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:[br][br]Suppose [math]\alpha[/math] 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 [math]\angle SRA[/math] is the required trisected angle.[br][br][b]Question[/b]: Does this method work for any angle? If not, how would you modify Archimedes' method so that it will work for the remaining cases?