Tessellations
- Anna Oliva
- Apr 27, 2023
- 1 min read
As a child I would run my hands over the expanse of tiles that lined the floors of my grandmother’s kitchen. Little squares, triangles, even rhomboids were scattered in a dizzying array of color. Now, I live in a world of subway tiles and mosaics, of black and white squares of a chess board, surrounded by tilings. Like everything else, these patterns can be described mathematically.
Tiling is the study of planar subsets that cover the plane without gaps or overlaps. It’s a branch of mathematics that deals with different ways to tile the plane and seems a bit like a geometrically oriented cousin of graph theory. Tessellations are those tilings which continue infinitely. It has been a goal of mathematicians to find tessellations that never repeat with the smallest possible number of shapes. Until now that number has been two, as shown by Penrose tessellations. The goal has been to find the “einstein” shape which would singularly tile the plane aperiodically and infinitely. Recently, a 13-sided shape referred to by its discoverers as “the hat” has been mathematically shown to do just that.
More on the discovery:
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