Verse and Dimensions Wikia
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Verse and Dimensions Wikia

A Euclidean space is a zero-curve, infinitely large, real metric space that follows Euclidean geometry, and thus, all of Euclid's Postulates.

Euclidean spaces are constructed from repeated Cartesian products of a real line , and can be modelled with a real coordinate space (often, Euclidean spaces are denoted with , though can be used). This means that coordinates in a Euclidean space have to be an ordered tuple of real numbers, the number of numbers is the dimensionality of the space.

Euclidean spaces are typically known as "flat" spaces due to the fact that they have zero curvature.

Distances in a Euclidean space can be determined with the Pythagorean theorem.

Euclidean spaces can be generalised with Hilbert spaces, which can allow spaces to pertain an infinite dimensionality.

Spaces that don't follow Euclidean geometry do not follow one of the postulates, and may have curvature, imaginary dimensions, a different geometry.

See Also

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

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Glome

Tetrasphere

Pentasphere

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Heptasphere

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Enneasphere

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... Omegasphere

Real dimensionality 0 1 2 3 ...
Real space

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Real projective space

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Complex space

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Complex projective space

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Quaternionic space

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Quaternionic projective space

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Octonionic space

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Octonionic projective space

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