Creatively tiling a bathroom floor isn’t just a stressful task for DIY home renovators. It is also one of the hardest problems in mathematics. For centuries, experts have been studying the special ...

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 new 13-sided shape is the first example of an elusive "einstein" — a single shape that can be tiled infinitely without repeating a pattern. When you purchase through links on our site, we may earn ...

Infinitely many copies of a 13-sided shape can be arranged with no overlaps or gaps in a pattern that never repeats. David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss (CC BY ...

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 ...

Mathematicians have discovered a single shape that can be used to cover a surface completely without ever creating a repeating pattern. The long-sought shape is surprisingly simple but has taken ...

The original version of this story appeared in Quanta Magazine. If you want to tile a bathroom floor, square tiles are the simplest option—they fit together without any gaps in a grid pattern that can ...