(Paris) Searching for an “astounding” geometric shape: It’s a favorite pastime of David Smith, a quiet British pensioner, when he spotted a new shape with remarkable properties in November. Activists. And the admiration of scholars.
After he made his discovery public last March, these particular enthusiasts thought of printing the new pattern on T-shirts, making cookies with the design, and even tattooing it on their bodies.
This thirteen-sided polygon, known as the “hat”, is the first shape that can be ad infinitum without showing an overall repeating pattern – for example, a diamond among other diamonds will at some point form a larger diamond.
Thus, the “hat” is the first “Einstein”, named after a problem posed 60 years ago and which mathematicians considered insoluble.
David Smith, 64, did well with “Spectrum.” Because the “hat” had a small drawback: to avoid the appearance of the same pattern, the pattern had to be changed every seven moves (or every seven pieces, like a puzzle).
The retiree, with the help of three mathematicians, has demonstrated in an upcoming study that the “spectrum” is pure “Einstein.” This last name is derived from the German “Ein Stein” (a stone), and is unrelated to the famous physicist.
Hat, Tortoise and Spectrum
For Craig Kaplan, a computer science professor at Canada’s University of Waterloo, it was “a funny and almost ridiculous, but amazing story,” he told AFP.
A former printing technician in Yorkshire (North of England), Mr. He says Smith contacted him in November 2022: “It’s not going the way you’d expect.”
If several copies of this model are assembled on a table, the overall pattern will not appear. A computer program confirmed that this was the first “Einstein”, also known in scientific parlance as an “aperiodic mono-tile”.
Their work was noticed by Japanese researcher Yoshiaki Araki, a proponent of manipulating these shells, who created works of art using a variation called a “hat” and a “turtle”.
Encouraged, our British retiree tries to find a new form that doesn’t need to be returned from time to time. In the face of an incredulous Craig Kaplan, the task was accomplished within a week.
But an analysis has confirmed that this new tile is “an Einstein without upside down,” says the Canadian computer scientist. Also, the hobbyist and scientist also “improved” the form so that it could not be used in reverse. “The Spectre” was born.
“Falling from the Sky”
Both scientific papers are peer-reviewed in scientific journals before publication, but the mathematical world is not waiting to comment on the news.
AFP Marjorie Senechal, a mathematician at Smith College (Massachusetts) said the discovery was “exciting, surprising and surprising”. Who sees in this more than a beautiful story. The new motif and its variations “lead to a deeper understanding of the nature of order and order in nature”.
To Doris Schatznader, a mathematician at Moravian University (Pennsylvania), both patterns are “interesting.” Mathematician and 2020 Nobel in Physics Roger Penrose, an expert on aperiodic tiles, also doubted such a feat was possible, he notes.
The prestigious University of Oxford organizes an event in July to celebrate this discovery, a hatfest (hat party) featuring Roger Penrose.
Craig Kaplan asserts that the discovery is all the more surprising because “the answer fell from the sky and from the hands of an amateur.” “And in the most beautiful way, thanks to the lover of the subject who explores it outside of any professional aim”.