Inscribing a regular \(m\)-gon in a regular \(n\)-gon (Q601738)

The paper shows that a regular \(m\)-gon can be inscribed into a regular \(n\)-gon only if one of the following conditions hold: 1) \(m=3\), 2) \(m=4\), 3) \(m\geq 5\) and \(m\) divides \(n\) 4) \(m\) is even and \(n\) is an odd multiple of \(m/2\). Furthermore, for each pair of \(m\) and \(n\) satisfying one of these condition, there is an \(m\)-gon inscribed into an \(n\)-gon.