A 13-sided shape known as “the hat” has mathematicians lifting their caps.
Identified by David Smith, a nonprofessional mathematician who describes himself as an “imaginative tinkerer of shapes,” and reported in a paper posted online March 20 at arXiv.org,— a bunch of smaller kite shapes stuck together.
. From there, “It was natural to wonder, could there be a single tile that does this?” says mathematician Casey Mann of the University of Washington Bothell, who was not involved with the research. That one has finally been found, “it’s huge.” The second proof relied on the fact that the hat is part of a continuum of shapes: By gradually changing the relative lengths of the sides of the hat, the mathematicians were able to form a family of tiles that can take on the same nonrepeating pattern. By considering the relative sizes and shapes of the tiles at the extremes of that family — one shaped like a chevron and the other reminiscent of a comet — the team was able to show that the hat couldn’t be arranged in a periodic pattern.
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