Estimating Pi Observation

Below are several circles, each of radius 1.45 units. The circles in the first group have polygons inscribed inside of them, while the ones in the second group have polygons circumscribed about them. The perimeters of the polygons is given. Your task is to take the perimeter of each polygon and divide it by the diameter of the circle. Record each quotient.

Questions to think about:
When calculating with the inscribed polygons, what number were the quotients getting close to? What about the circumscribed polygons? Is there something special about this number? Why that number?

(Hint: What is the circumference of each circle? (It will be the same, since all of the circles have the same radius.) What number do you get when you divide the circumference by the diameter? Does it make sense now?)

Why were the inscribed polygons all less than that number? Why were the circumscribed polygons all greater than that number?

Brian Bisignani, July 22, 2008, Created with GeoGebra