We all know we live in three-dimensional space. But what does it mean when people talk about four dimensions? Is it just a bigger kind of space? Is it "space-time," the popular idea which emerged from ...

Tie a trefoil knot in a piece of string, seal the ends together, and try to wiggle it free without cutting. In three-dimensional space, the knot holds firm. Add a fourth spatial dimension, however, ...

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 ...

The notion of dimension at first seems intuitive. Glancing out the window we might see a crow sitting atop a cramped flagpole experiencing zero dimensions, a robin on a telephone wire constrained to ...

When dealing with higher dimensions in geometry, it is often instructive to start with lower ones and work your way up. If we start with two points, which are by definition each of zero dimension, we ...