Cyclic Transformations of Polygons and the Generalized Inverse

Abstract

By a polygon with n vertices (an n-gon) we shall mean an ordered n-tuple of complex numbers (z1, z2, … , zn). The numbers zi will be called the vertices of the polygon. The zi may or may not be distinct, and it shall not matter whether a “conventional” polygon can be drawn with the zi as vertices. We shall operate in the spirit of the book of Bachmann and Schmidt [2] though not at the same level of algebraic generality inasmuch as these authors allow zi to belong to a general field.