alt Hacker News> if you exclude the parallel postulate but use all of the other axioms from Euclid you get hyperbolic geometry
No, you don't.
(You need to replace the parallel postulate with a different one)
> if you exclude the parallel postulate but use all of the other axioms from Euclid you get hyperbolic geometry
No, you don't.
(You need to replace the parallel postulate with a different one)
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).
https://en.wikipedia.org/wiki/Pringles