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Labelled as ‘one of mathematics’ most intriguing visual mysteries’, clever  people have forever tried to find a shape that can be ‘arranged in a tile formation, interlocking with itself ad infinitum’, without creating a pattern that repeats itself over and over again.

For those of us that flunked maths after the curriculum moved beyond 1+2, just think of your bathroom tiles: No matter how they are arranged, there is always a repeating pattern visible. What researchers were looking for was a shape that always fits into itself, but never repeats the same pattern. Still confused? Well, as my math teacher said, maybe a video will help. Behold the aperiodic monotile:

Called the Hat, the 13-sided shape can be arranged in tile formation forever and it will never repeat a pattern. In other words, there was no way to tile them so that the overall pattern created a repeating grid.

Cookies. I will put a cutter on Printables a bit later. pic.twitter.com/hH2E8BH7zY

— Nikolay Tumanov (@ntumanov_Xray) March 28, 2023

One of the super nerds who are excited about this find is Dr Craig Kaplan, an associate professor of computer science at the University of Waterloo in Ontario.

“There’s been a thread of beautiful mathematics over the last 60 years or so searching for ever smaller sets of shapes that do this. The first example of an aperiodic set of shapes had over 20,000 shapes in it. And of course, mathematicians worked to get that number down over time. And the furthest we got was in the 1970s”

According to The Guardian, the intriguing shape was largely found by David Smith of the East Riding of Yorkshire, who had a long-time curiosity about the shape. After cutting out a sample in cardboard, Smith managed to ‘grid’ about 32 shapes together without seeing a pattern emerge. It was at this point that he called the big boys.

Kaplan said that Smith managed to get halfway through the problem, but together they “were able to sort of fill in the rest of the puzzle and provide the rest of a proof”.

That proof was fueled by another stunning finding: after discovering “the hat”, Smith landed on another shape that did the same job and looks a bit like a turtle.

Smith has now been credited as a co-author on the paper detailing their findings.

Exactly what this will change in the cut-throat world of international mathematics is likely beyond us to understand, but Dr. Kaplan says “There are lots of great real-world applications in art, design, architecture”. Besides all that, the race is apparently on among the interested folks to see who can tile their bathroom first with ‘The Hat’.

For a mathematically stunted person like myself, this means little, except possibly ‘inventing’ an investment opportunity that’s definitely not a pyramid. It’s a hat, as per science.

Anybody in?

[source:guardian]