A new mathematical technique shows how to build small objects in any dimension that roll like a wheel, expanding our understanding of higher dimensional space
. 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 .
Wheels roll because they are objects with “constant width”—they appear to be the same width from every angle. Thisallows wheels to maintain a constant distance between two parallel planes, such as the ground and a car, as they move. Essentially, a shape has constant width if it can roll smoothly without wobbling.
To represent this in two dimensions, again draw an equilateral triangle, followed by a circle centered around one of the triangle’s vertices, with a radius as long as each of the triangle’s legs. Then imagine moving that circle so that its center point follows the outline of the triangle, going up each leg and past each vertex before returning to where it started. As the circle moves, there are some places that it consistently occupies.
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