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 a 24-sided polygon, and finally 48- and 96-sided polygons, Archimedes was able to bring the two perimeters ever closer in length to the circumference of the circle and thereby come up with his approximation. Values are shown in decimal notation rather than the fractions that Archimedes used.
actual value of [pi] = 3.1416
Note: All figures rounded off to four decimal places.