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Chloe Cheung

The Hat

In the world of mathematics, there are millions of shapes; ones that have many corners and sides, while some have none at all. Yet only a certain amount of shapes can form an infinite pattern. But even with these shapes, the patterns that they form are continuous, with it being carbon copies of one another. This is called mono tiling, and can be seen with something like a square or a hexagon. No matter what angle you put a square on, it will create the same pattern over and over and over again. For more than 60 years, mathematicians have been searching for an aperiodic mono tiling shape, one that when continuously tiled together, will create an infinite amount of intricate and unique patterns. Such a shape has never been found. That is until The Hat was created. David Smith, a retired printing technician in Yorkshire, England created it, a thirteen sided shape with its appearance very similar to a fedora. If you were to put this shape with itself on a plan continuously, no pattern that it creates is the same. It is known as an einstein shape, not because of the physicists, but because of the German meaning of “one stone”, with a single tile fitting together to create an irregular but infinite design.



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