Mathematicians have sought this never-ending pattern for 50 years

Mathematicians have sought this never-ending pattern for 50 years

For the tiles in your bathroom, do you like repeating patterns? Otherwise, today’s mathematicians give you the opportunity to divide the entire room in one shape, without the pattern repeating itself.

It is made up of eight kites attached to its ends. And this polygon, with its thirteen sides, vaguely resembles a hat. But you can imagine that’s not what caught the researchers’ attention. No, the extraordinary thing about this model is that it can cover a surface, leaving no space or showing any overlap, and above all, without ever repeating itself. The theory predicted the existence of such a figure, but no mathematician has ever succeeded in embodying it.

In the 1970s, physicist Roger Penrose proposed an example of such a tiling that researchers called aperiodic. The famous Penrose tiles. But his motivation was based on two different forms. This time, it’s actually a non-cyclic monochromatic thatinternational team They huddle behind the present of an ordinary mathematician. Much sought after “Einstein”. It has nothing to do with the famous tongue physicist. But in the German sense of “Eye Stein”And ” to forbid “.

Einstein hats in your bathroom?

Mathematicians have been searching for such a figure for half a century now. Some even end up thinking it doesn’t exist. Or at least by imagining a very complex shape. while this “hat” It looks very simple.

To prove the extraordinary nature of this funny figure, the researchers relied on powerful computers. but also on the strength of the human spirit. The first clue was found: the fact that the “hats” In question they organize themselves into groups – called metatiles – then into larger groups – supertiles – and so on. This is what mathematicians observe in all non-periodic bishops. But the final evidence came from the severe distortions applied to “hat”.

Quasicrystals continue to fascinate physicists

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This work naturally excites researchers on a theoretical level. But they can also find practical applications in the field of quasicrystals, patterns found in robots from the Terminator type through to the Kleenex. And if you like it, it might be time to give your bathroom a crazy makeover and renovate its tiles…

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