The notion of a Riemannian manifold evolved from more concrete objects like surfaces in three-dimensional Euclidean space. But how much more general is this concept?
Nash's embedding theorem gives one answer to the question whether or not a Riemannian manifold can be isometrically embedded into Euclidean space. It provides surprising and, at first glance, inconsistent results which we want to illustrate by considering the example of a flat torus.