After repeating these steps infinite times we will get a figure with an area S2. Let's F(r)=S2/S1. It's clear that F(0)=1 and F(½)=0.
(a) What is this function for square?
(b) What is this function for equilateral triangle?
(c) Is it possible to get a circle from a square or from an equilateral triangle this way?
(d) Is it possible that this function is universal for all triangles, or for all rectangles, or for all polygons?