Why is the value of pi the same no matter the size of the circle?

Because is defined as the ratio between the circumference and the radius.

This ratio happens to remain constant in every circle: no matter how big or small you make it: the circumference will always be a multiple of the radius, and the constant of proportionality is always be

Of course difference circles will have different circumference, but doesn't depend on the circumference because, when you divide it by the radius, the result will always be the same.

A similar example is the fact that the square of a diagonal is always , if s is the side length. No matter how big or small the side is, the diagonal will always be times the side.

It's the constant of proprtionality that matters, not the specific values involved in the proportion!

i want to die

what the hell man, i just want the points lol