What is "dimension"

Dimension \Di*men"sion\, n. [L. dimensio, fr. dimensus, p. p. of dimetiri to measure out; di- = dis- + metiri to measure: cf. F. dimension. See Measure.]

1. Measure in a single line, as length, breadth, height, thickness, or circumference; extension; measurement; -- usually, in the plural, measure in length and breadth, or in length, breadth, and thickness; extent; size; as, the dimensions of a room, or of a ship; the dimensions of a farm, of a kingdom.

   Gentlemen of more than ordinary dimensions.
   --W. Irving.

   Space of dimension, extension that has length but no breadth or thickness; a straight or curved line.

   Space of two dimensions, extension which has length and breadth, but no thickness; a plane or curved surface.

   Space of three dimensions, extension which has length, breadth, and thickness; a solid.

   Space of four dimensions, as imaginary kind of extension, which is assumed to have length, breadth, thickness, and also a fourth imaginary dimension. Space of five or six, or more dimensions is also sometimes assumed in mathematics.

2. Extent; reach; scope; importance; as, a project of large dimensions.

3. (Math.) The degree of manifoldness of a quantity; as, time is quantity having one dimension; volume has three dimensions, relative to extension.

4. (Alg.) A literal factor, as numbered in characterizing a term. The term dimensions forms with the cardinal numbers a phrase equivalent to degree with the ordinal; thus, a^ 2b^ 2c is a term of five dimensions, or of the fifth degree.

5. pl. (Phys.) The manifoldness with which the fundamental units of time, length, and mass are involved in determining the units of other physical quantities.

   Note: Thus, since the unit of velocity varies directly as the unit of length and inversely as the unit of time, the dimensions of velocity are said to be length [divby] time; the dimensions of work are mass [times] (length)^ 2 [divby] (time)^ 2; the dimensions of density are mass [divby] (length)^ 3.

   Dimensional lumber, Dimension lumber, Dimension scantling, or Dimension stock (Carp.), lumber for building, etc., cut to the sizes usually in demand, or to special sizes as ordered.

   Dimension stone, stone delivered from the quarry rough, but brought to such sizes as are requisite for cutting to dimensions given.

late 14c., "measurement, size," from Latin dimensionem (nominative dimensio) "a measuring," noun of action from past participle stem of dimetri "to measure out," from dis- (see dis-) + metiri "to measure" (see measure). Meaning "any component of a situation" is from 1929. Related: Dimensional; dimensions.

n. 1 A single aspect of a given thing. 2 A measure of spatial extent in a particular direction, such as height, width or breadth, or depth. vb. (context transitive English) To mark, cut or shape something to specified dimensions.

1. n. the magnitude of something in a particular direction (especially length or width or height)

2. a construct whereby objects or individuals can be distinguished; "self-confidence is not an endearing property" [syn: property, attribute]

3. one of three cartesian coordinates that determine a position in space

4. magnitude or extent; "a building of vast proportions" [syn: proportion]

5. v. indicate the dimensions on; "These techniques permit us to dimension the human heart"

6. shape or form to required dimensions

In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V over its base field.

For every vector space there exists a basis, and all bases of a vector space have equal cardinality; as a result, the dimension of a vector space is uniquely defined. We say V is if the dimension of V is finite, and if its dimension is infinite.

The dimension of the vector space V over the field F can be written as dim(V) or as [V : F], read "dimension of V over F". When F can be inferred from context, dim(V) is typically written.

The dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Dimension or dimensions may also refer to:

"Dimension" is a song by Australian hard rock band Wolfmother, featured on their 2005 debut studio album Wolfmother. Written by band members Andrew Stockdale, Chris Ross and Myles Heskett, it was released as the second single from the album in Europe (and the third single overall) on 17 April 2006, charting at number 49 on the UK Singles Chart.

Dimension is a short film written and directed by Lars von Trier, released in 2010. The film was shot from 1991 to 1997. The original intention was to continue production in three-minute segments every year for a period of 33 years for a final release in 2024. However, von Trier lost interest in the project and it was shelved. The short film consists of the completed footage at the time the film was abandoned.

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| From left to right: the square, the cube and the tesseract. The two-dimensional (2d) square is bounded by one-dimensional (1d) lines; the three-dimensional (3d) cube by two-dimensional areas; and the four-dimensional (4d) tesseract by three-dimensional volumes. For display on a two-dimensional surface such as a screen, the 3d cube and 4d tesseract require projection.

]] [[ levels.svg|thumb

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| The first four spatial dimensions.

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In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on itfor example, the point at 5 on a number line. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on itfor example, both a latitude and longitude are required to locate a point on the surface of a sphere. The inside of a cube, a cylinder or a sphere is three-dimensional because three coordinates are needed to locate a point within these spaces.

In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that was found necessary to describe electromagnetism. The four dimensions of spacetime consist of events that are not absolutely defined spatially and temporally, but rather are known relative to the motion of an observer. Minkowski space first approximates the universe without gravity; the pseudo-Riemannian manifolds of general relativity describe spacetime with matter and gravity. Ten dimensions are used to describe string theory, and the state-space of quantum mechanics is an infinite-dimensional function space.

The concept of dimension is not restricted to physical objects. s frequently occur in mathematics and the sciences. They may be parameter spaces or configuration spaces such as in Lagrangian or Hamiltonian mechanics; these are abstract spaces, independent of the physical space we live in.

A dimension is a structure that categorizes facts and measures in order to enable users to answer business questions. Commonly used dimensions are people, products, place and time.

In a data warehouse, dimensions provide structured labeling information to otherwise unordered numeric measures. The dimension is a data set composed of individual, non-overlapping data elements. The primary functions of dimensions are threefold: to provide filtering, grouping and labelling.

These functions are often described as "slice and dice". Slicing refers to filtering data. Dicing refers to grouping data. A common data warehouse example involves sales as the measure, with customer and product as dimensions. In each sale a customer buys a product. The data can be sliced by removing all customers except for a group under study, and then diced by grouping by product.

A dimensional data element is similar to a categorical variable in statistics.

Typically dimensions in a data warehouse are organized internally into one or more hierarchies. "Date" is a common dimension, with several possible hierarchies:

• "Days (are grouped into) Months (which are grouped into) Years",
• "Days (are grouped into) Weeks (which are grouped into) Years"
• "Days (are grouped into) Months (which are grouped into) Quarters (which are grouped into) Years"
• etc.

In metadata, dimension is a set of equivalent units of measure, where equivalence between two units of measure is determined by the existence of a quantity preserving one-to-one correspondence between values measured in one unit of measure and values measured in the other unit of measure, independent of context, and where characterizing operations are the same.

The equivalence defined here forms an equivalence relation on the set of all units of measure. Each equivalence class corresponds to a dimensionality. The units of measure "temperature in degrees Fahrenheit" and "temperature in degrees Celsius" have the same dimensionality, because given a value measured in degrees Fahrenheit there is a value measured in degrees Celsius with the same quantity, and vice versa. Quantity preserving one-to-one correspondences are the well-known equations Cº = (5/9)*(Fº − 32) and Fº = (9/5)*(Cº) + 32.

Units of measure are not limited to physical categories.Examples of physical categories are: linear measure, area, volume, mass, velocity, time duration.Examples of non-physical categories are: currency, quality indicator, colour intensity.

Quantities may be grouped together into categories of quantities which are mutually comparable. Lengths, diameters, distances, heights, wavelengths and so on would constitute such a category. Mutually comparable quantities have the same dimensionality. ISO 31-0 calls these quantities of the same kind.

Dimension Shampoo was a heavily perfumed shampoo product, which was produced in the early 1980s. This was by the personal products division of Lever Brothers, and marketed by Ogilvy. The shampoo came in a distinctive dark yellow bottle, and left a strong muskone and civetone aroma on the hair. There was also a companion conditioner marketed with this product. It has been stated by many previous users of dimension shampoo that it caused their hair to fall out, due to the extreme astringency of the product.

On April 18, 1985, Lever Brothers reorganized their marketing structure and moved their personal products division business to J. Walter Thompson.

At the time, Dimension was a highly popular brand. (Lever spent an estimated $12.5M in advertising the brand in 1984.) However, shortly after Lever's marketing reorganization, Dimension ran-out on store shelves, and never returned. Lever Brothers never made any public explanation for the disappearance of the product; although they referred to the marketing reorganization as a consolidation of the personal products brands, and stated that the decision in-part had to do with its plans for international marketing.

In mathematics, and particularly in graph theory, the dimension of a graph is the least integer n such that there exists a "classical representation" of the graph in the Euclidean space of dimension n with all the edges having unit length.

In a classical representation, the vertices must be distinct points, but the edges may cross one another.

The dimension of a graph G is written: dim G.

For example, the Petersen graph can be drawn with unit edges in E, but not in E: its dimension is therefore 2 (see the figure to the right).

This concept was introduced in 1965 by Paul Erdős, Frank Harary and William Tutte. It generalises the concept of unit distance graph to more than 2 dimensions.