FPG3: Axioms, Desargue, The Fano Plane

In this lecture we describe Coexeter s six axioms for the projective plane. We take Desargue s Theorem as one of the axioms, however we also take a detailed look at the converse of Desargue s Theorem, and the interesting way it is proved, using Desargue s Configuration. After setting out the axioms, we show several results which can be inferred from them. Comparing these results to the initial axioms makes it clear that points and lines are dual objects to one another, with respect to the projective plane. br, br,