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, in physics, an expression of the character of a derived quantity in relation to fundamental quantities, without regard for its numerical value. In any system of measurement, such as the metric system, certain quantities are considered fundamental, and all others are considered to be derived from them. Systems in which length (L), time (T), and mass (M) are taken as fundamental quantities are called absolute systems. In an absolute system force is a derived quantity whose dimensions are defined by Newton's second law of motion as ML/T², in terms of the fundamental quantities. Pressure (force per unit area) then has dimensions M/LT²; work or energy (force times distance) has dimensions ML²/T²; and power (energy per unit time) has dimensions ML²/T³. Additional fundamental quantities are also defined, such as electric charge and luminous intensity. The expression of any particular quantity in terms of fundamental quantities is known as dimensional analysis and often provides physical insight into the results of a mathematical calculation.

In mathematics, a number indicating the fewest coordinates necessary to identify a point in a geometric space; more generally, a number indicating a measurement of length (see length, area, and volume). One-dimensional space can be represented by a numbered line, on which a single number identifies a point. In two-dimensional space, a coordinate system may be superimposed, requiring only two numbers to identify a point. Three numbers suffice in three-dimensional space, and so on.

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