Archimedes determined the upper and lower range of pi by finding the perimeters of inscribed and circumscribed polygons. By doubling the number of sides of the hexagon to a 12-sided polygon ...

It finds an approximation of pi by determining the length of the perimeter of a polygon inscribed within a circle (which is less than the circumference of the circle) and the perimeter of a ...

He developed rigorous logical proofs using the method of exhaustion to back up his calculations ... If we continue this process indefinitely and study the resulting sequence of inscribed regular ...