2006/02/09 by Eliahu Levy, Levy, Eliahu
Mathematics · Social Sciences · #FOS: Mathematics #History and Overview (math.HO) #History and Theory of Mathematics #Mathematics Education and Teaching Techniques #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.math/0602190
openalex publication_date 2006/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.