How to Derive Pi(π) Using Archimedes' Method

Pi is one of the most used special numbers in Geometry, yet not many people really know where it came from. Let's see how Archimedes did it using the "method of exhaustion".

None is needed!

Pi is defined as C/d, or Circumference divided by diameter.

We start by inscribing a polygon inside the circle and circumscribing a polygon outside the shape. We know that the perimeter of the larger polygon is larger than the circumference of the circle and the perimeter of the smaller polygon is less than the circumference of the circle. So we can get Pi by (Perimeter of smaller figure)<π<(Perimeter of larger figure).

The perimeter of the inscribed triangle is about 2.598 and the perimeter of the circumscribed triangle is about 5.196. So we end up getting 2.598<π<5.196.

Using a unit circle with radius of 1, we get that 2.83<π<4.

Using the unit circle again, we get 3.131<π<3.1427. Theoretically, we could go on in infinity, and we would eventually get that π is about 3.14159265359.