Transformations of geometrical objects in middle Egyptian mathematical texts.

Abstract

This paper analyzes the algorithmic structure of geometrical problems in Egyptian papyri of the first half of the second millennium B.C. Processes of transformation of quantities from "false" values into actual values, and conversions from quantities expressed in the abstract system of numbers into metrological quantities, are known in Egyptian mathematics. Three further processes are identified in the present contribution: transformations of "false" dimensions of geometrical objects into true dimensions; transformations of geometrical objects into other geometrical objects; transformations of linear measures of monuments. These processes have relevant implications on the algorithmic structure of the problem texts, resulting in particular in the embedding of sub-algorithms and the creation of parallel structures. More in general, their wide employment in Egyptian mathematics has significant philosophic and cultural implications.