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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Measures of $ N$-fold symmetry for convex sets

Authors: Charles K. Chui and Milton N. Parnes
Journal: Proc. Amer. Math. Soc. 26 (1970), 480-486
MSC: Primary 52.30
MathSciNet review: 0264514
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Abstract: If a convex set $ S$ is $ 3$-fold symmetric about a point $ 0 \in S$, then any $ 3$-star contained in $ S$ with vertex 0 is no smaller than any other parallel $ 3$-star contained in $ S$. In this paper, among other results, we establish the converse. Consequently, we find two measures of $ n$-fold symmetry, one for $ n = 2,3$ and the other for each $ n \geqq 2$.

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Keywords: $ N$-fold symmetry, convex sets, similarity invariant measure, $ n$-maximal property, $ n$-supporting-line property, $ n$-star
Article copyright: © Copyright 1970 American Mathematical Society

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