Question

how was pie's formulae formed?

Answer 1

The following is a list of significant formulae involving the mathematical constant π. The list contains only formulae whose significance is established either in the article on the formula itself, the article Pi, or the article Approximations of π

Succinctly, pi—which is written as the Greek letter for p, or π—is the ratio of the circumference of any circle to the diameter of that circle. Regardless of the circle's size, this ratio willi always equal pi. In decimal form, the value of pi is approximately 3.14. But pi is an irrational number, meaning that its decimal form neither ends (like 1/4 = 0.25) nor becomes repetitive (like 1/6 = 0.166666...). (To only 18 decimal places, pi is 3.141592653589793238.) Hence, it is useful to have shorthand for this ratio of circumference to diameter.

I think it's useful to you