Web edition: July 26, 2004
Print edition: July 31, 2004; Vol.166 #5 (p. 79)
While reading about the amazing properties of Archimedes' Stomachion ("Glimpses of Genius," SN: 5/15/04, p. 314: http://www.sciencenews.org/articles/20040515/bob9.asp), I wondered whether a mere child's toy would exhibit such mathematical precision, with each vertex falling on a lattice point of a 12-by-12 grid. Perhaps Archimedes took the basic plan of the toy and tweaked it to see what properties he could induce.
Jeffry D. Mueller
Just for kicks, I drew the puzzle in a computer-assisted drawing program and looked at the areas of each one of the shapes. I was sure that they would add up to 144 units (assuming a box that is 12 units square), but I was unprepared to discover that each shape is a precise multiple of 3 units in area. Another amazing property of this puzzle!
William B. Tracy
Greenwood Village, Colo.
Archimedes's work on the Stomachion is fascinating, but even more so is the very existence of the puzzle itself. If it were meant to be a child's toy, what type of rare individual would have been the "toy maker"? What type of rare child would have played with it, or, better yet, solved it? My children played with tangrams when they were young, but their difficulty is not in the same league with that of the Stomachion.
Kathleen L. Housley
How enlightening, or at least delightful, it would have been for those of us who aren't geniuses, if you had shown at least one other of the 268 possible tiling patterns.