A plane is defined by being 2-dimensional. But if it is curved (like a hyperbolic plane), it requires an extra dimension, that is, it is curved in a 3-dimensional space. So it seems, 2-D coordinates wouldn't be enough to describe this plane. What is it's dimension? Should it be considered as 2 < D < 3 (some sort of fractal dimension)?
I'm not sure whether this question is suitable for Philosophy... please comment.