We proved in this paper that 14 triangles are necessary to triangulate a
square with every angle no more than 72◦, answering an unsolved problem
proposed by Professor D.Eppstein. At first, computer is used to search for
topologically feasible solutions of triangulations of a rectangle. Then the
geometric feasibility is analyzed case by case by plane geometry. We also
proved that any rectangle can be 72◦ triangulated if the number of triangles
is not limited.