I love this tile pattern, which is pretty common in old institutional bathrooms, like in train stations or aging university buildings. When our downstairs bathroom flooded a few years ago, I had the tile replaced with this pattern. The color in the picture is pretty blown out, but in the lower right corner you can see the pattern of black and white hex tiles. If the tiles are regular and the edges of the hexagons have length 1, the diagonal pitch of the black "squares" in one direction is 6 and in the other direction is 4*sqrt(3) -- almost 7. So not squares. On Sun, Jul 21, 2019 at 6:04 PM Bill Gosper <billgosper@gmail.com> wrote:
I'm pretty sure this is the pattern in Oren's Hummus bathrooms on Castro St;
Can you find a short proof or disproof that the dark tiles form a square grid? —Bill (During the 70s, I stared at (slowly, in those days) evolving Life patterns so habitually that the AI Lab bathroom tiles would run a couple of steps when I looked down. But those were square tiles, randomly dark and light.) _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun