Converting the Old Babylonian Tablet ‘Plimpton 322’ into the Decimal System as a Classroom Exercise: Introduction

Because they are ancient, mysterious yet tangible objects that were frequently inscribed with mathematics, cuneiform tablets can provide appealing additions to secondary and undergraduate mathematics classrooms. With its apparent references to Pythagorean triples, the Old Babylonian clay tablet known as Plimpton 322 (so named for the collection at Columbia University in which it is held) may be a particularly tempting subject for a lesson. For instance, Daniel E. Otero has suggested activities for encouraging students to think about how numbers are expressed, to experiment with algorithms in arithmetic, and to further mastery of quadratic equations [Otero 2011]. Meanwhile, Amy Ackerberg-Hastings has used a version—in which the original values were replaced with familiar base-10 Pythagorean triples—to introduce mathematical and historical thinking in seven sections of a general-education science course on the history of science (see Appendix).

Even though debate persists among historians about what Plimpton 322 was actually designed to accomplish [e.g., Robson 2002; Britton, Proust, and Shnider 2011; Mansfield and Wildberger 2017], this tablet continues to stimulate a variety of classroom projects. In this article, we present an activity that guides students through the construction of a decimal analogue to the sexagesimal entries on the tablet, and we explain how such an activity is an enriching mathematical exercise that allows students to experience mathematics from the Old Babylonian period while remaining in the comfort zone of base 10.