Find the mistake:;

nice 1!
but Aryabhatta not Archemedes!!

Well I will try it out!

haha nice q :D. checkout http://www.crazyengineers.com/community/threads/pi-4-paradox-explain-this.38433/

but i'm still not conviced!!!

Probably because the guys in that forum are not even close to convincing, and most of their statements are bs . (:P)

Yes,the actual explanation comes from topology, I found that one in Mathlinks. (But I don't understand it )

I think I have the answer

Even after removing infinite number of squares we will find that the shape will have infinite number of spikes on its perimeter as against a circle which should have a smooth circumference.

Hence there is a difference in perimeter.