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 ...

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 ...

Remember the graph paper you used at school, the kind that's covered with tiny squares? It's the perfect illustration of what mathematicians call a "periodic tiling of space", with shapes covering an ...

What just happened? A group of mathematicians created a "new" polygon previously known to exist only in theory. It's a 13-sided shape that they dubbed "the hat," even though it only vaguely resembles ...