In this in-class exercise, students will learn how to determine the approximate area of a circle using rectangles.
Various methods of finding the area under curves (and of circles) have been used since the time of the ancient Egyptians. In addition to the ancient Greeks, Sir Isaac Newton used a similar method to find the area under a curve. Some texts refer to this method as the “Method of Quadrature.” This technique forms the fundamental basis for integral calculus (which is well beyond the scope of this lecture and exercise).
In this exercise, a number of adjacent rectangles are drawn within a circle (we’ll use a quarter of a circle to speed up the process), the area of each rectangle is calculated, and the approximate area of the circle is determined by adding up the areas of the rectangles.
Skills for this activity include (1) Measuring the length of a line segment; (2) Calculating the area of a rectangle; (3) Calculating the area of a circle; (4) Calculating error using absolute value; (5) Comparing data to arrive at a conclusion.