This research was inspired by two lovely pieces of mathematics. The first is the discovery by William T. Tutte, A. H. Stone, R. L. Brooks, and C. A. B. Smith of squares with integral sides that can be tiled by smaller squares with integral sides, no two alike. Tutte tells the story in "Squaring the Square," a beautifully written article that conveys vividly the excitement of mathematical research [9]. It be came widely-read in 1958 when it was reprinted in Martin Gardner's "Mathematical Games" column in Scientific American. It undoubtedly played a role in inspiring many to become mathematicians.