On the Arithmetization of School Geometry in the Setting of Modern Axiomatics.

Abstract

By arithmetized geometry we mean an axiomatic presentation of geometrywhich presupposes the system of real numbers. In this paper we analyzearithmetized geometry from a semantical point of view and compare it withclassical synthetic exposition of school geometry. We also analyze, from thesame point of view, the didactical use of one particular system ofarithmetized geometry, namely Pogorelov‘s system, in the Greek Lyceum(16–17 year old students).