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 ...

The perimeter of the inscribed blue hexagon has to be smaller than the ... figured out how to estimate the perimeters for polygons with twice as many sides. He went from a 6-sided polygon, to ...

It finds an approximation of pi by determining the length of the perimeter of a polygon inscribed within a circle ... By doubling the number of sides of the hexagon to a 12-sided polygon, then ...