The Story of the Contractor and the Hexagonal Tiles
After Hales proved in 1999 the Hexagonal Honeycomb Conjecture—that regular hexagons provide the least-perimeter, minimal-interface way to tile the plane with unit areas—I decided I wanted hexagonal tiles for my kitchen:
In the middle of the job, the contractor ran out of grout for the interfaces between the tiles. He had an excuse: he explained that hexagonal tiles apparently required more grout! That was the wrong time and place for that excuse. I had to respond: “Actually…”.
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