These are examples of geometric tilings ... in walls and floors everywhere. In math, tilings are often appreciated for their regular patterns. But mathematicians also find beauty in irregularity. It’s ...

A new 13-sided shape is the first example ... in mathematics), you could find a position where the floor looks exactly the same as before, proving that it's a repeating pattern.

It is also one of the hardest problems in mathematics ... without ever creating a repeating design. In these special cases, called aperiodic tilings, there’s no pattern that you can copy ...

They found patterns that compute prime numbers, and even patterns that can execute arbitrarily complicated algorithms. Abstractions navigates promising ideas in science and mathematics. Journey with ...

Frank A. Farris does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations ...

Infinitely many copies of a 13-sided shape can be arranged with no overlaps or gaps in a pattern that ... investigations—for example, shapes that form non-repeating tilings could help design ...

Mathematicians solved a decades-long mystery earlier this year when they discovered a shape that can cover a surface completely without ever creating a repeating pattern. But the breakthrough had ...

but never make a repeating pattern. Periodic tilings have translational symmetry: a honeycomb pattern, for example, can be repeated forever and looks identical after being shifted in any of six ...