In computational geometry, polygon triangulation is the decomposition of a polygonal area (simple polygon) $P$ into a set of triangles, i.e., finding a set of triangles with pairwise non-intersecting interiors whose union is $P$.
Question : Prove that every triangulation of a finite point set $S$ contains $3|S|-3-h$ edges, where the boundary of $ConvexHull(S)$ contains $h$ edges.
Note : I think the method of proof is induction. But, I don't know which variable i should use for the induction.