Using polygons to approximate the area of curved shapes is a technique that has been known since ancient times. The concept is simple: draw polygons such as triangles or rectangles within the confines of a curved shape, calculate the area of those triangles and polygons, and you have approximated the area of a curved shape or under a curved line. Today, the technique is called a Riemann sum and is named after Bernhard Riemann, a German mathematician from the nineteenth century.
This recipe provides a method of approximating the area under a curve based upon the Riemann sum technique.
