In March 2023 an aperiodic tessellating tile was announced. It marked the a significant milestone in mathematics, a single tile that tessellated, but the layout of the tiles did not create a repeating pattern, ever. The tile is called the ein stien tile, a play on words. In German this means “one stone” and also sounds like a well known genius… the tile has been given the nick name the “hat.”

The properties of this tile give us lots of interesting learning opportunities in the classroom. This resource is designed for teachers to take this tile as a starting point to investigate tessellations, map theory, 2D shape, Euclidean geometry,construction of simple shapes using compass, pencil and ruler, you can take it in any direction you wish. There is even a 3D printing element built into this. We have created a resource box of 200 3D printed tiles to accompany this, please contact us if you want more information about where to obtain this from.

Since the first iteration of this resource was uploaded, I have added some additional challenges for students to get their teeth into, the final challenge encourages students to investigate the external angles of the “hat tile” and then use this information, plus the dimension information they worked out from earlier investigations, to create an ein stein tile in Scratch. If you would like to see the code to do this, you can see the example I have created here. Obviously, this is not something to share with the students, but is designed to help you support them through the challenge and look like a coding boss as you do!

If you want us to make more of this kind of resource please contact us at david@dakinane.com and we will make more resources to share with you, related to your need. If you want to gain access to a copy of the teaching resource shown above please contact us also.