I read this question somewhere
Let a square of length 1 unit and a circle is inscribed in it such that it touches the sides of square.
Now cut small portion(outside the circle) of square from each corner. 
As you can se the perimeter of square is still 4 after removing this portion.
Continue this process i.e. cut the square in such a way that shape of cutting square tends to the shape of circle.
Now the main thing is
Perimeter of square =$4$
Perimeter of circle= $2\pi \frac{1}{2}$=$\pi$
Since the the shape of square tends to the shape of circle
Therefore perimter of square $=$ Perimeter of circle ( or may be approximately equal to circle)
That is $\pi =4\ or\ approx \ 4$
If we take side of square of length $a,a>0$ we also reached to the same result.
Can anyone explain whats wrong in this. I am unable to figure out.
Any help appreciated.
