[masraum]

The math nerd in me loves this.

https://www.smithsonianmag.com/smart-news/at-long-last-mathematicians-have-found-a-shape-with-a-pattern-that-never-repeats-180981899/



(Not the full article, only excerpts)

After decades of searching for what mathematicians call an “einstein tile”—an elusive shape that would never repeat—researchers say they have finally identified one. The 13-sided figure is the first that can fill an infinite surface with a pattern that is always original.

Repeating patterns have translational symmetry, meaning you can shift one part of the pattern and it will overlap perfectly with another part, without being rotated or reflected. The shape described in a new paper does not have translational symmetry—each section of its tiling looks different from every part that comes before it.

David Smith, a retired printing technician and nonprofessional mathematician, was the first to come up with the shape that could be a solution to the long-standing “einstein problem.” He shared his ideas with scientists who took on the challenge of trying to mathematically prove his conjecture, per the New York Times’ Siobhan Roberts.

The team published a preprint paper detailing the findings on the site arXiv last week, and it has not been peer-reviewed yet. But experts say the work is expected to be supported with further investigation, per Science News.

“This appears to be a remarkable discovery,” Joshua Socolar, a physicist at Duke University who did not contribute to the finding, tells the Times. “The most significant aspect for me is that the tiling does not clearly fall into any of the familiar classes of structures that we understand.”