Why we use Pi in many formula and from where it derived?

Babylonians and Egyptians simply made a big circle, and then measured the circumference and diameter 
with a piece of rope.

They used this method to find that pi was slightly greater than 3.

The first mathematician to calculate pi with reasonable accuracy was Archimedes, around 250 B.C.

 He approximated pi by considering regular polygons with many sides inscribed in and circumscribed around a 
circle.

The value of Pi is 3.14159265358979323846 ...

Pi is an irrational number and and hence the decimal expansion of Pi is non-terminating and non-recurring.

 

And we need to use Pi in so many calculations.

 

The most approximate rational number equivalent to Pi is