Why Is This Shape So Terrible to Pack?

For centuries, mathematicians suspected that hexagonal tiles are the best possible way to fill space. By this they mean that if you want to subdivide a large area into tiles of equal size while minimizing the perimeter of each tile, you can’t do any better than hexagons. In 1999, Thomas Hales of the University of Pittsburgh finally proved it. They’re better than squares, triangles…

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