A British retiree surprises mathematicians with an unprecedented geometric shape

A retired 64-year-old British fan of mathhas surprised experts in geometry with an unprecedented discovery: a polygon that can be assembled infinitely, without recreating the same shape on a larger scale.

Any two-dimensional geometric shape, such as a rhombus, that is assembled on a flat surface, will end up forming a larger rhombus.

But this is not what happens with the so-called “hat” of 13 sides that David Smith invented last March.

It’s about a “aperiodic monotyl”that is, in a unique way and that does not generate a repetitive pattern.

In the mathematical jargon, it is a “einstein”, without this word alluding to the German genius who discovered the theory of relativity.

“Einstein” comes from german “ein stein”: “a stone”.

discover a einstein” was a challenge in the world of geometry for 60 years.

As the discovery has gained popularity, fans of the modest East Yorkshire retiree, who worked in a printing shop, have taken to stamping the polygon on T-shirts, or baking cookies in the shape.

Now David Smith has just returned to demonstrate his genius with a new “stoned”: a new baptized polygon “spectrum”.

The only drawback of “hat”was that every seven times it had to be given a twist, to avoid the appearance of the same shape.

With the “spectrum”, that Smith has just created with the help of three mathematicians, the monotile does not need to be rotated.

Is “a funny and almost ridiculous story, wonderful”said Craig Kaplan, a professor of computer science at Canada’s University of Waterloo.

This new “spectrum” has already been put to the test using powerful computer programs.

While waiting for the publication of two scientific articles that would demonstrate the effectiveness of this monotyl, the experts declare themselves fascinated.

Both ways are “impressive”in the words of Doris Schattschneider, a mathematician at the University of Moravia (Pennsylvania), while the 2020 Nobel Prize in Physics, Roger Penrose, a specialist in the field, plans to participate in an event in Oxford in June, to celebrate the event.

Fountain. AFP