The Shape That Broke the Rules
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A fan letter to Tile(1,1): the chiral aperiodic monotile
The chiral aperiodic monotile. It’s unique. It’s unpredictable. In some ways, it’s just like us.
A Quick History of Mathematical Chaos
For decades, mathematicians were obsessed with one nasty question: Can a single shape tile an infinite plane aperiodically?
Many shapes repeat forever. Grids, honeycomb, houndstooth – Boring! They’re so simple. We don’t do simple, we’re elegantly complex.
In the 70’s, genius physicist Sir Roger Penrose created the famous Penrose tilings: two-shape aperiodic patterns that never repeat.
Close. But not quite one shape. The world waited. Until March 2023.
Enter The Aperiodic Monotile
David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss published a history-making discovery: a family of shapes called einstein tiles that could tile a plane endlessly without repeating.
The first was The Hat - Tile(1,0)
Soon after, even better, the rarer chiral version was identified: Tile(1,1)
What makes it different?
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The Hat is achiral → it must be flipped or reflected to tile, so two shapes.
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Tile(1,1) is chiral → It exists in only ONE orientation. Left- or Right-Handedness
To The Mathematicians: Respect.
David, Joseph, Craig, Goldan-Strauss — you are legendary. You solved the mystery. Also: shirts are on us
Keep it Real. Stay AIn’t.