How to axiomatize school geometry

Abstract

This is an attempt to present axioms for Euclidean geometry, aiming at the following goals: to work with geometric notions (thus not merely identify points with pairs of numbers, giving a special status to a particular coordinate system); to be appropriate to the way geometry is done in science and engineering - not to conceal its algebraic nature; to respond to the desire that one would accept intuitively/empirically that the axioms are valid in our physical everyday world (or rather in the idealization that geometry is) - that seemingly disfavoring taking the theorem of Pythagoras as an axiom; to have accessible the rigor and standards of "pure" mathematics. The style in this note is that of usual mathematical writings - for an unsophisticated audience the style of the presentation must surely be quite different.