Editing Spherical geometry (section)

==Relation to similar geometries==
Because a sphere and a plane differ geometrically, (intrinsic) spherical geometry has some features of a [[non-Euclidean geometry]] and is sometimes described as being one.  However, spherical geometry was not considered a full-fledged non-Euclidean geometry sufficient to resolve the ancient problem of whether the [[parallel postulate]] is a logical consequence of the rest of Euclid's axioms of plane geometry, because it requires another axiom to be modified.  The resolution was found instead in [[elliptic geometry]], to which spherical geometry is closely related, and [[hyperbolic geometry]]; each of these new geometries makes a different change to the parallel postulate.

The principles of any of these geometries can be extended to any number of dimensions.

An important geometry related to that of the sphere is that of the [[real projective plane]]; it is obtained by identifying [[antipodal point]]s (pairs of opposite points) on the sphere. Locally, the projective plane has all the properties of spherical geometry, but it has different global properties. In particular, it is [[orientability|non-orientable]], or one-sided, and unlike the sphere it cannot be drawn as a surface in 3-dimensional space without intersecting itself.

Concepts of spherical geometry may also be applied to the [[Spheroid|oblong sphere]], though minor modifications must be implemented on certain formulas.