The Power of Recursion: Connecting Mathematical Ideas
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Mathematicians Craig S. Kaplan, David Smith, Chaim Goodman-Strauss, and Joseph Samuel Myers embarked on a quest to find an aperiodic monotile, a shape that tiles the plane without repeating periodically. Smith discovered a shape called the 'hat' and reached out to Kaplan, leading to a collaboration to study the hat's properties. They developed substitution rules and proved that the hat is an aperiodic monotile. Later, they discovered the 'turtle,' which turned out to be a disguised version of the hat. They also explored the Tile(1,1) continuum and found a family of shapes called 'spectres' that are chiral aperiodic monotiles. The mathematicians hope their work will inspire others to explore tiling theory.
Mathematicians are still learning new things about the nature of numbers, shapes, an...
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