Dimension

In <a href="/facts/Physics/a7aH2y08">physics</a> and <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the dimension of a <a href="/facts/Space_(mathematics)/G6rt4bQ8">mathematical space</a> (or <a href="/facts/Mathematical_object/Juhyow9M">object</a>) is informally defined as the minimum number of <a href="/facts/Coordinates/Mtd0q4SP">coordinates</a> needed to specify any <a href="/facts/Point_(geometry)/6YPAvX2a">point</a> within it. Thus, a <a href="/facts/Line_(geometry)/gJqsr4Gj">line</a> has a <a href="/facts/One-dimensional_space/bC4W2dHd">dimension of one</a> (1D) because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A <a href="/facts/Surface_(mathematics)/whF08jvy">surface</a>, such as the <a href="/facts/Boundary_(mathematics)/WgdH18kp">boundary</a> of a <a href="/facts/Cylinder_(geometry)/0wQPPr3k">cylinder</a> or <a href="/facts/Sphere/4Ivb1cTj">sphere</a>, has a <a href="/facts/Two-dimensional_space/f4b397W8">dimension of two</a> (2D) because two coordinates are needed to specify a point on it – for example, both a <a href="/facts/Latitude/IBYqkjhU">latitude</a> and <a href="/facts/Longitude/HsC61ML9">longitude</a> are required to locate a point on the surface of a sphere. A <a href="/facts/Two-dimensional_Euclidean_space/f4b397W8">two-dimensional Euclidean space</a> is a two-dimensional space on the <a href="/facts/Euclidean_plane/tAUtRFcn">plane</a>. The inside of a <a href="/facts/Cube/65lUaAqN">cube</a>, a cylinder or a sphere is <a href="/facts/Three-dimensional/KAqKWUbS">three-dimensional</a> (3D) because three coordinates are needed to locate a point within these spaces.
In <a href="/facts/Classical_mechanics/ykG8upsN">classical mechanics</a>, <a href="/facts/Space/tq6LUM3C">space</a> and <a href="/facts/Time/3ShdpqLx">time</a> are different categories and refer to <a href="/facts/Absolute_space_and_time/g8sJ1EbD">absolute space and time</a>. That conception of the world is a <a href="/facts/Four-dimensional_space/vFQd0M7T">four-dimensional space</a> but not the one that was found necessary to describe <a href="/facts/Electromagnetism/oAkmALHT">electromagnetism</a>. The four dimensions (4D) of <a href="/facts/Spacetime/uRIN1x4b">spacetime</a> consist of <a href="/facts/Event_(relativity)/qRgszk7U">events</a> that are not absolutely defined spatially and temporally, but rather are known relative to the motion of an <a href="/facts/Observer_(special_relativity)/t3yB2Bt9">observer</a>. <a href="/facts/Minkowski_space/vDkfkQJn">Minkowski space</a> first approximates the universe without <a href="/facts/Gravity/bqAN7DdQ">gravity</a>; the <a href="/facts/Pseudo-Riemannian_manifold/VFXsVjqb">pseudo-Riemannian manifolds</a> of <a href="/facts/General_relativity/jVsoIg8X">general relativity</a> describe spacetime with matter and gravity. 10 dimensions are used to describe <a href="/facts/Superstring_theory/1gY26F0D">superstring theory</a> (6D <a href="/facts/Hyperspace/RyNnQNdL">hyperspace</a> + 4D), 11 dimensions can describe <a href="/facts/Supergravity/jeNk3aAB">supergravity</a> and <a href="/facts/M-theory/5KJgrr9P">M-theory</a> (7D hyperspace + 4D), and the state-space of <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a> is an infinite-dimensional <a href="/facts/Function_space/lLUE2R1t">function space</a>.
The concept of dimension is not restricted to physical objects. High-dimensional spaces frequently occur in mathematics and the <a href="/facts/Science/IJoaD7rs">sciences</a>. They may be <a href="/facts/Euclidean_space/R2UbzmzM">Euclidean spaces</a> or more general <a href="/facts/Parameter_space/LpdMY5gc">parameter spaces</a> or <a href="/facts/Configuration_space_(mathematics)/qBdhCN3z">configuration spaces</a> such as in <a href="/facts/Lagrangian_mechanics/sTxyqWz8">Lagrangian</a> or <a href="/facts/Hamiltonian_mechanics/2ReerlNA">Hamiltonian mechanics</a>; these are <a href="/facts/Space_(mathematics)/G6rt4bQ8">abstract spaces</a>, independent of the <a href="/facts/Physical_space/tq6LUM3C">physical space</a>.

Dimension open-in-new

Dimension