For the tiles in your bathroom, do you like repeating patterns? Otherwise, mathematicians today give you the opportunity to tile the whole room with a single shape, without the pattern ever repeating itself.
It is made up of eight kites connected by their edges. And with its 13 sides, this polygon vaguely resembles a hat. But you can imagine, that’s not what caught the attention of researchers about it. No, what is quite exceptional about this form is that it can cover a surface, without leaving space or showing any overlap, and above all, without ever repeating itself. The theory predicted the existence of such a form, but no mathematician had yet succeeded in materializing it.
In the 1970s, physicist Roger Penrose proposed an example of such a tiling that researchers call aperiodic. The famous Penrose tiling. But his motive was based on two different forms. This time, it is indeed an aperiodic monotile that the international team gathered behind a non-professional mathematician presents. The much sought after “einstein”. Unrelated to the famous tongue-twister physicist. But with the German meaning of “ein Stein”, ” a stone “.
Einstein hats in your bathroom?
Mathematicians have been searching for such a shape for half a century now. Some even ended up thinking that it didn’t exist. Or at least by imagining an extremely complex shape. While this ” hat “ appears disarmingly simple.
To prove the exceptional nature of this funny shape, the researchers relied on powerful computers. But also on the strength of the human spirit. The first clue found: the fact that the “hats” in question organize themselves into groups – called metatiles – and then into larger groups – supertiles – and so on. This is what mathematicians observe in all aperiodic tilings. But the ultimate proof came from extreme deformations applied to the ” hat “.
This work naturally excites researchers on the theoretical level. But they could also find practical applications in the field of quasi-crystals, patterns found in Terminator-type robots up to Kleenex. And if you feel like it, it may be time to give your bathroom a crazy look and revamp its tiling…
