR-661-64, Air Force Office of Scientific Research.

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Devalcourt, B.A. Measures of axial symmetry for ovals. Israel J. Math. 4, 65–82 (1966). https://doi.org/10.1007/BF02937452

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  • DOI: https://doi.org/10.1007/BF02937452

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