I think I see what you're getting at, but I guess I still don't fully understand. Any thoughts on proving that the perimeter is pi without using the knowledge t

I think I see what you're getting at, but I guess I still don't fully understand. Any thoughts on proving that the perimeter is pi without using the knowledge that the limiting shape is a circle? Does that question make sense? To me it seems strange that for any integer number N (number of times this chunking operation is applied), the perimeter is 4, but somehow in the limit the perimeter is not 4. Edit: Nevermind, reading cousin_it's posting I think I've got a handle on it. My confusion was exactly the difference between a sequence of approximations, and the limit itself.