Originally Posted by CSflim

No, he's not talking about three dimensional geometry, he's talking about two dimensional geometry on a curved surface (e.g. drawing a map of the world on a globe: don't forget, we are talking about the surface of the globe which is 2D, not the actual globe itself, which is 3D). So they would be two-dimensional, just non-euclidean. They are still referred to as "circles", they just don't have the same properties as circles in a euclidean geometry (most pertinently, the fact that c/d does not equal pi).