It is rare for a shape to make a splash, but this year one did just that with the announcement of the first ever single tile that can cover a surface without forming repeating patterns. The discovery of this 鈥�aperiodic monotile鈥� in March has since inspired everything from jigsaw puzzles to serious research papers.
鈥淚t鈥檚 more than I can keep up with in terms of the amount and even, to some extent, the level and depth of the material, because I鈥檓 not really a practising mathematician, I鈥檓 more of a computer scientist,鈥� says at the University of Waterloo, Canada. He is on the team that found the shape, which it called the 鈥渉at鈥�. Mathematicians had sought such an object for decades.
After revealing the tile in March, the team unveiled a second shape in May, the 鈥渟pectre鈥�, which improved on the hat by not requiring its mirror image to tile fully, making it more useful for real surfaces.
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The hat has since appeared on , , bags and as cutters that allow you to make your own ceramic versions.
It has also sparked more than a dozen papers in fields from engineering to chemistry. Researchers have investigated how the structure and the likely physical properties of a . Others have found that structures built with repeating hat shapes could be than a honeycomb pattern, which is renowned for its strength.
Kaplan says a scientific instrument company has also expressed an interest in using a mesh with hat-shaped gaps to collect atmospheric samples on Mars, as it believes that the pattern may be less susceptible to problems than squares.
鈥淚t鈥檚 a bit bittersweet,鈥� says Kaplan. 鈥淲e鈥檝e set these ideas free into the world and they鈥檝e taken off, which is wonderful, but leaves me a little bit melancholy because it鈥檚 not mine any more.鈥�
However, the team has no desire to commercialise the hat, he says. 鈥淭he four of us agreed early on that we鈥檇 much rather let this be free and see what wonderful things people do with it, rather than trying to protect it in any way. Patents are something that, as mathematicians, we find distasteful.鈥�
