Project III 2014-2015

Frieze patterns

Anna Felikson


Frieze patterns are sequences of positive integers satisfying some multiplication rules. They were introduced by Conway and Coxeter in the 70's, and their very simple definition yields surprising combinatorial properties. Frieze patterns are closely connected to regular polytopes (complex and real), triangulations of polygons, Fibonacci numbers, Catalan numbers, linear recurrence relations, associahedra, Pentagramma Mirificum, Farey sequence, pentagram map, continued fractions, mutations and many other beautiful things in algebra, geometry, combinatorics and dynamical systems.

Relationship of friezes with the recent theory of cluster algebras has led to numerous recent insights, results and generalisations, many of them accessible at the student level.

    Prerequisites and expectations: nothing special is required but it will be useful if you like geometry and/or combinatorics.


    One can get the first idea about the friezes here. R.E.Schwartz wrote a beautiful applet to illustrate some properties of friezes. More references may be found here.

    email: Anna Felikson