Area and circumference of the unit circle
The challenge is to find the area and the circumference of a circle of radius 1 (= unit circle). One idea ist to approximate both unknown values by using regular polygons.
We inscribe a regular polygon in the circle (blue). Furthermore, we circumscribe a regular polygon with equal number of edges about the circle (red). Modify the number of edges n by using the slider and watch the computed approximations of the area and the circumference.
What do you notice about the values A_1, A_2 and P_1, P_2? Write down your observations and come up with a conjecture about the values of the area and the circumference of the unit circle! We are going to discuss that.