Have you ever heard of the “Einstein” card? She is not related to the famous physicist, but she nevertheless revolutionized the world of mathematics and geometry. This small shape, ingenious in its own way, has a "clever" name that recalls the famous scientist but also takes inspiration from the German language.
“Ein Stein”, in fact, simply means “a stone”. Only one, with a shape that however has the ability to cover an infinite surface without ever repeating itself. And it does so in a way that no other known form can. If this seems like a joke to you, know that his discovery was a real challenge that required decades of research.
An unrepeatable shape
In the 70s, the mathematician Roger penrose he had created an aperiodic tessellation, that is, a shape that never repeats. However, to make it he had used two different tiles. Since then, mathematicians have wondered whether it was possible to create an aperiodic tessellation with just one tile. The answer has only arrived now, thanks to the intuition of david smith and his team of researchers. The “Einstein” tile is made up of a set of polygons joined together to form a complex and irregular structure. What makes it special is its ability to arrange itself in such a way as to create ever larger structures, without ever repeating itself. To demonstrate its aperiodicity, the researchers used a mix of powerful computer calculations and human creativity. The study was published in ArxiV (I link it here).
What can such a card be used for?
You can finally have a bathroom full of tiles that are smarter than you. No, I'm joking. What a bad joke, I respect my readers. Ok, full of tiles smarter than me. Apart from this, however, the discovery of the “Einstein” card has considerable importance for geometry, mathematics and materials science. Aperiodic tilings are fundamental in the development of the so-calledquasicrystals“, which in turn are crucial in many fields, from robotics to medicine. And of course, by golly: the design.
Mainly, it shows how mathematical research can lead to surprising and unexpected discoveries, with implications that go far beyond the academic field. Apparently human creativity is still essential for solving complex problems. This must be why mathematicians all over the world are crazy about it.
