One of the oldest and simplest problems in geometry has caught mathematicians off guard—and not for the first time. Since antiquity, artists and geometers have wondered how shapes can tile the entire ...

This is a preview. Log in through your library . Abstract We construct a counterexample to the "hot spots" conjecture; there exists a bounded connected planar domain (with two holes) such that the ...

How to safely reopen offices, schools and other public spaces while keeping people six feet apart comes down to a question mathematicians have been studying for centuries. Sphere packing might seem ...

IN a recent number (NATURE, vol. xviii. p. 263) we took occasion to suggest that the usefulness of a school scientific society might still further be increased by calling in the assistance of ...

Mathematicians are “reinventing the wheel” by giving it a new shape. Their newly imagined wheel looks like a many-dimensional guitar pick, and it could theoretically roll in ways beyond our ...

Before high school, statistics and geometry often get shunted to the end of the academic year, increasing the odds that teachers may not get to them. The tips, examples, and resources below can help ...

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Crows are able to look at a handful of four-sided shapes and correctly distinguish those that exhibit geometric regularity from those that don't, according to a provocative new study. It's the first ...

In October 2015, a young mathematician named Clemens Sämann was flying home to Austria from a conference in Turin, Italy, when he had a chance encounter. He found himself seated beside Michael ...