.png){kind=link}
 - Vertical.png){kind=link}
.png){kind=link}
 - Vertical.png){kind=link}
.svg){kind=link}
.png){kind=link}
Non-Euclidean Geometries
Non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean Geometry.
As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the 5th postulate (parallel postulate) with an alternative, or by relaxing the metric requirement.
If the parallel postulate is replaced, we get hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries.
If the metric requirement is relaxed, then there are affine planes associated with the planar algebras, which give rise to kinematic geometries which have also been called non-Euclidean geometries.
Examples
- e.g. Lovecraftian worlds, for example, the city of R'lyeh in Cthulhu Mythos are non-Euclidean simply because they do not follow the laws of this universe, and not because he chose an alternate geometric model.