Then, in 2023, Kaplan and collaborators stunned the mathematics world when they found the elusive einstein tile — a single shape that can fill a floor only with a never-repeating pattern ...

Although he enjoyed math in high school ... When in November he found a tile that seemed to fill the plane without a repeating pattern, he emailed Craig Kaplan, a co-author and a computer ...

Kaplan and Chaim Goodman-Strauss (CC BY 4.0) From bathroom floors to honeycombs or even groups of cells, tilings surround ... first that can fill an infinite surface with a pattern that is ...

This approach revealed that the hat tiling could fill an entire infinite plane, and that its pattern would not repeat. The second proof relied on the fact that the hat is part of a continuum of ...