Hobbyist Mathematician Invents 13-Sided “Einstein” Shape

David Smith, a hobbyist mathematician based in the UK’s East Yorkshire, is largely responsible for figuring out one of the most puzzling visual mathematical problems: “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?” The search for this “Einstein” shape—an aperiodic monotile—has been predicted to exist, but never figured out until now. Smith’s 13-sided shape, known as “the hat,” has no translational symmetry, meaning it can be tiled but will never repeat its pattern. After creating “the hat,” Smith contacted University of Waterloo’s Dr Craig Kaplan and they (along with mathematician Dr Chaim Goodman-Strauss and software developer Dr Joseph Myers) co-authored a paper on the shape. “The miracle is that this little tile disrupts order at all scales,” Goodman-Strauss says. “These tiles are just sitting next to each other and somehow have these effects at any length scale: miles, 10 miles, 100bn light years, these little guys are somehow causing effects at these arbitrary long distances.” Find out more at The Guardian.

Image courtesy of David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss