This animation illustrates Archimedes's method of using the perimeters of polygons to approximate the circumference of circles. Move the slider to step through the animation. In this presentation, polygons of 6, 12, 24, 48, and 96 sides are shown, as well as a circle. The table shows half the length of the perimeter of each inscribed and circumscribed polygon, as well as the average of those two values.
As you step through the animation, observe what happens to the difference between the polygons and the circle. Also observe what happens to the measures of the half-perimeters shown on the table.