Exploring the transition from special to general relativity

In a previous paper we discussed two examples of circular motion which are especially useful in relativity courses because they lead to predictions verified by experiments with macroscopic objects. We analyzed these examples by considering motion around an N-gon and then taking the limit as N ->infinity and the N-gon becomes a circle. In this paper we use the same approach to illustrate how generalizing special relativity to a theory that includes non-inertial frames can lead to a non-Euclidean geometry. We also derive two properties of clocks at rest in a reference frame traveling on a circular path.