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 three-dimensional understanding.
This breakthrough solves a decades-old geometry problem by showing how to build objects in dimensions that we cannot envision.
The results prove that unfathomable objects can be constructed in any dimension at a fraction of the size of more traditional rolling shapes like circles or spheres.
Wheels roll because they are objects with constant width, maintaining a constant distance between two parallel planes. A shape has constant width if it can roll smoothly without wobbling.
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