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.

dimension (dimensionality) of an array. The number of subscripts or indexes needed to locate any element in the array.