>>11008933The corners are always more inefficient at crossing the arc length distance than the actual arc length. At every step there are associated corners, and arc lengths underneath them, but the corners don't get more efficient as they add up. The shape isn't actually approaching a circle, you could always shave off the bits tangent to the corners and be more accurate.
Compare this to pic related. The outer polygon always has more area than the circle, but the process continually sheds this area which is always greater. By infinitely reducing something that is always greater you approach, in this case, Pi.
