The Roles of Geometry and Arithmetic in the Development of Algebra: Historical Remarks from a Didactic Perspective

Abstract

ln order to provide a brief overview of some of the historical affiliations between geometry and arithmetic in the emergence of algebra, we discuss some hypotheses on the origins of Diophantus' algebraic ideas, based on recent historical data. The first part deals with the concept of unknown and its links to two different currents of Babylonian mathematics (one arithmetical and the other geometric). The second part deals with the concepts offormula and variable. Our study suggests that the historical conceptual structure of our main modern elementary algebraic concepts, that of unknown and that ofvariable, are quite different. The historical discussion allows us to raise some questions concerning the raie geometry and arithmetic could play in the teaching of basic concepts of algebra in junior high school.