MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

Mathematical Properties 71
Figure 2.62: Perfect Triangulation [310]
any nonequilateral triangle can be tiled by smaller unequal triangles similar to
itself.
Figure 2.63: Convex Tilings [294]
Property 78 (Convex Tilings). In 1996, R. T. Wainwright posed the question:
What is the largest convex area that can be tiled with a given number of
equilateral triangles whose sides are integers, where, to avoid trivially scaling
up the size of a given tiling, the sizes of the tiles are further constrained to
have no overall common divisor [294]?