Regions in complete graph

mcnkevin

Say you draw the n'th complete graph in such a way that no three (or more) edges intersect at any one point (other then the vertices). Basically, the graphs are drawn such that they are equally spaced around a circle.

Always drawn as it shows here http://en.wikipedia.org/wiki/Complete_graph

How many regions (triangles) are in the Knth complete graph? What is the logic behind this?