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 ...
Roger Penrose makes his own rules. He is one of the world's most distinguished mathematical physicists and most inventive thinkers. Penrose’s work on the theory of general relativity in the 1960s led ...
The first such non-repeating, or aperiodic, pattern relied on a set of 20,426 different tiles. Mathematicians wanted to know if they could drive that number down. By the mid-1970s, Roger Penrose (who ...
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