Pi is the ratio of the circumference of a circle to it's diameter .

To seven places pi is 3.1415927.

You find pi by approximating the length around a circle with the

length around an inscribed regular polygon then divide this by the circle diameter.

By summing the lengths of the sides of a regular polygon that is inscribed

within a circle you approximate the circumference of a circle.

The more sides on a polygon the closer you come to the true circumference

of a circle.


Let us start with a circle of radius R=1. Inscribe within this circle a regular

polygon having N=6 sides.

Using trigonometry we get formula (2) below. This along with formula (3)

Will give an approximate circumference of 6x2x1xsin(180/6)=6.

Using the traditional formula(1) for circumference gives


If the polygon had more sides the answer would be more accurate.

We arrive at formula (4) to give the circumference of a circle.

If we set equal formula (1) and (4) then factors 2xR cancel out

giveing Pi equal to formula (5).

Using formula (5) you get pi=3.1407433 for a polygon of 78 sides.

For 1303 sides you get Pi=3.1415897. With 45000 sides pi

is calculated as 3.1415927.