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, ...

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 ...

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 ...

A pair of identical particles swapping places sounds like a small move. In quantum physics, it is a defining one.