Curves of constant diameter and inscribed polygons (Q835323)

A simple closed curve \(\Gamma\) in the plane has property \(C_n(D)\) if \(\forall x\in \Gamma\) there is a unique regular \(n\)-gon with edges of length \(D\) which is inscribed in \(\Gamma\) so that \(x\) is its vertex. The author demonstrates that for all \(n\geq 2\) and \(D>0\) there are \(C^\infty\) regular simple closed non circular curves \(\Gamma\) with property \(C_n(D)\).