Student Colloquium talk by Professor Daniel Visscher, Ithaca College
Title: The Dynamics of Continued Fractions
Abstract: While only rational numbers have a fraction representation, all real numbers have a continued fraction representation. Continued fractions illuminate interesting structure in real numbers, for example, by giving a way to express how close a real number is to being rational. In this talk, we investigate continued fractions from the point of view of a dynamicist, framing the topic in terms of iterating a function and asking questions about how orbits distribute. Multiple flavors of π will be present, and the golden ratio will make approximately 1.618 appearances.