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Q: "On models of elementary elliptic geometry"

José Hdz. Stgo.While perusing p. 237 of the 3rd ed. of Marvin Greenberg's book on Euclidean and non-Euclidean geometries, I learned that it can actually be proven that "all possible models of hyperbolic geometry are isomorphic to one another, i.e., that the axioms for hyperbolic geometry are categorical". This ...

Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect. However, unlike in spherical geometry, two lines are usually assumed to intersect at a single point (rather than two). Because of this, the elliptic geometry described in this article is sometimes referred to as single elliptic geometry whereas spherical geometry is sometimes referred to as double elliptic geometry. The appearance of this geometry in the nineteenth century stimulated the development of...
 

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