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 ...

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 ...

Have you ever admired how the slats of a hardwood floor fit together so cleanly, or how the hexagons underneath your bathroom rug perfectly meet up? These are examples of geometric tilings, ...

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 ...

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 continue indefinitely. That square grid has a property shared ...