Maplets for the area of the unit circle

Abstract

In this paper, we use Maplets to illustrate several different methods of estimating the area of the unit circle. The first method uses regular inscribed and circumscribed polygons. The second method uses inner, outer, and middle rectangles each of which corresponds to a Riemann sum. The third method uses small, included squares. The Maplets illustrate the area problem from both graphical and numerical points of view, and can be valuable in teaching certain integral concepts and for historical background.