golygon

A golygon, or more generally a serial isogon of 90°, is any polygon with all right angles (a rectilinear polygon) whose sides are consecutive integer lengths. Golygons were invented and named by Lee Sallows, and popularized by A.K. Dewdney in a 1990 Scientific American column (Smith). Variations on the definition of golygons involve allowing edges to cross, using sequences of edge lengths other than the consecutive integers, and considering turn angles other than 90°. Properties In any golygon, all horizontal edges have the same parity as each other, as do all vertical edges. Therefore, the number n of sides must allow the solution of the system of equations It follows from this that n must be a multiple of 8. For example, in the figure we have and . The number of golygons for a given permissible value of n may be computed efficiently using generating functions . The number of golygons for permissible values of n is 4, 112, 8432, 909288, etc. Finding the number of solutions that correspond to non-crossing golygons seems to be significantly more difficult.