Groemer-Wallen measure of asymmetry for Reuleaux polygons (Q1685529)

Groemer and Wallen defined the asymmetry function \(\alpha(K)\) for a Reuleaux polygon \(K\) [\textit{H. Groemer} and \textit{L. J. Wallen}, Beitr. Algebra Geom. 42, No. 2, 517--521 (2001; Zbl 0996.52001)]. The authors prove that the minimum of \(\alpha(K)\) occurs for regular Reuleaux polygons of order \(n\) (\(n\geq 5\), \(n\) odd).