On Feb 15, 2012, at 9:18 PM, Michael Reid wrote:
Veit, or others, do you have a reference for the two-piece dissection problem? Perhaps Trigg's book has one, or is the origin of it, but I haven't seen the book.
Michael Reid
When I posed the puzzle I thought it was original. I've found two, countably infinite families of triangles that dissect into a pair of mirror-symmetric pieces (which may then be reassembled into the mirror triangle). In one family the ratio of two angles equals the ratio of consecutive integers; in the other family the ratio equals the ratio of consecutive even or odd integers. Thanks for the JRM reference. My interest in this dates back to high school when I worked through Dudeney's book of puzzles and believed I had a better solution for the dissection of a heart into a spade. The triangle dissection was my "cleaner" version of the same principle. Veit