Circular reasoning

The author discusses two interesting relationships between circles and lines. There should be a computer graphics application that can use the first topic to run faster or better. The second topic is Ptolemy´s Theorem, which is a generalization of the triangle inequality. The author shows how it can be used to derive the angle addition formulas. He considers how Ptolemy´s Theorem can be used to prove that Snell´s Law and Fermat´s Principle of Least Time both lead to the same geometry of refraction