Math’s acclaimed ‘einstein tile’ finds a new home among physicists
Discovered by an amateur mathematician in 2022, this strange construct can tile an infinite surface without repeating. But can it be useful in the real world?
An unconventional mathematical construct, referred to as the "hat" tile, discovered by amateur mathematician David Smith in 2022, has found a new application in the realm of physics. This tile, when used to cover an infinite surface, does so without repeating a pattern. The "hat" tile's name is a pun on the German phrase "ein stein," meaning "one stone."
Researchers from the University of Tokyo's Institute of Industrial Science have now examined the tile's physical properties in search of practical applications beyond the world of mathematics. They aimed to determine if the unique shape could generate any unexpected physical phenomena. By using a diffraction measurement technique involving a laser and a thin film of silicon nitride etched with a pattern of holes based on the hat tile's shape, the researchers discovered a distinct "handedness" in the resulting light pattern.
This unusual characteristic, caused by the asymmetry of the underlying hat tile, has led the researchers to believe that the tiling may offer a new way to manipulate the handedness of laser light, known as its "polarization." This property is crucial for various applications, including telecommunications and quantum cryptography.
The researchers hope that the mathematical curiosity behind the hat tile may lead to advancements in optical devices, ultimately unlocking potential benefits that go beyond the original mathematical wonder.
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