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dimension

dimension, in mathematics, number of parameters or coordinates required locally to describe points in a mathematical object (usually geometric in character). For example, the space we inhabit is three-dimensional, a plane or surface is two-dimensional, a line or curve is one-dimensional, and a point is zero-dimensional. By means of a coordinate system one can specify any point with respect to a chosen origin (and coordinate axes through the origin, in the case of two or more dimensions). Thus, a point on a line is specified by a number x giving its distance from the origin, with one direction chosen as positive and the other as negative; a point on a plane is specified by an ordered pair of numbers ( x,y ) giving its distances from the two coordinate axes; a point in space is specified by an ordered triple of numbers ( x,y,z ) giving its distances from three coordinate axes. Mathematicians are thus led by analogy to define an ordered set of four, five, or more numbers as representing a point in what they define as a space of four, five, or more dimensions. Although such spaces cannot be visualized, they may nevertheless by physically significant. For example, the quadruple of numbers ( x,y,z,t ), where t represents time, is sometimes interpreted as a point in four-dimensional space-time (see relativity). The state of the weather or the economy, in current models, is a point in a many-dimensional space. Many features of plane and solid Euclidean geometry have mathematical analogues in higher dimensional spaces.

The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.

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