Comment by seanhunter
20 hours ago
Thank you for the correction I actually didn't realise that so have learned something.
Specifically for people who are interested it seems you have to replace the parallel postulate with a postulate that says every point is a saddle point (which is like the centre point of a pringle if you know what that looks like).
You can also replace it with a different postulate and get projective geometry, IIRC.