Objectives

• This will show students how to use regular polygons to derive the formula to calculate the area of a circle. Students will learn by visualizing how a regular polygon will approach a circle as its number of sides increases to infinity.
• By now, the students should have learned how to calculate the area of any regular polygon. Therefore, we use a regular polygon to approach a circle and use the area of a regular polygon to approximate the area of a circle.
• As the experiment shows, the regular polygon will become a perfect circle when the number of sides approaches infinity. Thus, its area approaches the area of the circle.

User´s Guide

1. Use the slider bar "Circle Radius" to change the radius of the circle to a desired value.
2. Use the slide bar "Polygon Sides" to adjust the number of the polygon sides.
3. Use the button "Keep data" to permanently display the area of the current polygon on screen. The area of the circle is always displayed on screen.

1. The starting polygon is an equilateral triangle. Click the button "Keep data" to save its area.
2. Drag the slider "Polygon Sides" toward the center. Save two or three pieces of data along the way.
3. Now drag the slider all the way to the maximum and save the data. Can you see how the areas of polygons approach the area of the circle?
4. Adjust the radius of the circle to a new value and repeat step 1 through 3.