Corrupt Land Inspectors: Solving Equations with Picture-Language in Ancient Mesopotamia—A Dialogue

Abstract

This paper incorporates a scripted one-act play involving two actors, which can be used in the classroom. The dialogue aims to be an entertaining piece of mathematical theatre displaying ancient Mesopotamian cultural perceptions of mathematics, while illustrating some fundamental aspects of mathematical practice. It also aims to demonstrate the power of theatre (and history of mathematics) to motivate learners in algebra. The play takes place in a Mesopotamian scribal school, nearly four thousand years ago. The original verbal approach, sand-tray pictures and cut-and-paste geometrical methods are presented as authentically as possible, and a transcription is given in modern mathematical notation of the procedures, which we would think of as solving quadratic equations. The Head Scribe uses as motivation his student’s concern over the way tax collectors are defrauding the poorest farmers by walking the perimeter to arrive at the tax bracket. Two kinds of problems are discussed, including ‘An unknown square is the same as a given rectangle on the unknown square-side and a given area’. Different methods are shown for picturing and solving such problems. The Head Scribe forecasts a great future for his student and celebrates the scribes’ role in seeking justice, by reading an old praise-poem.