The perimeter of the inscribed blue hexagon has to be smaller than the circumference of the circle, since the hexagon fits entirely inside the circle. The six sides of the hexagon all have length ...

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, then ...

This interactive feature illustrates Archimedes' basic approach to calculating pi. It finds an approximation by determining the length of the perimeter of a polygon inscribed within a circle and ...