[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.)