Markov chains and dynamic geometry of polygons (Q1873712)

In the paper under review, an \(n\)-sided plane polygon is called cyclic if it can be inscribed in a circle. The authors study the connection between the geometry and linear algebra of cyclic polygons. They construct sequences of cyclic polygons which converge to a unique polygon. Two special cases are considered in details. The first case is a limiting polygon of these sequences to be regular, and the second one is a sequence of triangles. The main tools used in the proofs are non-negative matrices and Markov chains.