Continued Fractions: The Stairway to Perfection

There are many ways to think about numbers. We can use binary or decimal systems, write numbers as fractions or as solutions of various equations. In this advanced level semilab we will learn how to represent numbers as infinite or “continued” fractions. Continued fractions appear in different areas of mathematics and are useful when we are looking for best approximations of irrational numbers by simple fractions, predicting alignments of planets in solar system, constructing musical scales or trying to understand chaos in dynamical systems. We will talk about these and other applications of continued fractions and look at our old friends numbers pi, e, and golden mean from a different angle.