Searching for an “incredible” geometric pattern: This is the favorite pastime of David Smith, a British pensioner, who indulged in it when he found a new shape with fantastic properties in November, which unleashed the enthusiasm of the community. and the admiration of scholars.
After he announced his discovery last March, these particular enthusiasts printed this new shape on T-shirts, made cookies with this design and even got tattoos on their bodies.
This thirteen-sided polygon, called a hat, is the first pattern that can be stacked infinity without creating an extensive repeating pattern—for example, a diamond that has been stacked to infinity will produce other diamonds in the At some point, a big dilemma. As such, the “hat” is the first “Einstein,” named after a problem posed 60 years ago that mathematicians assumed was unsolvable.
David Smith, 64, has done better since then, however, with “Spectrum.” Because the “hat” had a small drawback: you had to turn the pattern over once every seven moves (or every seven pieces, like a puzzle) to avoid the same repeated shape appearing.
Retired, with the help of three mathematicians, showed in a forthcoming study that the “spectrum” was pure “Einstein”. This last name is from the German “ein Stein” (stone), and has nothing to do with the famous physicist’s name.
hat and ghost
David Smith contacted him in November 2022, says Craig Kaplan, a professor of computer science at Canada’s University of Waterloo: He found a pattern that “doesn’t behave the way one would expect.”
If several copies of this pattern are stacked on a table, no general pattern will appear. A computer program confirmed that it was the first “Einstein”, which in scientific language is also called a “non-periodic monad”.
Encouraged, the British pensioner then tries to find a new cause that does not require returning periodically. Job completed in less than a week. But an analysis confirmed that this new square was an “Einstein without a reflection,” adds Computer Scientist. To be sure, the hobbyist and scientist “optimized” the figure, so that it could not be used with a reflection. The “Ghost” was born.
Finding ‘exciting, amazing, amazing’
Both scientific papers are still being considered in scientific journals before publication, but the mathematician did not wait to comment on the news.
This discovery is “exciting, amazing, amazing,” Marjorie Senich, a mathematician at Smith College (Massachusetts) told AFP. Who sees in it more than just a beautiful story. The new design and its variants should lead to “a deeper understanding of the system in nature and the nature of the system”.
For Doris Schachneider, a mathematician at Moravian University (Pennsylvania), the two figures are “impressive.” Even 2020 Nobel mathematician and physicist Roger Penrose, who specializes in aperiodic tiles, doubted that such a feat was possible, she noted.
