Bill, That's a fairly common exhibit that I've seen at many science museums. As you point out, one of its limitations is that it only demonstrates the theorem for a single triangle. For MoMath, I wanted to create all new exhibits, not found anywhere else. So I came up with a variation in which the triangle was adjustable. The C^2 is always the same, but the right angle moves along a semicircle, so the legs can vary and sliding components change the leg squares appropriately. We engineered a way where it was feasible, not with a fluid (which would leak), but with a fixed volume of small beads. In the end it didn't make the final cut of exhibits. However, it's possible it may show up as a replacement exhibit at some time in the future. George http://georgehart.com/ On 12/17/2012 1:03 AM, Bill Gosper wrote:
Doug Hofstadter found this nice YouTube: http://www.youtube.com/watch?v=CAkMUdeB06o&sns=em Regardless of its rigor, it makes the statement of the theorem unmistakable and unforgettable. Perhaps adjacent could be the isosceles case, in case anyone thinks it only works for 3-4-5, and the equilateral and obtuse cases, with just enough liquid for the "largest" square, failing dissimilarly. --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun