Dan, do you mean to exclude the near-trivial family related to the Pythagorean tiling? Any two squares tile a square torus. I don't know of any *other* examples, though. On Thu, Jul 23, 2020 at 8:19 PM Dan Asimov <dasimov@earthlink.net> wrote:

Has anyone ever found a squared square torus that wasn't a squared square?

—Dan

----- https://community.wolfram.com/groups/-/m/t/2044450

Jim Williams recently finished a multi-year search for all simple perfect squared squares up to order 37. More details will eventually by at squaring.net. For orders 21 to 37, there are {1, 8, 12, 26, 160, 441, 1152, 3001, 7901, 20566, 54541, 144161, 378197, 990981, 2578081, 6674067, 17086918} such squares (A006983).

Codes, numbers, and pictures at the link. -----

_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun