Some Comments On: A Historical Note On The Proof Of The Area Of A Circle

Abstract

In a recent paper by Wilamowsky et al. [6], an intuitive proof of the area of the circle dating back to the twelfth century was presented. They discuss challenges made to this proof and offer simple rebuttals to these challenges. The alternative solution presented by them is simple and elegant and can be explained rather easily to non-mathematics majors. As business school faculty ourselves, we are in agreement with the authors. Our article is motivated by them and we present yet another alternative method. While we do not make an argument that our proposed method is any simpler, we do feel it may be easier to communicate to business school students. In addition, we present a solution using a rectangle which could be left as an exercise for the student after a brief explanation in class. Finding the area of a stack of rectangles with a rectangle as a starting point may seem redundant at first. However, we show that it is actually an excellent algebraic exercise for students since it offers a certain challenge which a square does not. We also solve this exercise using the quicker triangular approach and feel it can be appreciated by students in an Introduction to Calculus course. We also provide two interesting links that demonstrate the work of the ancient mathematicians for this well known problem.