I see, it's crucial to the puzzle that we can't actually see the boundaries between the white tiles ... otherwise we could count the hexes. However, perhaps you could use the "give" of the tile grout to squeeze the rhumbuses into squares? On Mon, Jul 22, 2019 at 1:26 PM Bill Gosper <billgosper@gmail.com> wrote:
[Math-fun: For pic, see recent mail] Spoiler: Ideal would be a proof that there is no square grid in a honeycomb tiling, analogous to no equilateral triangles in a square grid. (Despite note 3 to 5 o'clock, 6 to 8 o'clock <http://gosper.org/p24backrakes.png>) Rectangle Arithmetic (see pp 12+13 of 14) <http://gosper.org/rectarith12.pdf> And yet contractors are condemned to build rectangular bathrooms. Perhaps they bribe the general contractor to make the house very slightly rhombic. —rwg
On Sun, Jul 21, 2019 at 6:03 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.)
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