Abstract
In a previous paper, we showed that for regular Reuleaux polygons R n the equality \({{\rm as}_\infty(R_n) = 1/(2\cos \frac\pi{2n} -1)}\) holds, where \({{\rm as}_\infty(\cdot)}\) denotes the Minkowski measure of asymmetry for convex bodies, and \({{\rm as}_\infty(K)\leq \frac 12(\sqrt{3}+1)}\) for all convex domains K of constant width, with equality holds iff K is a Reuleaux triangle. In this paper, we investigate the Minkowski measures of asymmetry among all Reuleaux polygons of order n and show that regular Reuleaux polygons of order n (n ≥ 3 and odd) have the minimal Minkowski measure of asymmetry.
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Project supported by The NSF of Jiangsu Higher Education (08KJD110016).
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Guo, Q., Jin, H. On a measure of asymmetry for Reuleaux polygons. J. Geom. 102, 73–79 (2011). https://doi.org/10.1007/s00022-011-0096-9
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DOI: https://doi.org/10.1007/s00022-011-0096-9