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 ...

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 ...

The perimeter of the inscribed blue hexagon has to ... which is accurate to two places. Archimedes' method of approximating π with polygons, and similar techniques developed in China and India ...

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 ...