5 - Adapting the Medieval “Rule of Double False Position” to the Modern Classroom

Summary

Introduction

The rule of double false position is an arithmetical procedure for evaluating linearly-related quantities. The method does not rely on variables or equations, but is based instead on interpolating between, or extrapolating from, two guesses, or suppositions. Although the technique is seldom mentioned today in North American curricula, it was routinely used in much of Europe, Asia, and North Africa from medieval times to the 19th Century, and is still taught in many classrooms there today. Historically, the approach was especially convenient for practical tradesmen whose knowledge did not normally extend to a mastery of algebra; they could pull the algorithm from their mathematical toolkits whenever needed and deploy it as a rote arithmetical procedure.

I have adapted for instructional use a North African version of the rule of double false position. The topic is well suited to college or high school courses in College Algebra, Precalculus, Calculus, Applied Calculus, and Linear Algebra. In my experience, only 30–50 minutes of class time needs to be devoted to teaching the method in order for students to grasp the mechanics, justification, and various applications. Instruction can take any of various forms, ranging from a traditional lecture to a self-guided instructional module for individual or group work. I describe such a module below, in the section “In the Classroom”.

Covering a technique that students will find handy in solving certain problems helps round out their technical skills. In addition, it helps introduce them to the contributions of a variety of cultures, and provides some historical perspective on mathematics.