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> 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 parall
by BigTTYGothGF 6mo ago
> 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)
- seanhunter 6mo agoThank 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 https://en.wikipedia.org/wiki/Pringles
- lmm 6mo agoYou can also replace it with a different postulate and get projective geometry, IIRC.