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A dimension is a degree of freedom in which position can vary. Each degree of freedom can be indexed by a single variable, which means that the dimensionality of a space is the number of coordinates needed to specify a point in that space. For example, a solid cube requires an x, y and z coordinate to define a position within, so it is three-dimensional.

In many physical theories, dimensions can either be spatial, temporal, or compact. Spatial dimensions are typical dimensions, allowing for free movement in all directions. Temporal dimensions correspond to time, and only allow changes to propagate in one direction. Compact dimensions are small, finite and periodic, meaning that they do not have a clear extent macroscopically but alter the behavior of microscopic phenomena.

In mathematics, other notions of the word "dimension" can be considered and serve as useful for studying more complicated objects such as fractals. One of these notions is Hausdorff dimensionality. The Hausdorff dimension of a metric space is the infimum of the set of all such that the -dimensional Hausdorff measure of is 0.

Dimensionality Negative One Zero One Two Three Four Five Six Seven Eight Nine Ten ... Aleph null
Hyperbolic space

Hyperbolic plane

Hyperbolic realm

Hyperbolic flune

Hyperbolic pentrealm

Hyperbolic hexealm

Hyperbolic heptealm

Hyperbolic octealm

Hyperbolic ennealm

Hyperbolic decealm

... Hyperbolic omegealm

Euclidean space

Null polytope

Point

Euclidean line

Euclidean plane

Euclidean realm

Euclidean flune

Euclidean pentrealm

Euclidean hexealm

Euclidean heptealm

Euclidean octealm

Euclidean ennealm

Euclidean decealm

... Euclidean omegealm

Hypersphere

Point pair

Circle

Sphere

Glome

Tetrasphere

Pentasphere

Hexasphere

Heptasphere

Octasphere

Enneasphere

Dekasphere

... Omegasphere