Impossible to answer?

[ledwix]

Actually, the curvature of the universe is not a term relating directly to the geometric shape of it, if I recall correctly. It refers to something regarding the average matter/energy density of the universe. A flat universe is one in which the mass/energy density hovers or stays very close to a critical value and therefore, once the cosmos reaches a maximum size, all expansion stops, and the universe stays the same size for the rest of eternity. Curvature can be either positive or negative. Positive curvature implies that the mass/energy density of the universe is higher than some critical value, and therefore, there is enough mass in the universe to make it collapse back into itself after a certain point. Negative curvature implies that the initial expansion forces and the cosmological constant propel the universe outward forever, as the forces of gravity drop off and become too weak compared to the cosmological constant. Under this scenario, the universe expands forever.

I believe the term curvature itself is used because of the way gravity (i.e. mass) causes curvatures and distortions in spacetime according to relativity.