Meet a New Shape: “The Hat”

A newly discovered shape may be able to do what no other shape can do: completely cover a surface without any pattern repeating.


Photo courtesy of CNN.

The Discovery

Created by retired printing technician David Smith in northern England, the shape has been dubbed “The hat” because of how it resembles a fedora. Unlike any other shape, when you use “The hat” as a wallpaper or tile it can cover the entire surface with no gaps and no repeating clusters- aka an “einstein”.


Smith was never passionate about math but started his hunt for the shape in 2016. Once he realized what he discovered, he reached out to Craig Kaplan a professor in the School of Computer Science at the University of Waterloo in Canada, to work with him on confirming the find.


What’s The Big Deal?

In the early 1960s, mathematicians believed that the possibility of aperiodic tiles (another term for einsteins) existing was impossible. Eventually, it was discovered that a set of 20,426 tiles could be used without repeating when used together. That number eventually dwindled to 100, six, and finally, two, where it stayed for decades with Penrose tiling.


Once peer review confirms the discovery, the tiling can be applied across many fields, including chemistry and physics.


The Future of “The Hat”

Smith and Kaplan self-published a paper with their findings in 2022. Now, they await peer review to be verified by other scientists and mathematicians.

Kaplan has stated that they will not try to protect the hat shape through copyrights, and it’s currently available to the public.


Smith has since discovered another einstein shape called “The Turtle.”