Finding equal-diameter triangulations in polygons (Q747574)

A plane polygon is called simple if the edges do not cross each other. The authors give a constructive proof that every simple plane polygon can be partitioned into a finite number of equal-diameter triangles such that the intersection of any two triangles is either empty or consists of a vertex or an edge. They also show that every simple plane polygon can be partitioned into infinitely many equal-perimeter triangles.