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 [math]\theta.[/math] There is a line drawn from each such point to the point with angle [math]m\theta.[/math] 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).[br][br]The bottom applet is the same except we draw lines rather than line segments.

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