2-Dimensional space

A 2-Dimensional Space is a space in which every position can be described using a pair of numbers, such as with a complex number (every complex number can be described with a pair of real numbers).

Types of 2-Dimensional Space

The types of a two-dimensional space can be sorted according to their curvature. Roughly, positive curvature causes parallel lines to meet, and negative curvature causes parallel lines to diverge.

Spherical

The spherical plane has a positive curvature, and can be thought of as the two-dimensional space being a sphere, on the surface of a ball. Two parallel lines will eventually wrap around the sphere and meet again, and similarly walking in a straight line will eventually return an entity in a spherical space to its original location.

Euclidean

The Euclidean plane has a zero curvature, and is the ordinary flat plane that follows the postulates of Euclidean geometry.

Hyperbolic

The hyperbolic plane has a negative curvature. This means that two parallel lines will diverge, giving them the name ultraparallel.

Verses

A two-dimensional verse is called a planeverse.

See Also

Dimensionality	Negative One	Zero	One	Two	Three	Four	Five	Six	Seven	Eight	Nine	Ten	...	Aleph null
Hyperbolic space $\mathbb H^{n}$	—	—	—	Hyperbolic plane $\mathbb H^{2}$	Hyperbolic realm $\mathbb H^{3}$	Hyperbolic flune $\mathbb H^{4}$	Hyperbolic pentrealm $\mathbb H^{5}$	Hyperbolic hexealm $\mathbb H^{6}$	Hyperbolic heptealm $\mathbb H^{7}$	Hyperbolic octealm $\mathbb H^{8}$	Hyperbolic ennealm $\mathbb H^{9}$	Hyperbolic decealm $\mathbb H^{10}$	...	Hyperbolic omegealm $\mathbb H^{\aleph_0}$
Euclidean space $\R^n$	Null polytope $\emptyset$	Point $\mathbb R^{0}$	Euclidean line $\mathbb R^{1}$	Euclidean plane $\mathbb R^{2}$	Euclidean realm $\mathbb R^{3}$	Euclidean flune $\mathbb R^{4}$	Euclidean pentrealm $\mathbb R^{5}$	Euclidean hexealm $\mathbb R^{6}$	Euclidean heptealm $\mathbb R^{7}$	Euclidean octealm $\mathbb R^{8}$	Euclidean ennealm $\mathbb R^{9}$	Euclidean decealm $\mathbb R^{10}$	...	Euclidean omegealm $\mathbb R^{\aleph_0}$
Hypersphere $\mathbb S^{n}$		Point pair $\mathbb S^{0}$	Circle $\mathbb S^{1}$	Sphere $\mathbb S^{2}$	Glome $\mathbb S^{3}$	Tetrasphere $\mathbb S^{4}$	Pentasphere $\mathbb S^{5}$	Hexasphere $\mathbb S^{6}$	Heptasphere $\mathbb S^{7}$	Octasphere $\mathbb S^{8}$	Enneasphere $\mathbb S^{9}$	Dekasphere $\mathbb S^{10}$	...	Omegasphere $\mathbb S^{\aleph_0}$