The polygon approximation method uses the perimeters of polygons to approximate pi and "was the first theoretical, rather than measured, calculation of pi", but even if it worked very well for Archimedes in his time, its practicality is limited today (Groleau). To estimate pi, Archimedes used a circle in which a polygon was inscribed and circumscribed, then found the perimeter of each polygon and used these values ​​as the upper and lower limits of pi (Groleau). He started with a hexagon as the interior polygon of a circle of diameter 1 whose perimeter equals 6r when r is the radius of the circle (McKeeman). This meant that since the circumference of the circle was 2πr, 6r < 2πr and the lower limit of pi was 3 (McKeeman). He then found the perimeter of the outer hexagon to calculate the upper limit and then doubled the number of sides and repeated the operation.