A geometry problem that has been puzzling scientists for 60 years has likely just been solved by an amateur mathematician with a newly discovered 13-sided shape. Called “The hat” because it vaguely ...

A 13-sided shape known as “the hat” has mathematicians tipping their caps. It’s the first true example of an “einstein,” a single shape that forms a special tiling of a plane: Like bathroom floor tile ...

For some, tiles are rarely thought of unless it’s time for home renovations, but for mathematicians, they present plenty of conundrums—and a clever team has just cracked a particularly tricky one.

On March 20, 2023, a team of four researchers announced that they had discovered a shape. This was big news in the world of mathematics and was widely reported in the media. The reason for the ...

The recently discovered “hat” aperiodic monotile admits tilings of the plane, but none that are periodic [SMKGS23]. This polygon settles the question of whether a single shape—a closed topological ...