Fun with lines and modular arithmetic

In the applet below, n is the number equally-spaced points on the circumference of the circle. Each point corresponds to an angle There is a line drawn from each such point to the point with angle Another way to view this is that the points represent the values {0,1,2,3,...,n-1}. We then join each point labeled k to the point labeled mk (mod n). The bottom applet is the same except we draw lines rather than line segments.