Two-dimensional tilings are admired all around the world, both for their beauty — as seen in the artistry of mosaics in cathedrals and mosques around the world — and for their utility, in walls and ...

Another take on tiling with regular polygons comes from Johannes Kepler, today best known for his discoveries about planetary motion. In 1619, he showed that even if you use more than one regular ...

Then, in 2023, Kaplan and collaborators stunned the mathematics world when they found the elusive einstein tile — a single shape that can fill a floor only with a never-repeating pattern ...

A new shape called an einstein has taken the math world by storm. The craggy, hat-shaped tile can cover an infinite plane with patterns that never repeat.

This week, mathematicians announced the discovery of a single tile shape that produces aperiodic patterns. ... The Math of Putting Tiles Together. By Siobhan Roberts March 30, 2023.

An “aperiodic monotile,” or einstein, is a shape that tiles an infinite flat surface in a nonrepeating pattern. The authors of a new paper called their einstein “the hat,” as it resembles ...

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 ...