Mathematics Colloquia and Seminars

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Frieze patterns are beautiful combinatorial objects, introduced by Coxeter in the early 1970s. He was about 30 years ahead of time: only in this century, frieze patterns have become a popular object of study, in particular, due to their relation to the emerging theory of cluster algebras and to the theory of completely integrable systems. I shall introduce frieze patterns and prove the theorem of Conway and Coxeter that relates arithmetical frieze patterns with triangulations of polygons. There is an intimate and somewhat unexpected relation between three objects: frieze patterns, 2nd order linear difference equations, and polygons in the projective line (or ideal polygons in the hyperbolic plane). Time permitting, I shall mention some recent work on frieze patterns.