Converging Polygons by a Dynamic Process to a Perfect Polygon

Abstract

We give an interesting description of a dynamic process in which a polygon inscribed in a circle converges to a perfect polygon, and also of the convergence of a triangle where in a stage-by-stage manner one constructs a triangle, the length of whose sides are the averages of the side lengths of the previous triangle, which monotonically converges by a dynamic process to an equilateral triangle. Mathematical proofs are given to the convergence to a perfect polygon, and the stages are presented visually using computerized dynamic applets which one can reach by links that exist in the paper.