What a good question.

- 3.14
- 3.141592653589793238462643385276…
- 4

Which is it? Well, it’s not 3.14 because pi is not rational, and that is the same process for 4, right?

Well, if you thought so, Congratulations! You are

WRONG!

It’s actually 4.

Take a square with perimeter 4 (side length 1) and a circle exactly in the square with perimeter pi (diameter 1). Cut the corners with squares the largest it can go. Repeat as much as possible, again and again, …

Can you see the flaw?