Triangle dissections and addition chains

Abstract

In this paper, we study relations between dissections of convex polygons into triangles by non-intersecting diagonals and addition chains. Especially, we will show that the minimum number of incongruent triangles in a dissection of a regular convex m-gon equals ℓ(m) - 1 where ℓ(m) denotes the minimum length of an addition chain for m. Moreover, all different dissections with minimum number of incongruent triangles are determined for all m with binary representation of Hamming weight at most two.