a property of space; extension in a given direction: A straight line has one dimension, a parallelogram has two dimensions, and a parallelepiped has three dimensions.
b.
the generalization of this property to spaces with curvilinear extension, as the surface of a sphere.
c.
the generalization of this property to vector spaces and to Hilbert space.
d.
the generalization of this property to fractals, which can have dimensions that are noninteger real numbers.
e.
extension in time: Space-time has three dimensions of space and one of time.
a magnitude that, independently or in conjunction with other such magnitudes, serves to define the location of an element within a given set, as of a point on a line, an object in a space, or an event in space-time.
b.
the number of elements in a finite basis of a given vector space.
6.
Physics. any of a set of basic kinds of quantity, as mass, length, and time, in terms of which all other kinds of quantity can be expressed; usually denoted by capital letters, with appropriate exponents, placed in brackets: The dimensions of velocity are [LT−1].Compare dimensional analysis.
7.
dimensions, Informal. the measurements of a woman's bust, waist, and hips, in that order: The chorus girl's dimensions were 38-24-36.
to shape or fashion to the desired dimensions: Dimension the shelves so that they fit securely into the cabinet.
10.
to indicate the dimensions of an item, area, etc., on (a sketch or drawing).
[Origin: 1375–1425; late ME dimensioun (< AF) < L dīménsiōn- (s. of dīménsiō) a measuring, equiv. to dīméns(us) measured out (ptp. of dīmétīrī, equiv. to dī-di-2+ métīrī to measure) + -iōn--ion]
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.
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