Constructing All Convex Shapes Using a Modified Version of the Traditional Chinese Tangram Puzzle

Abstract

It is well known that there are 13 convex tangram figures for the classical Chinese Tangram puzzle. In this paper, the focus shifts to a different variant where it is demonstrated that there are 11 such convex tangram figures. Furthermore, it is established that any convex tangram figure must have all of its border vertices situated on a single lattice. A computer program is developed to solve Diophantine equations and inequalities in order to identify candidate polygons. Subsequently, a manual construction process is employed to validate whether each candidate polygon qualifies as a legitimate tangram construction.