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Measures of N-Fold Symmetry for Convex Sets

Charles K. Chui and Milton N. Parnes
Proceedings of the American Mathematical Society
Vol. 26, No. 3 (Nov., 1970), pp. 480-486
DOI: 10.2307/2037364
Stable URL: http://www.jstor.org/stable/2037364
Page Count: 7
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Measures of N-Fold Symmetry for Convex Sets
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Abstract

If a convex set S is 3-fold symmetric about a point 0 ∈ 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 ≥ 2.

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