Flat surfacesA flat surface is a surface composed of a finite number of polygons glued together at the edges neatly---nothing left over, edges perfectly matched, each edge is shared by exactly two polygons. The result is a surface with no boundary. It has a finite number of singular points (the ends of edges). These points are called "cone points". The angle measure of a cone point is the sum of the angles of the polygons meeting at that point. If the sum is an integral multiple of {$2\pi$}, then the flat surface is a "translation surface." Geodesics on such surfaces are studied. |