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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
-verse Nullverse Protoverse Lineverse Planeverse Realmverse Fluneverse Pentrealmverse Hexealmverse Heptealmverse Octealmverse Ennealmverse Decealmverse Hendecealmverse Dodecealmverse Tridecealmverse Tetradecealmverse Pentadecealmverse Hexadecealmverse ... Omegealmverse
Hyperbolic space

\mathbb H^{n}

Null polytope

\emptyset

Point

\mathbb H^{0}

Hyperbolic branch

\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}

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