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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 pieces laid face side down—and some critics argued this meant two different tiles had been used. Now, Smith and colleagues have tweaked the shape to create one they call a “Spectre.” It produces a tiling that includes no mirror images , they reported last week in a preprint posted on arXiv—leaving no space for objections. LABOR RELATIONS NIH fellows move to unionize Early-career researchers at the U.S. National Institutes of Health (NIH) last week took a step toward forming a union, which would be the first to represent research fellows working at a federal agency. Organizers gathered signatures in support from roughly 3000 of the 4800 postdocs, graduate students, and other junior researchers who woul...
Source: ScienceNOW - Category: Science Source Type: news