Pi is a lie?

[Socrates]

Imagine you are finger painting and are trying to color something in between two lines, but your finger itself is fatter than the gap. Every time you put your finger down, the paint ends up slightly off. A little too much on the left, a little too much on the right, back to the left again. You keep trying, and every pass the paint inside the area you are trying to color gets darker and thicker than the surrounding area and the shape you are trying to color starts to become clear, but only with unsightly smudges surrounding it.

You'll never get a perfectly sharp edge, because your finger is just too fat.

[Socrates]

The Pythagorean theorem:

C^2 = (A + B)^2 - 2AB

The union of two numerical sets in set theory:

(A U B) = A + B - (A n B)

There's something there, but I can't make it click in my head right.