Question

Why is the value of pi the same NO MATTER the size of the circle?

Answer 1

Because
`\pi` 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
`\pi`

Of course difference circles will have different circumference, but
`\pi` 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
`√(2)s`, if s is the side length. No matter how big or small the side is, the diagonal will always be
`√(2)` times the side.

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

Answer 2

3.14? That’s PI’s value. I don’t understand what your asking.