bendyspace=noneuclidean space. Euclidean space is not bent, any non bent space is Euclidean. So a geometry that is non euclidean is ??.
Strawberries are red. Any non-red fruit is certainly not a strawberry. So a fruit that is red and not a strawberry is ??.
Oh, that's right, a red apple.
Well shit son.
The fact that Euclidean geometries are not bent doesn't mean that all non-bent geometries are Euclidean.
name a non-bent non euclidean geometry
did I ever claim that because euclidean space is not bent, that all non bent geometries are euclidean? no. I just gave an iff statement.
*Sigh*
lrn2uniquiness
any geometry that satisfies the postulates of euclidean geometry are euclidean, because all the theorems of euclidean geometry follow the postulates
Any geometry where the fifth postulate ALWAYS holds true is in euclidean space. A geometry is not "bent" if this holds true.
So if it doesn't always hold true, it can be curved. Do you understand now?
Its an axiomatic system, if the axioms hold, its euclidean.