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**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.