Ah, tiles. You can get square ones, and do a grid, or you can get fancier shapes and do something altogether more complex. By and large though, whatever pattern you choose, it will normally end up ...

One of the oldest and simplest problems in geometry has caught mathematicians off guard—and not for the first time. Since antiquity, artists and geometers have wondered how shapes can tile the entire ...

Consider the tiles on a bathroom floor or wall; they’re often arranged in a repeating pattern. But is there a single shape that tiles such a surface — an infinite one — in a pattern that never repeats ...

Ah, tiles. You can get square ones, and do a grid, or you can get fancier shapes and do something altogether more complex. By and large though, whatever pattern you choose, it will normally end up ...

(via Minutephysics) This video is about a better way to understand Penrose tilings (the famous tilings invented by Roger Penrose that never repeat themselves but still have some kind of order/pattern) ...

The first such non-repeating, or aperiodic, pattern relied on a set of 20,426 different tiles. Mathematicians wanted to know if they could drive that number down. By the mid-1970s, Roger Penrose (who ...