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 ...

Using some basic geometry and trigonometry, Archimedes observed that the length of each of the sides of the inscribed blue hexagon would be 1/2, and the lengths of the sides of the circumscribed ...

It finds an approximation of pi by determining the length of the perimeter of a polygon inscribed within a circle ... and the perimeter of a polygon circumscribed outside a circle (which is ...