New 13-Sided Shape Discovered By Mathematicians

Meet the one shape that can cover all. Just kidding, it’s still a new discovery, regardless. 

Einstein is a 13-sided shape discovered by computer scientists that is capable of covering a plane without repeating a pattern. In the field of mathematics, this is called an  "aperiodic monotile," a figure that can tile a plane but never repeat. 

Craig Kaplan, computer science from the University of Waterloo and one of the paper's four authors shared that this is the first true monotile. "We prove that this shape, a polykite that we call 'the hat,' must assemble into tilings based on a substitution system," he wrote. 

Kaplan and his associates were looking for a one-in-a-million thing. One of his co-authors, Chaim Goodman-Strauss, shared that you start by exploring around 999,999 possibilities.  "You filter out the 999,999 of the boring ones, then you've got something that's weird, and then that's worth further exploration. And then by hand you start examining them, try to understand them, and start to pull out the structure," he told New Scientist.

Image credit: Craig S. Kaplan/Twitter

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