British pensioner surprises mathematicians with unique geometric shape

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Thirteen-sided polygon can be assembled infinitely without creating the same shape on a larger scale. Geometric shape discovered by retiree that can be infinitely assembled, without creating the same shape on a larger scale. Craig S. Kaplan/University of Waterloo via AFP A 64-year-old British retiree with a passion for mathematics has surprised geometry experts with a first-of-its-kind discovery: a polygon that can be assembled infinitely, without creating the same shape on a larger scale. Any two-dimensional geometric shape, such as a rhombus, when mounted on a flat surface will eventually form a larger rhombus. But that’s not the case with the so-called 13-sided “hat” invented by David Smith last March. It is an “aperiodic monostyle”, that is, a unique shape that does not generate a repetitive pattern. In mathematical parlance, it’s an “Einstein”, although that word doesn’t refer to the genius German scientist who discovered the Theory of Relativity. “Einstein” comes from the German “ein stein”, which means “a stone”. Finding an “Einstein” has been a challenge in the world of geometry for 60 years. As the discovery gained popularity, fans of this modest East Yorkshire pensioner, who worked in a print shop, began stamping the polygon on T-shirts, or baking cookies in the shape. Now, David Smith has just demonstrated his genius again with a new “stone”: a new polygon named “spectrum”. The only drawback of the “hat” was that every seven times it was necessary to turn it in order to avoid the apparition in the same way. With the “spectrum”, which Smith has just created with the help of three mathematicians, it is not necessary to rotate the monotyl. It’s “a fun, almost ridiculous, wonderful story,” said Craig Kaplan, a professor of computer science at the University of Waterloo in Canada. This new “spectrum” has already been tested using powerful computer programs. Waiting for the publication of two scientific articles that will demonstrate the effectiveness of this monotyl, specialists declare themselves fascinated. Both forms 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, an expert in the field, plans to attend an event in Oxford in June to celebrate the event.

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