Approximate Angle Trisection
Here is a procedure for getting an approximate angle trisection using a compass and straightedge. The procedure is carried out for you in the applet below. The error in the trisection is shown.
1. Construct the blue angle to be trisected. (Do this in the applet by moving the two blue points, A and B.)
2. Construct the green angle bisector.
3. Construct a red angle with vertex C having the green line as an angle bisector (you can use any angle that is not too large).
4. Duplicate the red angle above it and below it to get the two orange lines. (Note, the two red rays divide the orange angle into three equal angles. This is geometrically possible because we are tripling an angle not trisecting an angle.)
5. The orange and blue lines cross at two points, D and E. Construct a circle through D and E with center A.
6. This circle passes through the red lines at two points F and G.
7. The purple rays AF and AG *almost* trisect the blue angle, DAE.