The dissection of a polygon into nearly equilateral triangles

Abstract

Every polygon can be dissected into acute triangles. In this paper we prove that every polygon, such that the interior angles are at least π/5, can be dissected into triangles with interior angles all less than or equal to 2π/5. We find necessary conditions on the interior angles of the polygon in order to obtain a dissection into triangles with interior angles all ⩽α (where π/3<α<2π/5). The conjecture can be stated that these conditions are also sufficient.