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Aperiodic Monotile: Hobbyist Solves Mathematical Mystery

Updated: Oct 11, 2023

One of mathematics’ most intriguing visual mysteries has finally been solved – thanks to a hobbyist in England.

An aperiodic monotile
An aperiodic monotile never repeats a formation, no matter how long the pattern. Credit: David Smith, Joseph S Myers, Craig S. Kaplan, and C. Goodman-Strauss

The conundrum: is there a shape that can be arranged in a tile formation, interlocking with itself ad infinitum, without the resulting pattern repeating over and over again? Such a shape would be known as an aperiodic monotile, or “einstein” shape, meaning, in roughly translated German, “one stone” (and conveniently echoing the name of a certain theoretical physicist).

Now, mathematicians appear to have found what they were looking for: a 13-sided shape they call “the hat”. The discovery was largely the work of David Smith of Yorkshire, who had a longstanding interest in the question and, after a decade of failed attempts, finally cracked the conundrum.

Once he had landed on the hat, he contacted Kaplan, an associate professor of computer science at the University of Waterloo in Canada. Together they worked to confirm that the hat was indeed an einstein shape, and early this year they enlisted the help of two others – Dr Chaim Goodman-Strauss, a University of Arkansas mathematician, and Dr Joseph Myers, a software developer in Cambridge, England.

It’s unclear what the discovery could lead to outside the world of mathematics, but “there are lots of great real-world applications in art, design, architecture”, says Kaplan. “The race is on to be the first person to take a photo of their bathroom floor tiled in hats.”

For mathematicians, the discovery appears to answer a long-standing question in the field of geometry. But for the rest of us, perhaps it represents a funky new option for bathroom tiles.


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