OK, a proof for this simple result. Let's take a circle of center O1 (point in the plane) and radius R1 (length of the radius). Call this circle C1. We define the number π1 as (circumference of the circle C1)/ (2R1). Let's take another circle of center O2 and radius R2 called C2. Define π2= (circumference of the circle C2)/ (2R2). Now prove that π1=π2. Ideas ? My idea was to show that the equality (perimeter/side) holds for the 2 squares inscribed in the 2 circles. Then it holds for the 2 squares circumscribed to the 2 circles. Then take hexagons, octogons,..., generally regular-n'gons. Then grow n arbitrarily and get a proof for the 2 circles. Is this ok as a proof ?