6th to 8th, High School
The Greek mathematician Archimedes approximated pi by inscribing and circumscribing polygons about a circle and calculating their perimeters. Similarly, the value of pi can be approximated by calculating the areas of inscribed and circumscribed polygons. This activity allows for the investigation and comparison of both methods.
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?