Approximating the circumference, area of a circle

Area, Circle
This applet shows the ratios of the area and perimeter of an inscribed polygon to the area and circumference of the bounding circle. The number of sides of the polygon "n" is set with a slider. Using a formula for the polygon area (derived in the attached PDF), an estimate of Pi is obtained, along with the relative error in that estimate. The radius of the circle "R" can be adjusted with a slider. Step-by-step adjustments in the polygon sides are made by selecting the "n" slider, then use the arrow keys. Selecting the "n" slider and then pressing the space bar will animate the polygon sizes. The ratios shown are for the area and circumference of the circle to the respective estimate.

Circle Circumference and Area