I am trying to get my head around the differences and similarities between Euclidean and Minkowski plane geometry.
AS far as I understand it they are both affine geometries meaning the parallel postulate holds in both geometries.
but what is the differnce between them?
Coxeter's "Non euclidean geometry" writes that (as i understand it it) has to do how many points at infinity a line has :
if the ideal point is singular (elliptical polarity) gives Euclidean geometry while if there are an infinite number of ideal points (hyperbolic polarity) it gives Minkowski geometry
But that makes it no clearer for me either, what is that polarity thing?
is there not an easier way to understand there differeces?
Is there no difference in axioms or so?
ADDED LATER:
I had a look at wikipedia's
https://en.wikipedia.org/wiki/Minkowski_space
and https://en.wikipedia.org/wiki/Minkowski_plane
and to me they look to be about two unrelated subjects, are they related?
I am interested in the geometry of the Minkowski plane if that is the one Coxeter is refering to.