Pi is 4 video

I mentioned the “proof” of π=4 in a previous post. In time for Pi Day on Monday, I’ve created a new video setting out the problem.

For those not inclined to view videos here is the problem:

Take a circle of diameter 1. Its circumference is π since its radius is 1/2 and a circumference is 2π times radius.


Now put a square round it.
circle in square

The length of the perimeter of the square is 4 since each side has length equal to the diameter of the circle. Now fold in the corners like so.

corners in

Since there was no stretching or shrinking, the length of this new curve is also 4.

Do the process again, i.e., fold in all the corners.

corners in again

The length of this curve is still 4 since no stretching or shrinking was involved.

Do it again.

corners in yet again

The length is again 4.

We can take the limit of this process. The limit is a circle.


Since the jagged curve gets closer and closer to the circle and always has length 4 we can see that the perimeter of the circle has length 4. But the perimeter length is also equal to π.

Therefore, π is 4.

Where is the mistake?

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