Pure Colloquium Seminar - Coxeter's friezes, the modular group and Farey graphs, Ian Short (Open U) Seminar

Event details

In the 1970's, Coxeter studied certain arrays of integers that form friezes in the plane. He and Conway discovered an elegant way of classifying these friezes using triangulated polygons. Recently, there has been a good deal of interest in expanding Conway and Coxeter's ideas and relating them to other mathematical structures. Building on work of researchers in the field, we will demonstrate how some basic techniques from the theory of hyperbolic geometry involving the modular group and continued fractions can be used to shed light on some of the recent advances in the subject. In particular, we will see how integer friezes can be interpreted using the Farey graph.