How do you get pi (not an estimate)?

Because π is an irrational number, its decimal representation does not repeat, and therefore does not terminate. It is not possible to calculate its exact value by finite number of algebraic operations. Instead, there are numerous methods of approximate calculation utilizing convergent infinite series. By addition of certain number of terms we can achieve accuracy to desired number of decimal places.

Here's one possible method

π = √12 * (1 - 1/(3*3) + 1/(5*3²) - 1/(7*3³) + 1/(9*3⁴) - 1/(11*3⁵) + ....)

this six first terms as written here yield π =3.1413....

This one is very easy to remember

π = 4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11....

but unfortunately converges (i.e. approaches to π) very slowly - these six first terms give π=2.976...

Some methods are very old. In 3rd century BC Archimedes used to calculate the perimeter of a regular polygon with n sides circumscribed around a circle with diameter d, and then to compute the limit of a sequence as n increases to infinity. It's also possible to apply mean value of perimeters of two polygons, one inscribed, and other circumscribed.

In modern times there are some algorithms (procedures) which are very difficult to perform on paper because they are specially designed for calculation of π on computers.

π = 16 arctan (1/5) - 4 arctan (1/239)

one way is to take the natural log of -1

ln(-1) is 3.141592765.........i

I hope that this helps some!!