Convex curves whose points are vertices of billiard triangles
On a smooth convex curve of constant width all points are vertices of periodic orbits of billiard balls with period two. On ellipses every point is a vertex of a billiard n-gon for all \(n\geq 3\). The author shows that the converse is not true if the assumption is restricted to \(n=3\). More precisely, smooth convex curves are constructed which are different from an ellipse such that all points are vertices of billiard triangles, i.e. vertices of orbits of period three.
scientific article; zbMATH DE number 4054462
scientific article