In a hypertorus model of the Universe, motion in a straight line will return you to your original location, even in an uncurved (flat) spacetime. The Universe could also be closed and positively curved: like a hypersphere. (ESO AND DEVIANTART USER INTHESTARLIGHTGARDEN)

Ask Ethan: Why Is The Universe Flat?

It could have had any curvature at all. So why is it flat?

What is the shape of the Universe? If you had come along before the 1800s, it likely never would have occurred to you that the Universe itself could even have a shape. Like everyone else, you would have learned geometry starting from the rules of Euclid, where space is nothing more than a three-dimensional grid. Then you would have applied Newton’s laws of physics and presumed that things like forces between any two objects would act along the one and only straight line connecting that. But we’ve come a long way in our understanding since then, and not only can space itself be curved by the presence of matter and energy, but we can witness those effects. Yet somehow, when it comes to the Universe as a whole, space itself appears indistinguishable from perfectly flat. Why is this? That’s what Stan Echols wants to know, writing in to ask:

“Why is the universe relatively flat instead of being shaped like a sphere? Doesn’t the universe also expand perpendicularly to the relatively flat surface?”

Let’s start off with the old definition of space, which is probably what most of us picture: some sort of three-dimensional grid.