• In this applet, polygons are inscribed and circumscribed around circles of radius and diameter 1.
• Underneath the diagrams, the area and perimeter (labeled "Circumference") of the polygons are calculated on a number line. Note that the location of pi is also shown for reference.
• Use the blue slider to change the value of n, the number of sides in the polygons, and notice how the calculations of the areas and perimeters begin to approximate pi.

The inscribed polygon is blue, and the circumscribed polygon is red. Not surprisingly, the blue polygon gives an underestimate, and the red polygon gives an overestimate. But by how much?

• Choose an arbitrary value of n. For the area model, which is closer to the actual value of π, the estimate given by the blue or red polygon? At what point between the blue and red estimates does the actual value of π occur?
• For the perimeter model, which is closer to the actual value of π? At what point between the blue and red estimates does the actual value of π occur?