Projective Space: Harmonicity and Projectivity

TL;DR

This paper explores axioms for three-dimensional projective space, demonstrating the duality between harmonicity and projectivity axioms and their equivalence in the spatial context.

Contribution

It introduces dual versions of harmonicity and projectivity axioms for 3D projective space and proves their equivalence, enriching the axiomatic foundation.

Findings

Harmonicity and projectivity axioms are dual in 3D projective space

Each axiom is shown to be equivalent to its spatial dual

Provides a refined axiomatic framework for projective geometry

Abstract

For an axiomatization of three-dimensional projective space based on points and planes, we discuss appropriate versions of the harmonicity axiom and the projectivity axiom, showing that each axiom is equivalent to its spatial dual.