One of the oldest and simplest problems in geometry has caught mathematicians off guard—and not for the first time. Since antiquity, artists and geometers have wondered how shapes can tile the entire ...
Mathematicians predicted that if they imposed enough restrictions on how a shape might tile space, they could force a periodic pattern to emerge. But they were wrong. One of the oldest and simplest ...
Surprisingly, the answer turns out to be yes—if you’re allowed to shift, rotate, and reflect the tile, and if the tile is disconnected, meaning that it has gaps. Those gaps get filled by other ...
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