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.
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