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.

At the time there was no evidence linking repeating pattern knowledge to later math outcomes ... Can you give me an example of what they did do in the studies? My favorite example is we asked ...

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 ...

What is unique about this geometrical figure is that it can tile a plane without creating a repeating pattern ... decades been purely theoretical. The math proved it existed, but nobody had ...

The math Newberry and his student Jingyi Gao used is based on fractals. These are patterns created by repeating the same smaller pattern within itself. Snowflakes are an example of this ...

Researchers have discovered a new 14-sided shape called the Spectre that can be used to tile a surface without ever creating a repeating pattern ... in the world of mathematics.

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 ...