An epitrochoid is the curve traced by a point on a wheel of radius r that rolls without slipping on a wheel of radius R. The wheel of radius r rotates w times faster and the ratio of the radii is (w-1) (ie R = (w-1)*r). The point that scribes the curve is a distance away from the center of the wheel of radius r. Please see this simple diagram.

Write a short script that draws an epitrochoid. The script starts with the usual header, assigns values to R, w, and a (good values are R=1, w=3 and a=0.5*r), then creates the vectors X and Y and plots the curve. The plot should look like this.

/r R /r R