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Thursday, June 8, 2023 - 13:41 in Physics & Chemistry

MATH Tweak of shape clinches discovery of nonrepeating tiling This time it’s final: Mathematicians have found a single shape for an abstract 2D tile that, in theory, can cover an infinite plane without leaving any gaps and without producing a repeating pattern. The first such “aperiodic tiling” was discovered in the 1960s and comprised 104 different shapes. In 1977, famed British mathematician Roger Penrose discovered two shapes that could do the trick. Then in March, David Smith, a hobbyist in England, and colleagues produced an aperiodic tiling using a single 13-sided shape they called a “hat.” But the proposed tiling contained some tiles that were mirror reflections of the hat—like puzzle...

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