From four-dimensional hexagons to the mind-bending amplituhedron, geometrical shapes are wilder than we learn at school - and they are a crucial tool for understanding reality ...

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 ...

Think about embedding a one-dimensional closed loop in the two-dimensional plane. The number of ways you can do it are as limitless as the number of ways you can place a loop of string on a table. But ...

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 ...

She doesn’t think they’ll find a three-dimensional tile, but she says it’s feasible that a 4D one could exist. And so, Iosevich said, they didn’t just disprove the periodic tiling conjecture: “They ...