Mathematicians define new class of shape seen throughout nature
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Mathematicians have described1 a new class of shape that characterizes forms commonly found in nature — from the chambers in the iconic spiral shell of the nautilus to the way in which seeds pack into plants.
The work considers the mathematical concept of ‘tiling’: how shapes tessellate on a surface. The problem of filling a plane with identical tiles has been so thoroughly explored since antiquity that it’s tempting to suppose that there is nothing left to be discovered about it. But the researchers deduced the principles of tilings with a new set of geometric building blocks that have rounded corners, which they term ‘soft cells’.
“Simply, no one has done this before”, says Chaim Goodman-Strauss, a mathematician at the National Museum of Mathematics in New York City, who was not involved in the work. “It’s really amazing how many basic things there are to consider.”
