How to calculate pi:

There are many ways to calculate pi. I will start out by showing the first-ever method used to calculate pi.

The Regular Polygon Method

This method was the earliest used method in history for calculating pi.

It works like this.

You draw a circle.

Then, you draw a circumscribed n-gon, and an inscribed n-gon.

You then calculate the perimeter and center to vertex distances in the polygons.

You then calculate the perimeter of those polygons.

You then can sandwich (perimeter of inscribed polygon)<π<(perimeter of circumscribed polygon).

Arctan Series For π Method

This is the slowest method, so almost nobody used it.

The arctan series for π is :

π/4 = 1 - 1/3 + 1/5 - 1/7 + ...

There are a lot of other series for π that go faster, but I won't list them here.