FANDOM


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.

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 First Zeroth First Second Third Fourth Fifth Sixth Seventh Eighth Ninth Tenth Eleventh Twelfth Thirteenth Fourteenth Fifteenth Sixteenth ... Omegath
Hyperbolic space

$ \mathbb H^{n} $

Null polytope

$ \emptyset $

Point

$ \mathbb H^{0} $

Hyperbola

$ \mathbb H^{1} $

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 hendecealm

$ \mathbb H^{11} $

Hyperbolic dodecealm

$ \mathbb H^{12} $

Hyperbolic tridecealm

$ \mathbb H^{13} $

Hyperbolic tetradecealm

$ \mathbb H^{14} $

Hyperbolic pentadecealm

$ \mathbb H^{15} $

Hyperbolic hexadecealm

$ \mathbb H^{16} $

... Hyperbolic omegealm

$ \mathbb H^{\aleph_0} $

Euclidean space

$ \mathbb 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 hendecealmverse

$ \mathbb R^{11} $

Euclidean dodecealmverse

$ \mathbb R^{12} $

Euclidean tridecealm

$ \mathbb R^{13} $

Euclidean tetradecealm

$ \mathbb R^{14} $

Euclidean pentadecealm

$ \mathbb R^{15} $

Euclidean hexadecealm

$ \mathbb R^{16} $

... Euclidean omegealm

$ \mathbb R^{\aleph_0} $

Hypersphere

$ \mathbb S^{n} $

Null polytope

$ \emptyset $

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} $

Hendekasphere

$ \mathbb S^{11} $

Dodekasphere

$ \mathbb S^{12} $

Tridekasphere

$ \mathbb S^{13} $

Tetradekasphere

$ \mathbb S^{14} $

Pentadekasphere

$ \mathbb S^{15} $

Hexadekasphere

$ \mathbb S^{16} $

... Omegasphere

$ \mathbb S^{\aleph_0} $