The surprisingly simple tile is the first single, connected tile that can fill the entire plane in a pattern that never repeats — and can’t be made to fill it in a repeating way. In mid-November of ...

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 ...

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 ...

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.

And it all began with a hobbyist “messing about and experimenting with shapes.” An “aperiodic monotile,” or einstein, is a shape that tiles an infinite flat surface in a nonrepeating pattern. The ...

Look carefully! Mathematicians have invented a new 13-sided shape that can be tiled infinitely without ever repeating a pattern. They call it "the einstein." For decades, mathematicians wondered if it ...

Earlier this spring, tiling aficionados thought maybe they’d found the shape of their dreams. Now they’re certain. By Siobhan Roberts In March, a team of mathematical tilers announced their solution ...

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 ...