Frieze patterns:   

> Frieze patterns were introduced and studied by Coxeter and then Conway-Coxeter in the 70's. They are arrays of a 
> finite number of shifted infinite rows of positive integers, satisfying the unimodular rule: in each square formed by four entries, 
> the product of the horizontal entries is one more than the product of the vertical entries. An example is here: 
> 
> 0 0 0 0 0 0 0 0 0 0 
>  1 1 1 1 1 1 1 1 1 
> 2 1 3 1 2 2 1 3 1 2
>  1 2 2 1 3 1 2 2 1 
> 1 1 1 1 1 1 1 1 1 
>  0 0 0 0 0 0 0 0 0 
> 
> Conway-Coxeter have shown that such patterns are invariant under a glide symmetry and hence are peridoci. Furthermore, 
> they are characterized by triangulations of polygons. We will briefly recall this and then consider infinite frieze patterns 
> of positive integers. We show that they are also characterized by triangulations of surfaces. As in the finite case, we are 
> able to give a geometric interpretation of all entries of an infinite frieze via matching numbers. This is joint work with M.J. Parsons 
> and M. Tschabold (both from Graz).