The figure shown is a triamond, a figure formed by joining three equilateral triangles at the edges (named on analogy with a diamond, which is formed by joining two such triangles). A triamond is therefore an isosceles trapezoid with base angles of 60. If a triamond has sides whose lengths are integers, it may be possible to cut it into smaller triamonds which also have integral sides. The puzzle this month is to take a triamond whose shortest sides are 11 units and dissect it into the smallest possible number of smaller triamonds. The smaller triamonds will be of assorted sizes -- not all the same size, nor all different. You could print out the image above to experiment upon, or you could use isometric-orthographic graph paper (marked in a triangular grid). I’ve seen the analogous puzzle about dissecting squares posted on a CompuServe forum, but I don’t know where it originated. I don’t know whether anyone else has tried dissecting a triamond into a minimal number of similar shapes, but so many problems of combinatorial geometry have occupied researchers that I wouldn’t be surprised. (Erich Friedmann, for instance, has a good webpage on combinatorial geometry.) Click here for the solution. |
