What about our actual universe on cosmological scales? Do we expect that its spatial geometry is Euclidean, or might it accord more closely with some other geometry, such as the remarkable hyperbolic geometry (but in three dimensions) that we have been examining in §§2.4–6. This is indeed a serious question. We know from Einstein’s general relativity (which we shall come to in §17.9 and §19.6) that Euclid’s geometry is only an (extraordinarily accurate) approximation to the actual geometry of physical space.
