Archimedes’ method of exhaustion involves finding the area of a region by inscribing a sequence of polygons inside the region and circumscribing a sequence of polygons outside the region. The region’s area then lies between the inscribed areas and the circumscribed areas. If the polygons are chosen appropriately, as the two sequences progress, all other possible values of the region’s area, except the correct value, are ultimately ‘exhausted’. Archimedes used this method to show that $3\frac{1}{7}<\pi <3\frac{10}{71}$.