C.a.R. > Applications> Similarity and Angles> Trisection by Iteration

This construction uses an iteration process to trisect an angle based on the Apollonius method. Start the iteration by shaking B a few times.

• P is any point near the correct solution
• Project P to the green line, and get Q.
• On PB the radius MB is taken at A. We get S.
• Now we fix P with a forward reference to S.

This is a logical circle. S depends on P and P on S. At each update we have an iteration S -> P -> S. In this case, the iteration converges.