Editing Dimension (section)

{{Short description|Property of a mathematical space}}
{{About|the dimension of a space|the dimension of an object|size|the dimension of a quantity|Dimensional analysis|other uses|Dimension (disambiguation)}}
[[File:Squarecubetesseract.png|thumb|upright=1.2|From left to right: a [[square (geometry)|square]], a [[cube]] and a [[tesseract]]. The square is two-dimensional (2D) and bounded by one-dimensional [[line segment]]s; the cube is three-dimensional (3D) and bounded by two-dimensional squares; the tesseract is four-dimensional (4D) and bounded by three-dimensional cubes.
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[[File:Dimension levels.svg|thumb|upright=1.2| The first four spatial dimensions, represented in a two-dimensional picture.
 {{ordered list
  | Two points <!--(These and subsequent points not identified in diagram:) A and B--> can be connected to create a [[line segment]].
  | Two parallel line segments <!--AB and CD--> can be connected to form a [[square]]<!-- (corners marked ABCD)-->.
  | Two parallel squares <!--ABCD and EFGH--> can be connected to form a [[cube]]<!-- (corners marked as ABCDEFGH)-->.
  | Two parallel cubes <!--ABCDEFGH and IJKLMNOP--> can be connected to form a [[tesseract]]<!-- (corners marked as ABCDEFGHIJKLMNOP)-->.
 }}
]]
{{General geometry|concepts}}

In [[physics]] and [[mathematics]], the '''dimension''' of a [[Space (mathematics)|mathematical space]] (or [[Mathematical object|object]]) is informally defined as the minimum number of [[coordinates]] needed to specify any [[Point (geometry)|point]] within it.<ref>{{cite web|url=http://curious.astro.cornell.edu/question.php?number=4 |title=Curious About Astronomy |publisher=Curious.astro.cornell.edu |access-date=2014-03-03 |url-status=dead |archive-url=https://web.archive.org/web/20140111191053/http://curious.astro.cornell.edu/question.php?number=4 |archive-date=2014-01-11 }}</ref><ref>{{cite web |url=http://mathworld.wolfram.com/Dimension.html |title=MathWorld: Dimension |publisher=Mathworld.wolfram.com |date=2014-02-27 |access-date=2014-03-03 |url-status=live |archive-url=https://web.archive.org/web/20140325220941/http://mathworld.wolfram.com/Dimension.html |archive-date=2014-03-25 }}</ref> Thus, a [[Line (geometry)|line]] has a [[One-dimensional space|dimension of one]] (1D) because only one coordinate is needed to specify a point on it{{spndash}}for example, the point at 5 on a number line. A [[Surface (mathematics)|surface]], such as the [[Boundary (mathematics)|boundary]] of a [[Cylinder (geometry)|cylinder]] or [[sphere]], has a [[Two-dimensional space|dimension of two]] (2D) because two coordinates are needed to specify a point on it{{spndash}}for example, both a [[latitude]] and [[longitude]] are required to locate a point on the surface of a sphere. A [[two-dimensional Euclidean space]] is a two-dimensional space on the [[Euclidean plane|plane]]. The inside of a [[cube]], a cylinder or a sphere is [[three-dimensional]] (3D) because three coordinates are needed to locate a point within these spaces.

In [[classical mechanics]], [[space]] and [[time]] are different categories and refer to [[absolute space and time]]. That conception of the world is a [[four-dimensional space]] but not the one that was found necessary to describe [[electromagnetism]]. The four dimensions (4D) of [[spacetime]] consist of [[event (relativity)|events]] that are not absolutely defined spatially and temporally, but rather are known relative to the motion of an [[observer (special relativity)|observer]]. [[Minkowski space]] first approximates the universe without [[gravity]]; the [[pseudo-Riemannian manifold]]s of [[general relativity]] describe spacetime with matter and gravity. 10 dimensions are used to describe [[superstring theory]] (6D [[hyperspace]] + 4D), 11 dimensions can describe [[supergravity]] and [[M-theory]] (7D hyperspace + 4D), and the state-space of [[quantum mechanics]] is an infinite-dimensional [[function space]].

The concept of dimension is not restricted to physical objects. '''{{vanchor|High-dimensional space|N-dimensional space|n dimensional space}}s''' frequently occur in mathematics and the [[science]]s. They may be [[Euclidean space]]s or more general [[parameter space]]s or [[Configuration space (mathematics)|configuration spaces]] such as in [[Lagrangian mechanics|Lagrangian]] or [[Hamiltonian mechanics]]; these are [[space (mathematics)|abstract spaces]], independent of the [[physical space]].