Can Number Theory be visualized? So I was thinking about a hard euclidean geometry problem, when it hit me just how much more difficult it would become without the aid of a diagram. This got me thinking: Wouldn't it be great if we could somehow find corresponding diagrams for something like number theory? It doesn't have to be euclidean geometry diagrams like the Greeks did with Algebra (which actually made it harder than without diagrams, as we all know), but instead we need to find a natural diagrammatical representation. Something like Ferrers diagram seems to be a tiny step in that direction, and I can imagine similar things being done for all of number theory.
Is this idea at all feasible? Please explain why.
EDIT: I will leave the above to make answers more interesting. However, a related question (as suggested by Omnomnomnom) that is perhaps more useful is the following: What kinds of diagrams already exist in number theory?
Eagerly awaiting any responses!

There is an area called arithmetic geoemetry that exploits links between arithmetic and algebro-geometric questions. 
For example, Fermat's famous equations $X^n + Y^n = Z^n$ can be thought of as a curve in projective space, called Fermat curves, and one can use geometric tools to study it. 
The affine part, so $X^n + Y^n = 1$ is somewhere between a circle and a square; for small $n$ close to a circle (well for $n=2$ it is of course a circle, but this is not relevant for FLT) an for large $n$ it approaches a square-like form. 
