We have already shown that it is impossible to trisect any angle by Euclidean construction. However, angle trisection can be easily done if we are allowed to use a marked ruler - a straightedge with two marks S and R on it such that RS = 1. The following applet illustrates the method discovered by Archimedes: Suppose is the angle at A to be trisected. Draw a unit circle as shown in the applet. Place the marked ruler such that S lies on the circle. Then is the required trisected angle. Question: Does this method work for any angle? If not, how would you modify Archimedes' method so that it will work for the remaining cases?