This sketch shows two approaches to approximating pi, the ratio of a circle's circumference to its diameter.
In the first approach, the perimeter of a polygon is compared to the diameter of an inner circle and an outer circle. You set the length of one side of the polygon, and the slider controls the number of sides.
In the second approach, the method used by Archimedes, the circle circumference is underestimated by an inside polygon, and overestimated by an outside polygon.
How do the methods compare? Will both work to find pi? Is one more efficient than the other?