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DIMENSION | English meaning - Cambridge Dictionary
DIMENSION | English meaning - Cambridge Dictionary
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Meaning of dimension in English
dimensionnoun uk
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/ˌdaɪˈmen.ʃən/ /ˌdɪˈmen.ʃən/ us
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/ˌdaɪˈmen.ʃən/ /ˌdɪˈmen.ʃən/
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B2 [ C often plural ] a measurement of something in a particular direction, especially its height, length, or width: Please specify the dimensions (= the height, length and width) of the room. a building of vast dimensions (= size)
B2 [ C ] a part or feature or way of considering something: His personality has several dimensions. These weapons add a new dimension to modern warfare. There is a spiritual dimension to her poetry.
SMART Vocabulary: related words and phrases
Measurements in general
altitude
bathymetric
bathymetrically
bathymetry
be running at something idiom
calibrate
distance
drop
elevation
factor
knee-length
metric
metrication
milli-
scale
setting
tera-
uncalibrated
unmeasurable
unsized
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You can also find related words, phrases, and synonyms in the topics:
Conditions and characteristics
(Definition of dimension from the Cambridge Advanced Learner's Dictionary & Thesaurus © Cambridge University Press)
dimension | American Dictionary
dimensionnoun [ C ] us
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/dəˈmen·ʃən/
dimension noun [C]
(MEASUREMENT)
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a measurement of something in a particular direction, esp. its height, length, or width: The dimensions of the room are 26 feet by 15 feet.
dimension noun [C]
(QUALITY)
a part or quality of a thing or situation that has an effect on the way you think about it: The new script gave the story a psychological dimension.
(Definition of dimension from the Cambridge Academic Content Dictionary © Cambridge University Press)
dimension | Business English
dimensionnoun [ C ] uk
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/ˌdaɪˈmenʃən/ us
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a measurement of something in a particular direction, especially its height, length, or width: The estate agent's brochure specifies the dimensions of each room. approximate/exact/precise dimensions
a part or feature of something: Good managers will analyse every dimension of job satisfaction. One other dimension of e-commerce readiness is integration between information systems. The information-based economy has the potential to add a new dimension to economic success.
(Definition of dimension from the Cambridge Business English Dictionary © Cambridge University Press)
Examples of dimension
dimension
Can we assess the role of dialect differences relative to other dimensions of situated discourse?
From the Cambridge English Corpus
A choice of 3,000 dimensions seems appropriate for the present data.
From the Cambridge English Corpus
In both cases these dimensions do not include the thickness of the cyst wall.
From the Cambridge English Corpus
A control of order -1 has the opposite behaviour: a direct relationship between rate of change of the control's value and the dimension's value.
From the Cambridge English Corpus
No sane human being would search through all the 221 dimensions of the model blindly hoping to find some optimal sound!
From the Cambridge English Corpus
The possibility of an event being in the 'active' state generalizes the 0-dimensional notion of state to higher dimensions.
From the Cambridge English Corpus
The four th and additional dimensions explain very little of the variance in the data.
From the Cambridge English Corpus
They found that higher-dimensional splines offered significant improvements over standard discretization methods (although for dimensions higher than three, their algorithms are still very time-consuming).
From the Cambridge English Corpus
However, this comes at the cost of weakening the ability of sunspot models to explain fluctuations along some dimensions.
From the Cambridge English Corpus
More indirectly, these two stylistic dimensions mark different epistemic relations to the discourse, emphasizing and privileging different kinds of information.
From the Cambridge English Corpus
Our purpose here is to elaborate these analytical dimensions in relation to workplace discourse.
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To encompass the two parties and seven issue dimensions, we estimated fourteen separate models.
From the Cambridge English Corpus
All results cover the important case when = 2 in one and two dimensions.
From the Cambridge English Corpus
Different permutations of the three dimensions generated multiple model types.
From the Cambridge English Corpus
How else can justice be done to its bigness, to the different dimensions of excess that are part of its history?
From the Cambridge English Corpus
See all examples of dimension
These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
Collocations with dimension
dimension
These are words often used in combination with dimension.Click on a collocation to see more examples of it.
added dimensionFuture versions of this model will generalize these preferences, but this brings in the added dimension of trying to determine optimal consumption, given current information.
From the Cambridge English Corpus
additional dimensionThis again would have placed an additional dimension to the publication, and made it less subjective.
From the Cambridge English Corpus
aesthetic dimensionNotably, they suggest that, for practical purposes at least, religious understanding has an aesthetic dimension in at least two ways.
From the Cambridge English Corpus
These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
See all collocations with dimension
What is the pronunciation of dimension?
B2,B2
Translations of dimension
in Chinese (Traditional)
空間,尺寸, 層面,維度, 特點…
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in Chinese (Simplified)
空间,尺寸, 层面,维度, 特点…
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in Spanish
dimensiones, dimensión, dimensión [feminine]…
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dimensões, dimensão, dimensão [feminine]…
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मोजमाप, आकारमान, कंगोरे…
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要素, 局面, 様相(ようそう)…
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yön, boyut, taraf…
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dimension [feminine], dimension…
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dimensió…
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afmeting…
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ஒரு குறிப்பிட்ட திசையில் எதையாவது அளவிடுதல், குறிப்பாக அதன் உயரம், நீளம் அல்லது அகலம்…
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(लंबाई, चौड़ाई, ऊँचाई का) आयाम…
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પરિમાણો (લંબાઈ, પહોળાઈ, ઊંચાઈ)…
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omfang, størrelse…
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mått, dimension…
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luas…
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das Maß…
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dimensjon [masculine], aspekt [neuter], dimensjon…
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بُعد, حدود, لمبائی، چوڑائی اور اونچائی یا گہرائی…
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вимір, розміри…
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измерение, аспект, размер…
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ఒక ప్రత్యేకమైన దారిలో ఒక దాని కొలత, ప్రత్యేకంగా దాని ఎత్తిలో, పొడువులో…
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بُعد…
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মাত্রা, একটি নির্দিষ্ট দিকের কিছুর পরিমাপ বিশেষত এর উচ্চতা, দৈর্ঘ্য বা প্রস্থ…
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rozměr…
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matra, dimensi…
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การหามิติ…
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kích thước…
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wymiar, aspekt, rozmiar…
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관점…
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dimensione, aspetto…
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Dimension - Wikipedia
Dimension - Wikipedia
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1In mathematics
Toggle In mathematics subsection
1.1Vector spaces
1.2Manifolds
1.2.1Complex dimension
1.3Varieties
1.4Krull dimension
1.5Topological spaces
1.6Hausdorff dimension
1.7Hilbert spaces
2In physics
Toggle In physics subsection
2.1Spatial dimensions
2.2Time
2.3Additional dimensions
3In computer graphics and spatial data
4More dimensions
5List of topics by dimension
6See also
7References
8Further reading
9External links
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Dimension
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From Wikipedia, the free encyclopedia
Property of a mathematical space
This article is about the dimension of a space. For the dimension of an object, see size. For the dimension of a quantity, see Dimensional analysis. For other uses, see Dimension (disambiguation).
From left to right: a square, a cube and a tesseract. The square is two-dimensional (2D) and bounded by one-dimensional line segments; the cube is three-dimensional (3D) and bounded by two-dimensional squares; the tesseract is four-dimensional (4D) and bounded by three-dimensional cubes.
The first four spatial dimensions, represented in a two-dimensional picture. Two points can be connected to create a line segment.Two parallel line segments can be connected to form a square.Two parallel squares can be connected to form a cube.Two parallel cubes can be connected to form a tesseract.
GeometryProjecting a sphere to a plane
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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.[1][2] Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) 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 (4D) 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. 10 dimensions are used to describe superstring theory (6D hyperspace + 4D), 11 dimensions can describe supergravity and M-theory (7D hyperspace + 4D), and the state-space of quantum mechanics is an infinite-dimensional function space.
The concept of dimension is not restricted to physical objects. High-dimensional spaces frequently occur in mathematics and the sciences. They may be Euclidean spaces or more general parameter spaces or configuration spaces such as in Lagrangian or Hamiltonian mechanics; these are abstract spaces, independent of the physical space.
In mathematics[edit]
In mathematics, the dimension of an object is, roughly speaking, the number of degrees of freedom of a point that moves on this object. In other words, the dimension is the number of independent parameters or coordinates that are needed for defining the position of a point that is constrained to be on the object. For example, the dimension of a point is zero; the dimension of a line is one, as a point can move on a line in only one direction (or its opposite); the dimension of a plane is two etc.
The dimension is an intrinsic property of an object, in the sense that it is independent of the dimension of the space in which the object is or can be embedded. For example, a curve, such as a circle, is of dimension one, because the position of a point on a curve is determined by its signed distance along the curve to a fixed point on the curve. This is independent from the fact that a curve cannot be embedded in a Euclidean space of dimension lower than two, unless it is a line.
The dimension of Euclidean n-space En is n. When trying to generalize to other types of spaces, one is faced with the question "what makes En n-dimensional?" One answer is that to cover a fixed ball in En by small balls of radius ε, one needs on the order of ε−n such small balls. This observation leads to the definition of the Minkowski dimension and its more sophisticated variant, the Hausdorff dimension, but there are also other answers to that question. For example, the boundary of a ball in En looks locally like En-1 and this leads to the notion of the inductive dimension. While these notions agree on En, they turn out to be different when one looks at more general spaces.
A tesseract is an example of a four-dimensional object. Whereas outside mathematics the use of the term "dimension" is as in: "A tesseract has four dimensions", mathematicians usually express this as: "The tesseract has dimension 4", or: "The dimension of the tesseract is 4" or: 4D.
Although the notion of higher dimensions goes back to René Descartes, substantial development of a higher-dimensional geometry only began in the 19th century, via the work of Arthur Cayley, William Rowan Hamilton, Ludwig Schläfli and Bernhard Riemann. Riemann's 1854 Habilitationsschrift, Schläfli's 1852 Theorie der vielfachen Kontinuität, and Hamilton's discovery of the quaternions and John T. Graves' discovery of the octonions in 1843 marked the beginning of higher-dimensional geometry.
The rest of this section examines some of the more important mathematical definitions of dimension.
Vector spaces[edit]
Main article: Dimension (vector space)
The dimension of a vector space is the number of vectors in any basis for the space, i.e. the number of coordinates necessary to specify any vector. This notion of dimension (the cardinality of a basis) is often referred to as the Hamel dimension or algebraic dimension to distinguish it from other notions of dimension.
For the non-free case, this generalizes to the notion of the length of a module.
Manifolds[edit]
The uniquely defined dimension of every connected topological manifold can be calculated. A connected topological manifold is locally homeomorphic to Euclidean n-space, in which the number n is the manifold's dimension.
For connected differentiable manifolds, the dimension is also the dimension of the tangent vector space at any point.
In geometric topology, the theory of manifolds is characterized by the way dimensions 1 and 2 are relatively elementary, the high-dimensional cases n > 4 are simplified by having extra space in which to "work"; and the cases n = 3 and 4 are in some senses the most difficult. This state of affairs was highly marked in the various cases of the Poincaré conjecture, in which four different proof methods are applied.
Complex dimension[edit]
The dimension of a manifold depends on the base field with respect to which Euclidean space is defined. While analysis usually assumes a manifold to be over the real numbers, it is sometimes useful in the study of complex manifolds and algebraic varieties to work over the complex numbers instead. A complex number (x + iy) has a real part x and an imaginary part y, in which x and y are both real numbers; hence, the complex dimension is half the real dimension.
Conversely, in algebraically unconstrained contexts, a single complex coordinate system may be applied to an object having two real dimensions. For example, an ordinary two-dimensional spherical surface, when given a complex metric, becomes a Riemann sphere of one complex dimension.[3]
Varieties[edit]
Main article: Dimension of an algebraic variety
The dimension of an algebraic variety may be defined in various equivalent ways. The most intuitive way is probably the dimension of the tangent space at any Regular point of an algebraic variety. Another intuitive way is to define the dimension as the number of hyperplanes that are needed in order to have an intersection with the variety that is reduced to a finite number of points (dimension zero). This definition is based on the fact that the intersection of a variety with a hyperplane reduces the dimension by one unless if the hyperplane contains the variety.
An algebraic set being a finite union of algebraic varieties, its dimension is the maximum of the dimensions of its components. It is equal to the maximal length of the chains
V
0
⊊
V
1
⊊
⋯
⊊
V
d
{\displaystyle V_{0}\subsetneq V_{1}\subsetneq \cdots \subsetneq V_{d}}
of sub-varieties of the given algebraic set (the length of such a chain is the number of "
⊊
{\displaystyle \subsetneq }
").
Each variety can be considered as an algebraic stack, and its dimension as variety agrees with its dimension as stack. There are however many stacks which do not correspond to varieties, and some of these have negative dimension. Specifically, if V is a variety of dimension m and G is an algebraic group of dimension n acting on V, then the quotient stack [V/G] has dimension m − n.[4]
Krull dimension[edit]
The Krull dimension of a commutative ring is the maximal length of chains of prime ideals in it, a chain of length n being a sequence
P
0
⊊
P
1
⊊
⋯
⊊
P
n
{\displaystyle {\mathcal {P}}_{0}\subsetneq {\mathcal {P}}_{1}\subsetneq \cdots \subsetneq {\mathcal {P}}_{n}}
of prime ideals related by inclusion. It is strongly related to the dimension of an algebraic variety, because of the natural correspondence between sub-varieties and prime ideals of the ring of the polynomials on the variety.
For an algebra over a field, the dimension as vector space is finite if and only if its Krull dimension is 0.
Topological spaces[edit]
For any normal topological space X, the Lebesgue covering dimension of X is defined to be the smallest integer n for which the following holds: any open cover has an open refinement (a second open cover in which each element is a subset of an element in the first cover) such that no point is included in more than n + 1 elements. In this case dim X = n. For X a manifold, this coincides with the dimension mentioned above. If no such integer n exists, then the dimension of X is said to be infinite, and one writes dim X = ∞. Moreover, X has dimension −1, i.e. dim X = −1 if and only if X is empty. This definition of covering dimension can be extended from the class of normal spaces to all Tychonoff spaces merely by replacing the term "open" in the definition by the term "functionally open".
An inductive dimension may be defined inductively as follows. Consider a discrete set of points (such as a finite collection of points) to be 0-dimensional. By dragging a 0-dimensional object in some direction, one obtains a 1-dimensional object. By dragging a 1-dimensional object in a new direction, one obtains a 2-dimensional object. In general one obtains an (n + 1)-dimensional object by dragging an n-dimensional object in a new direction. The inductive dimension of a topological space may refer to the small inductive dimension or the large inductive dimension, and is based on the analogy that, in the case of metric spaces, (n + 1)-dimensional balls have n-dimensional boundaries, permitting an inductive definition based on the dimension of the boundaries of open sets. Moreover, the boundary of a discrete set of points is the empty set, and therefore the empty set can be taken to have dimension -1.[5]
Similarly, for the class of CW complexes, the dimension of an object is the largest n for which the n-skeleton is nontrivial. Intuitively, this can be described as follows: if the original space can be continuously deformed into a collection of higher-dimensional triangles joined at their faces with a complicated surface, then the dimension of the object is the dimension of those triangles.[citation needed]
See also: dimension of a scheme
Hausdorff dimension[edit]
The Hausdorff dimension is useful for studying structurally complicated sets, especially fractals. The Hausdorff dimension is defined for all metric spaces and, unlike the dimensions considered above, can also have non-integer real values.[6] The box dimension or Minkowski dimension is a variant of the same idea. In general, there exist more definitions of fractal dimensions that work for highly irregular sets and attain non-integer positive real values.
Hilbert spaces[edit]
Every Hilbert space admits an orthonormal basis, and any two such bases for a particular space have the same cardinality. This cardinality is called the dimension of the Hilbert space. This dimension is finite if and only if the space's Hamel dimension is finite, and in this case the two dimensions coincide.
In physics[edit]
Spatial dimensions[edit]
Classical physics theories describe three physical dimensions: from a particular point in space, the basic directions in which we can move are up/down, left/right, and forward/backward. Movement in any other direction can be expressed in terms of just these three. Moving down is the same as moving up a negative distance. Moving diagonally upward and forward is just as the name of the direction implies; i.e., moving in a linear combination of up and forward. In its simplest form: a line describes one dimension, a plane describes two dimensions, and a cube describes three dimensions. (See Space and Cartesian coordinate system.)
Number ofdimensions
Example co-ordinate systems
1
Number line
Angle
2
Cartesian (two-dimensional)
Polar
Latitude and longitude
3
Cartesian (three-dimensional)
Cylindrical
Spherical
Time[edit]
A temporal dimension, or time dimension, is a dimension of time. Time is often referred to as the "fourth dimension" for this reason, but that is not to imply that it is a spatial dimension[citation needed]. A temporal dimension is one way to measure physical change. It is perceived differently from the three spatial dimensions in that there is only one of it, and that we cannot move freely in time but subjectively move in one direction.
The equations used in physics to model reality do not treat time in the same way that humans commonly perceive it. The equations of classical mechanics are symmetric with respect to time, and equations of quantum mechanics are typically symmetric if both time and other quantities (such as charge and parity) are reversed. In these models, the perception of time flowing in one direction is an artifact of the laws of thermodynamics (we perceive time as flowing in the direction of increasing entropy).
The best-known treatment of time as a dimension is Poincaré and Einstein's special relativity (and extended to general relativity), which treats perceived space and time as components of a four-dimensional manifold, known as spacetime, and in the special, flat case as Minkowski space. Time is different from other spatial dimensions as time operates in all spatial dimensions. Time operates in the first, second and third as well as theoretical spatial dimensions such as a fourth spatial dimension. Time is not however present in a single point of absolute infinite singularity as defined as a geometric point, as an infinitely small point can have no change and therefore no time. Just as when an object moves through positions in space, it also moves through positions in time. In this sense the force moving any object to change is time.[7][8][9]
Additional dimensions[edit]
In physics, three dimensions of space and one of time is the accepted norm. However, there are theories that attempt to unify the four fundamental forces by introducing extra dimensions/hyperspace. Most notably, superstring theory requires 10 spacetime dimensions, and originates from a more fundamental 11-dimensional theory tentatively called M-theory which subsumes five previously distinct superstring theories. Supergravity theory also promotes 11D spacetime = 7D hyperspace + 4 common dimensions. To date, no direct experimental or observational evidence is available to support the existence of these extra dimensions. If hyperspace exists, it must be hidden from us by some physical mechanism. One well-studied possibility is that the extra dimensions may be "curled up" at such tiny scales as to be effectively invisible to current experiments.
In 1921, Kaluza–Klein theory presented 5D including an extra dimension of space. At the level of quantum field theory, Kaluza–Klein theory unifies gravity with gauge interactions, based on the realization that gravity propagating in small, compact extra dimensions is equivalent to gauge interactions at long distances. In particular when the geometry of the extra dimensions is trivial, it reproduces electromagnetism. However at sufficiently high energies or short distances, this setup still suffers from the same pathologies that famously obstruct direct attempts to describe quantum gravity. Therefore, these models still require a UV completion, of the kind that string theory is intended to provide. In particular, superstring theory requires six compact dimensions (6D hyperspace) forming a Calabi–Yau manifold. Thus Kaluza-Klein theory may be considered either as an incomplete description on its own, or as a subset of string theory model building.
In addition to small and curled up extra dimensions, there may be extra dimensions that instead are not apparent because the matter associated with our visible universe is localized on a (3 + 1)-dimensional subspace. Thus the extra dimensions need not be small and compact but may be large extra dimensions. D-branes are dynamical extended objects of various dimensionalities predicted by string theory that could play this role. They have the property that open string excitations, which are associated with gauge interactions, are confined to the brane by their endpoints, whereas the closed strings that mediate the gravitational interaction are free to propagate into the whole spacetime, or "the bulk". This could be related to why gravity is exponentially weaker than the other forces, as it effectively dilutes itself as it propagates into a higher-dimensional volume.
Some aspects of brane physics have been applied to cosmology. For example, brane gas cosmology[10][11] attempts to explain why there are three dimensions of space using topological and thermodynamic considerations. According to this idea it would be since three is the largest number of spatial dimensions in which strings can generically intersect. If initially there are many windings of strings around compact dimensions, space could only expand to macroscopic sizes once these windings are eliminated, which requires oppositely wound strings to find each other and annihilate. But strings can only find each other to annihilate at a meaningful rate in three dimensions, so it follows that only three dimensions of space are allowed to grow large given this kind of initial configuration.
Extra dimensions are said to be universal if all fields are equally free to propagate within them.
In computer graphics and spatial data[edit]
Main article: Geometric primitive
Several types of digital systems are based on the storage, analysis, and visualization of geometric shapes, including illustration software, Computer-aided design, and Geographic information systems. Different vector systems use a wide variety of data structures to represent shapes, but almost all are fundamentally based on a set of geometric primitives corresponding to the spatial dimensions:[12]
Point (0-dimensional), a single coordinate in a Cartesian coordinate system.
Line or Polyline (1-dimensional), usually represented as an ordered list of points sampled from a continuous line, whereupon the software is expected to interpolate the intervening shape of the line as straight or curved line segments.
Polygon (2-dimensional), usually represented as a line that closes at its endpoints, representing the boundary of a two-dimensional region. The software is expected to use this boundary to partition 2-dimensional space into an interior and exterior.
Surface (3-dimensional), represented using a variety of strategies, such as a polyhedron consisting of connected polygon faces. The software is expected to use this surface to partition 3-dimensional space into an interior and exterior.
Frequently in these systems, especially GIS and Cartography, a representation of a real-world phenomena may have a different (usually lower) dimension than the phenomenon being represented. For example, a city (a two-dimensional region) may be represented as a point, or a road (a three-dimensional volume of material) may be represented as a line. This dimensional generalization correlates with tendencies in spatial cognition. For example, asking the distance between two cities presumes a conceptual model of the cities as points, while giving directions involving travel "up," "down," or "along" a road imply a one-dimensional conceptual model. This is frequently done for purposes of data efficiency, visual simplicity, or cognitive efficiency, and is acceptable if the distinction between the representation and the represented is understood, but can cause confusion if information users assume that the digital shape is a perfect representation of reality (i.e., believing that roads really are lines).
More dimensions[edit]
Degrees of freedom
in mechanics
in physics and chemistry
in statistics
Exterior dimension
Hurst exponent
Isoperimetric dimension
Metric dimension
Order dimension
q-dimension
Fractal (q = 1)
Correlation (q = 2)
List of topics by dimension[edit]
Zero
Point
Zero-dimensional space
Integer
One
Line
Curve
Graph (combinatorics)
Real number
Length
Two
Plane
Surface
Polygon
Net
Complex number
Cartesian coordinate system
List of uniform tilings
Area
Three
Platonic solid
Polyhedron
Stereoscopy (3-D imaging)
3-manifold
Axis of rotation
Knots
Skew lines
Skew polygon
Volume
Four
Spacetime
Fourth spatial dimension
Convex regular 4-polytope
Quaternion
4-manifold
Polychoron
Rotations in 4-dimensional Euclidean space
Fourth dimension in art
Fourth dimension in literature
Higher dimensions
in mathematics
Octonion
Vector space
Plane of rotation
Curse of dimensionality
in physics
Kaluza–Klein theory
String theory
M-theory
Infinite
Hilbert space
Function space
See also[edit]
Dimension (data warehouse)
Dimension tables
Dimensional analysis
Hyperspace (disambiguation)
Intrinsic dimension
Multidimensional analysis
Space-filling curve
Mean dimension
Flatland
References[edit]
^ "Curious About Astronomy". Curious.astro.cornell.edu. Archived from the original on 2014-01-11. Retrieved 2014-03-03.
^ "MathWorld: Dimension". Mathworld.wolfram.com. 2014-02-27. Archived from the original on 2014-03-25. Retrieved 2014-03-03.
^ Yau, Shing-Tung; Nadis, Steve (2010). "4. Too Good to be True". The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions. Basic Books. pp. 60–. ISBN 978-0-465-02266-3.
^ Fantechi, Barbara (2001), "Stacks for everybody" (PDF), European Congress of Mathematics Volume I, Progr. Math., vol. 201, Birkhäuser, pp. 349–359, archived (PDF) from the original on 2006-01-17
^ Hurewicz, Witold; Wallman, Henry (2015). Dimension Theory (PMS-4), Volume 4. Princeton University Press. p. 24. ISBN 978-1-4008-7566-5. Extract of page 24
^ Fractal Dimension Archived 2006-10-27 at the Wayback Machine, Boston University Department of Mathematics and Statistics
^ Rylov, Yuri A. (2007). "Non-Euclidean method of the generalized geometry construction and its application to space-time geometry". arXiv:math/0702552.
^ Lane, Paul M.; Lindquist, Jay D. (May 22, 2015). "Definitions for The Fourth Dimension: A Proposed Time Classification System1". In Bahn, Kenneth D. (ed.). Proceedings of the 1988 Academy of Marketing Science (AMS) Annual Conference. Developments in Marketing Science: Proceedings of the Academy of Marketing Science. Springer International Publishing. pp. 38–46. doi:10.1007/978-3-319-17046-6_8. ISBN 978-3-319-17045-9 – via Springer Link.
^ Wilson, Edwin B.; Lewis, Gilbert N. (1912). "The Space-Time Manifold of Relativity. The Non-Euclidean Geometry of Mechanics and Electromagnetics". Proceedings of the American Academy of Arts and Sciences. 48 (11): 389–507. doi:10.2307/20022840. JSTOR 20022840 – via JSTOR.
^ Brandenberger, R.; Vafa, C. (1989). "Superstrings in the early universe". Nuclear Physics B. 316 (2): 391–410. Bibcode:1989NuPhB.316..391B. doi:10.1016/0550-3213(89)90037-0.
^ Scott Watson, Brane Gas Cosmology Archived 2014-10-27 at the Wayback Machine (pdf).
^ Vector Data Models, Essentials of Geographic Information Systems, Saylor Academy, 2012
Further reading[edit]
Murty, Katta G. (2014). "1. Systems of Simultaneous Linear Equations" (PDF). Computational and Algorithmic Linear Algebra and n-Dimensional Geometry. World Scientific Publishing. doi:10.1142/8261. ISBN 978-981-4366-62-5.
Abbott, Edwin A. (1884). Flatland: A Romance of Many Dimensions. London: Seely & Co.
—. Flatland: ... Project Gutenberg.
—; Stewart, Ian (2008). The Annotated Flatland: A Romance of Many Dimensions. Basic Books. ISBN 978-0-7867-2183-2.
Banchoff, Thomas F. (1996). Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions. Scientific American Library. ISBN 978-0-7167-6015-3.
Pickover, Clifford A. (2001). Surfing through Hyperspace: Understanding Higher Universes in Six Easy Lessons. Oxford University Press. ISBN 978-0-19-992381-6.
Rucker, Rudy (2014) [1984]. The Fourth Dimension: Toward a Geometry of Higher Reality. Courier Corporation. ISBN 978-0-486-77978-2. Google preview
Kaku, Michio (1994). Hyperspace, a Scientific Odyssey Through the 10th Dimension. Oxford University Press. ISBN 978-0-19-286189-4.
Krauss, Lawrence M. (2005). Hiding in the Mirror. Viking Press. ISBN 978-0-670-03395-9.
External links[edit]
Wikiquote has quotations related to Dimension.
Wikimedia Commons has media related to Dimensions.
Wikisource has the text of the 1911 Encyclopædia Britannica article "Dimension".
Copeland, Ed (2009). "Extra Dimensions". Sixty Symbols. Brady Haran for the University of Nottingham.
vteDimensionDimensional spaces
Vector space
Euclidean space
Affine space
Projective space
Free module
Manifold
Algebraic variety
Spacetime
Other dimensions
Krull
Lebesgue covering
Inductive
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Degrees of freedom
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Hyperplane
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Demihypercube
Hypersphere
Cross-polytope
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Hyperpyramid
Dimensions by number
Zero
One
Two
Three
Four
Five
Six
Seven
Eight
n-dimensions
See also
Hyperspace
Codimension
Category
vteTensorsGlossary of tensor theoryScopeMathematics
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Dyadic algebra
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PhysicsEngineering
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Continuum mechanics
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Notation
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Transpose (2nd-order tensors)
Relatedabstractions
Affine connection
Basis
Cartan formalism (physics)
Connection form
Covariance and contravariance of vectors
Differential form
Dimension
Exterior form
Fiber bundle
Geodesic
Levi-Civita connection
Linear map
Manifold
Matrix
Multivector
Pseudotensor
Spinor
Vector
Vector space
Notable tensorsMathematics
Kronecker delta
Levi-Civita symbol
Metric tensor
Nonmetricity tensor
Ricci curvature
Riemann curvature tensor
Torsion tensor
Weyl tensor
Physics
Moment of inertia
Angular momentum tensor
Spin tensor
Cauchy stress tensor
stress–energy tensor
Einstein tensor
EM tensor
Gluon field strength tensor
Metric tensor (GR)
Mathematicians
Élie Cartan
Augustin-Louis Cauchy
Elwin Bruno Christoffel
Albert Einstein
Leonhard Euler
Carl Friedrich Gauss
Hermann Grassmann
Tullio Levi-Civita
Gregorio Ricci-Curbastro
Bernhard Riemann
Jan Arnoldus Schouten
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dimension
1 of 2
noun
di·men·sion
də-ˈmen(t)-shən
also dī-
Synonyms of dimension
1
a
mathematics
(1)
: measure in one direction
the dimensions of the room
specifically
: one of three coordinates (see coordinate entry 3 sense 1a) determining a position in space or four coordinates determining a position in space and time
(2)
: one of a group of properties whose number is necessary and sufficient to determine uniquely each element of a system of usually mathematical entities (such as an aggregate of points in real or abstract space)
the surface of a sphere has two dimensions
also
: a parameter (see parameter sense 1) or coordinate variable assigned to such a property
the three dimensions of momentum
(3)
: the number of elements in a basis (see basis sense 5) of a vector space
b
: the quality of spatial extension : magnitude, size
… the town's modest dimensions and leisurely ways …—Jane Shellhase
c
: a lifelike or realistic quality
uses eccentric dialogue to add dimension to her characters
d
: the range over which or the degree to which something extends : scope
—usually used in pluralthe vast dimensions of the disaster
e
: one of the elements or factors making up a complete personality or entity : aspect
the social and political dimensions of the problem
2
obsolete
: bodily form or proportions
… my dimensions are as well compact, my mind as generous, and my shape as true …—Shakespeare
3
mathematics
: any of the fundamental units (as of mass, length, or time) on which a derived unit is based
also
: the power of such a unit
4
: wood or stone cut to pieces of specified size
5
: a level of existence or consciousness
… a secular as well as spiritual dimension …—Catherine Bates
dimensional
də-ˈmench-nəl
also dī-
-ˈmen(t)-shə-nᵊl
adjective
dimensionality
də-ˌmen(t)-shə-ˈna-lə-tē
also dī-
noun
dimensionally
də-ˈmench-nə-lē
also dī-
-ˈmen(t)-shə-nᵊl-ē
adverb
dimensionless
də-ˈmen(t)-shən-ləs
also dī-
adjective
dimension
2 of 2
verb
dimensioned; dimensioning
də-ˈmen(t)-shə-niŋ
also dī-
transitive verb
1
: to form to the required dimensions (see dimension entry 1 sense 1a(1))
a table dimensioned to fit the space
2
: to indicate the dimensions of (as on a drawing)
dimensioning the plans
Synonyms
Noun
bulk
extent
magnitude
measure
measurement
proportion
size
See all Synonyms & Antonyms in Thesaurus
Examples of dimension in a Sentence
Noun
She carefully measured each dimension of the room.
The social dimensions of the problem must also be taken into account.
Recent Examples on the WebNoun
Statistics from Mexico’s federal government paint an incomplete but helpful illustration of the true dimensions of the problem.
—Nathaniel Parish Flannery, Forbes, 28 Feb. 2024
Introduction For a true phase transition in one dimension, mathematicians had proved that two of these exponents must be greater than 2.
—Charlie Wood, Quanta Magazine, 26 Feb. 2024
In addition to the four familiar dimensions—three infinitely large spatial dimensions plus one of time—string theory suggests that there are six exceedingly tiny spatial dimensions.
—Steve Nadis, WIRED, 25 Feb. 2024
Note that this formula is for just one dimension (width or height) of your chip.
—Michael E. Bakich, Discover Magazine, 24 Feb. 2024
The original Nickelodeon show portrayed Aang’s bending with a bluish, swirling look, but the team behind Netflix’s adaptation had a challenge on their hands when rendering those techniques in three dimensions.
—Jordan Moreau, Variety, 24 Feb. 2024
Take the issue of grass fields that has fueled much conversation in recent months, only to surface in another dimension this week due to the questionable quality of the practice fields the San Francisco 49ers are using at UNLV in advance of Super Bowl 58.
—USA TODAY, 23 Feb. 2024
How was the study conducted? To identify the best and worst places for singles in the U.S., WalletHub experts evaluated 29 metrics under three main dimensions of dating economics, dating opportunities and romance and fun.
—Marina Johnson, The Courier-Journal, 23 Feb. 2024
Personality is merely one dimension explored in research on microtargeting.
—Stephan Lewandowsky, Scientific American, 21 Feb. 2024
Verb
Aaron Judge, New York Yankees: Another huge man with huge power playing in the same Little League-dimensioned ballpark as Stanton.
—Ted Berg, For The Win, 23 Feb. 2018
Each barn is covered top to bottom in oversized shingles dimensioned to make the volume look smaller.
—Joseph Giovannini, ELLE Decor, 2 July 2015
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These examples are programmatically compiled from various online sources to illustrate current usage of the word 'dimension.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.
Word History
Etymology
Noun and Verb
Middle English, from Anglo-French, from Latin dimension-, dimensio, from dimetiri to measure out, from dis- + metiri to measure — more at measure
First Known Use
Noun
14th century, in the meaning defined at sense 1a Verb
1754, in the meaning defined at sense 1
Time Traveler
The first known use of dimension was
in the 14th century
See more words from the same century
Phrases Containing dimension
third dimension
fourth dimension
Dictionary Entries Near dimension
dime novel
dimension
dimensional analysis
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Merriam-Webster
“Dimension.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/dimension. Accessed 12 Mar. 2024.
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Kids Definition
dimension
noun
di·men·sion
də-ˈmen-chən,
also dī-
1
a
: extension in one direction
the dimensions of length, width, and height
b
: measure of extension in one direction or in all directions : size
2
: the range over which something extends : scope
—usually used in plural
dimensional
-ˈmench-nəl
-ˈmen-chən-ᵊl
adjective
dimensionally
-ˈmench-nə-lē
-ˈmen-chən-ᵊl-ē
adverb
dimensionless
-ˈmen-chən-ləs
adjective
Etymology
Noun
Middle English dimensioun "dimension," from early French dimension (same meaning), from Latin dimensio "measurement, dimension," from dimetiri "to measure out," from di-, dis- "apart" and metiri "to measure" — related to immense, measure
Medical Definition
dimension
noun
di·men·sion
də-ˈmen-chən also dī-
: measure in one direction
specifically
: one of three or four coordinates determining a position in space or space and time
More from Merriam-Webster on dimension
Nglish: Translation of dimension for Spanish Speakers
Britannica English: Translation of dimension for Arabic Speakers
Britannica.com: Encyclopedia article about dimension
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2 Mar 2024
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DIMENSION | definition in the Cambridge English Dictionary
DIMENSION | definition in the Cambridge English Dictionary
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Meaning of dimension in English
dimensionnoun us
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/ˌdaɪˈmen.ʃən/ /ˌdɪˈmen.ʃən/ uk
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/ˌdaɪˈmen.ʃən/ /ˌdɪˈmen.ʃən/
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B2 [ C often plural ] a measurement of something in a particular direction, especially its height, length, or width: Please specify the dimensions (= the height, length and width) of the room. a building of vast dimensions (= size)
B2 [ C ] a part or feature or way of considering something: His personality has several dimensions. These weapons add a new dimension to modern warfare. There is a spiritual dimension to her poetry.
SMART Vocabulary: related words and phrases
Measurements in general
altitude
bathymetric
bathymetrically
bathymetry
be running at something idiom
caliber
distance
drop
elevation
factor
knee-length
metric
milli-
scale
setting
stopping distance
tera-
tire pressure
uncalibrated
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(Definition of dimension from the Cambridge Advanced Learner's Dictionary & Thesaurus © Cambridge University Press)
dimension | Intermediate English
dimensionnoun [ C ] us
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/dəˈmen·ʃən/
dimension noun [C]
(MEASUREMENT)
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a measurement of something in a particular direction, esp. its height, length, or width: The dimensions of the room are 26 feet by 15 feet.
dimension noun [C]
(QUALITY)
a part or quality of a thing or situation that has an effect on the way you think about it: The new script gave the story a psychological dimension.
(Definition of dimension from the Cambridge Academic Content Dictionary © Cambridge University Press)
dimension | Business English
dimensionnoun [ C ] uk
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/ˌdaɪˈmenʃən/ us
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a measurement of something in a particular direction, especially its height, length, or width: The estate agent's brochure specifies the dimensions of each room. approximate/exact/precise dimensions
a part or feature of something: Good managers will analyse every dimension of job satisfaction. One other dimension of e-commerce readiness is integration between information systems. The information-based economy has the potential to add a new dimension to economic success.
(Definition of dimension from the Cambridge Business English Dictionary © Cambridge University Press)
Examples of dimension
dimension
Of course these golf balls are moving in two dimensions.
From WIRED
I know that your photo may not fall into those exact high rez dimensions, so whatever native resolution you're using is fine. 6.
From Gizmodo
I became intrigued with understanding the origins of disease and illness among native communities and the biological, social, and cultural dimensions of the disease process.
From Huffington Post
The notion of the whole exerting "downward causality" on its parts is best understood as happening in two mutually influencing dimensions.
From Huffington Post
We are as lawbound as the ants, but we have an evolutionarily conferred dimension of freedom above raw genetic determinism.
From Huffington Post
Each pair is tailored to match its athlete's unique strengths, stride, and dimensions.
From WIRED
He gives them a dimension that not many teams have.
From USA TODAY
That is the social comparison dimension of awards.
From Los Angeles Times
She grasps the dimensions of her father's criminal past while gaining an appreciation for his heroic nature.
From Washington Post
Just bringing the other dimensions beyond a static painting -- story, action, movement, music, all those things.
From Los Angeles Times
With this data, they determined the channels' structures in three dimensions, down to the level of individual atoms.
From Phys.Org
Then later you hear there's a fourth dimension, time.
From NPR
Furthermore, it raises the possibility that objects with mass could exist in the 7 dimensions that we can not observe directly.
From TIME
Insecurity in these areas is driven by all four dimensions of vulnerability, but particularly by low resilience and poor governance.
From Phys.Org
As we move further and further toward a paperless society, that loop-the-loop form might become more familiar in two dimensions than in three.
From Slate Magazine
These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
Collocations with dimension
dimension
These are words often used in combination with dimension. Click on a collocation to see more examples of it.
added dimensionFuture versions of this model will generalize these preferences, but this brings in the added dimension of trying to determine optimal consumption, given current information.
From the Cambridge English Corpus
additional dimensionThis again would have placed an additional dimension to the publication, and made it less subjective.
From the Cambridge English Corpus
aesthetic dimensionNotably, they suggest that, for practical purposes at least, religious understanding has an aesthetic dimension in at least two ways.
From the Cambridge English Corpus
These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
See all collocations with dimension
What is the pronunciation of dimension?
B2,B2
Translations of dimension
in Chinese (Traditional)
空間,尺寸, 層面,維度, 特點…
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in Chinese (Simplified)
空间,尺寸, 层面,维度, 特点…
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in Spanish
dimensiones, dimensión, dimensión [feminine]…
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in Portuguese
dimensões, dimensão, dimensão [feminine]…
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मोजमाप, आकारमान, कंगोरे…
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要素, 局面, 様相(ようそう)…
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yön, boyut, taraf…
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dimension [feminine], dimension…
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dimensió…
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afmeting…
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ஒரு குறிப்பிட்ட திசையில் எதையாவது அளவிடுதல், குறிப்பாக அதன் உயரம், நீளம் அல்லது அகலம்…
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(लंबाई, चौड़ाई, ऊँचाई का) आयाम…
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પરિમાણો (લંબાઈ, પહોળાઈ, ઊંચાઈ)…
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omfang, størrelse…
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mått, dimension…
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luas…
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das Maß…
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dimensjon [masculine], aspekt [neuter], dimensjon…
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بُعد, حدود, لمبائی، چوڑائی اور اونچائی یا گہرائی…
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вимір, розміри…
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измерение, аспект, размер…
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ఒక ప్రత్యేకమైన దారిలో ఒక దాని కొలత, ప్రత్యేకంగా దాని ఎత్తిలో, పొడువులో…
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بُعد…
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মাত্রা, একটি নির্দিষ্ট দিকের কিছুর পরিমাপ বিশেষত এর উচ্চতা, দৈর্ঘ্য বা প্রস্থ…
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rozměr…
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matra, dimensi…
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การหามิติ…
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kích thước…
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wymiar, aspekt, rozmiar…
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관점…
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dimensione, aspetto…
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DIMENSION Definition & Usage Examples | Dictionary.com
DIMENSION Definition & Usage Examples | Dictionary.com
GamesDaily CrosswordWord PuzzleWord FinderAll gamesFeaturedWord of the DaySynonym of the DayWord of the YearNew wordsLanguage storiesAll featuredPop cultureSlangEmojiMemesAcronymsGender and sexualityAll pop cultureWriting tipsGrammar Coach™Writing hubGrammar essentialsCommonly confusedAll writing tipsGamesFeaturedPop cultureWriting tipsdimension[ dih-men-shuhn, dahy- ]show ipaSee synonyms for: dimensiondimensionsdimensionalitydimensional on Thesaurus.comnounMathematics. 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.the generalization of this property to spaces with curvilinear extension, as the surface of a sphere.the generalization of this property to vector spaces and to Hilbert space. the generalization of this property to fractals, which can have dimensions that are noninteger real numbers. extension in time: Space-time has three dimensions of space and one of time.Usually dimensions. measurement in length, width, and thickness.scope; importance: the dimensions of a problem. an aspect, feature, or angle: A study abroad experience can add a cultural dimension to your language learning.We haven't addressed that dimension of the issue.unit (def. 6). magnitude; size: Matter has dimension.Topology. 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.the number of elements in a finite basis of a given vector space.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. Also called al·ter·nate di·men·sion [awl-ter-nit di-men-shuhn, dahy-] /ˈɔl tər nɪt dɪˈmɛn ʃən, daɪ-/ . (in science fiction, fantasy, etc.) a hypothetical universe or world that is different from our known universe and reachable by traveling in directions that are not the perceptible axes of space and time, as with the use of futuristic technology or magic: Your enemies are villains, cultists, terrible monsters, and unfathomable entities from alternate dimensions or the cosmos beyond.: Compare parallel universe (def. 3). dimensions, Informal. the measurements of a woman's bust, waist, and hips, in that order: The dressmaker noted that the customer's dimensions were 38-24-36.dimension lumber. See moreverb (used with object)to shape or fashion to the desired dimensions: Dimension the shelves so that they fit securely into the cabinet.to indicate the dimensions of an item, area, etc., on (a sketch or drawing).Origin of dimension1First recorded in 1375–1425; late Middle English dimensioun, from Anglo-French or directly from Latin dīmēnsiōn- (stem of dīmēnsiō ) “a measuring,” equivalent to dīmēns(us) “measured out” (past participle of dīmētīrī, equivalent to dī- di-2 + mētīrī “to measure”) + -iōn- -ionOther words for dimension2b range, extent, reach, sweepSee synonyms for dimension on Thesaurus.comOther words from dimensiondi·men·sion·al, adjectivedi·men·sion·al·i·ty [dih-men-shuh-nal-i-tee, dahy-], /dɪˌmɛn ʃəˈnæl ɪ ti, daɪ-/, noundi·men·sion·al·ly, adverbdi·men·sion·less, adjectivemul·ti·di·men·sion·al, adjectivenon·di·men·sioned, adjectiveun·di·men·sioned, adjectiveWords Nearby dimensiondimedime a dozendime bagdimenhydrinatedime noveldimensiondimensional analysisdimensionless numberdimension lumberdimension stonedimerDictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2024How to use dimension in a sentenceAlmost every dimension of inequity has been accentuated here.‘There’s been some cracks:’ Bill Gates questions FDA’s credibility on a COVID-19 vaccine | Claire Zillman, reporter | September 16, 2020 | FortuneAt times he’s proposed worlds where the rules of the universe that we take for granted — about space, dimensions, the human body, the nature of dreams — are bent into strange new shapes.The ancient palindrome that explains Christopher Nolan’s Tenet | Alissa Wilkinson | September 4, 2020 | VoxAll the while, lidar measured the exact dimensions of their bodies.A robot referee can really keep its ‘eye’ on the ball | Kathryn Hulick | August 20, 2020 | Science News For StudentsPsychologists call this misleading feeling of helplessness the “pseudoinefficacy effect,” and it has a political dimension that may keep individuals from working to help others.Generation Z is ‘traumatized’ by climate change—and they’re the key to fighting it | matthewheimer | August 19, 2020 | FortuneA simple argument shows that once the conjecture is false in one dimension, it’s necessarily false in all higher dimensions.Computer Search Settles 90-Year-Old Math Problem | Kevin Hartnett | August 19, 2020 | Quanta MagazineA Europe which is no longer open to the transcendent dimension of life is a Europe which risks slowly losing its own soul.Pope’s Blistering Attack on ‘Haggard’ Europe | Nico Hines | November 26, 2014 | THE DAILY BEASTUnderneath, a miniature version of the bug-crazy man is revealed, himself thwacking away in an alternate dimension.‘Interstellar’ Is Wildly Ambitious, Very Flawed, and Absolutely Worth Seeing | Marlow Stern | November 7, 2014 | THE DAILY BEASTThere needs to be a fully thought out strategy with a political dimension that involves the opposition.Military Hates White House ‘Micromanagement’ of ISIS War | Josh Rogin, Eli Lake | October 31, 2014 | THE DAILY BEASTTrippy, echoing sound effects give “A Brain In A Bottle” a sense of fullness and dimension—as they do for “Guess Again!”Newest Album From Radiohead’s Thom Yorke Is No Online Afterthought | Noel Murray | September 27, 2014 | THE DAILY BEASTIn the case of Hollywood actresses, too, this expectation takes on an even more pernicious dimension.Jennifer Lawrence Shouldn’t Laugh Off Her Nude Photo Hack | Samantha Allen | September 2, 2014 | THE DAILY BEASTFor copying by engraving, &c. the exact dimension required of any picture may at once be given to be copied from.Notes and Queries, Number 194, July 16, 1853 | VariousBy varying the distances between a and c, and c and b, any dimension required may be given to the positive impression.Notes and Queries, Number 194, July 16, 1853 | VariousIt was a genuine western, with high horn and high cantle and two cinches, but much reduced in every dimension.David Lannarck, Midget | George S. Harneydimension lines and centre lines are best put in of different colour.An Introduction to Machine Drawing and Design | David Allan LowThe arrow-heads at the ends of the dimension lines are now put in with black ink, and so are the figures for the dimensions.An Introduction to Machine Drawing and Design | David Allan LowSee More ExamplesBritish Dictionary definitions for dimensiondimension/ (dɪˈmɛnʃən) /noun(often plural) a measurement of the size of something in a particular direction, such as the length, width, height, or diameter(often plural) scope; size; extent: a problem of enormous dimensionsaspect: a new dimension to politicsmaths the number of coordinates required to locate a point in spacephysics the product or the quotient of the fundamental physical quantities (such as mass, length, or time) raised to the appropriate power in a derived physical quantity: the dimensions of velocity are length divided by timethe power to which such a fundamental quantity has to be raised in a derived quantitySee moreverb(tr) mainly US to shape or cut to specified dimensionsto mark with specified dimensionsOrigin of dimension1C14: from Old French, from Latin dīmensiō an extent, from dīmētīrī to measure out, from mētīrīDerived forms of dimensiondimensional, adjectivedimensionality, noundimensionally, adverbdimensionless, adjectiveCollins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012Scientific definitions for dimensiondimension[ dĭ-mĕn′shən ]Any one of the three physical or spatial properties of length, area, and volume. In geometry, a point is said to have zero dimension; a figure having only length, such as a line, has one dimension; a plane or surface, two dimensions; and a figure having volume, three dimensions. The fourth dimension is often said to be time, as in the theory of General Relativity. Higher dimensions can be dealt with mathematically but cannot be represented visually.The measurement of a length, width, or thickness.A unit, such as mass, time, or charge, associated with a physical quantity and used as the basis for other measurements, such as acceleration.The American Heritage® Science Dictionary
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Written by
Robert Osserman
Special Projects Director, Mathematical Sciences Research Institute, Berkeley, California. Author of Two-dimensional Calculus; Poetry of the Universe: A Mathematical Exploration of the Cosmos.
Robert Osserman
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dimension, in common parlance, the measure of the size of an object, such as a box, usually given as length, width, and height. In mathematics, the notion of dimension is an extension of the idea that a line is one-dimensional, a plane is two-dimensional, and space is three-dimensional. In mathematics and physics one also considers higher-dimensional spaces, such as four-dimensional space-time, where four numbers are needed to characterize a point: three to fix a point in space and one to fix the time. Infinite-dimensional spaces, first studied early in the 20th century, have played an increasingly important role both in mathematics and in parts of physics such as quantum field theory, where they represent the space of possible states of a quantum mechanical system.In differential geometry one considers curves as one-dimensional, since a single number, or parameter, determines a point on a curve—for example, the distance, plus or minus, from a fixed point on the curve. A surface, such as the surface of the Earth, has two dimensions, since each point can be located by a pair of numbers—usually latitude and longitude. Higher-dimensional curved spaces were introduced by the German mathematician Bernhard Riemann in 1854 and have become both a major subject of study within mathematics and a basic component of modern physics, from Albert Einstein’s theory of general relativity and the subsequent development of cosmological models of the universe to late-20th-century superstring theory.
In 1918 the German mathematician Felix Hausdorff introduced the notion of fractional dimension. This concept has proved extremely fruitful, especially in the hands of the Polish-French mathematician Benoit Mandelbrot, who coined the word fractal and showed how fractional dimensions could be useful in many parts of applied mathematics.
Robert Osserman
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dimension
1 ENTRIES FOUND:
dimension (noun)
dimension
/dəˈmɛnʃən/
noun
plural
dimensions
dimension
/dəˈmɛnʃən/
noun
plural
dimensions
Britannica Dictionary definition of DIMENSION
[count]
1
:
the length, width, height, or depth of something
:
a measurement in one direction (such as the distance from the ceiling to the floor in a room)
She carefully measured each dimension of the room.
The room's dimensions [=its length, width, and height] were surprisingly small.
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2
:
the amount or number of things that something affects or influences
— usually plural
We underestimated the dimensions [=extent, range] of this problem.
the vast dimensions [=magnitude, scope] of the disaster
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3
:
a part of something
There are many dimensions [=aspects] to the problem.
The social/political/religious dimensions of the problem must also be taken into account.
The more powerful engine gives this car a (whole) new dimension. [=makes the car very different]
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— dimensional
/dəˈmɛnʃənl̟/
adjective
— usually used in combination
a multi-dimensional problem
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—
see also one-dimensional, two-dimensional, three-dimensional
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dimension noun - Definition, pictures, pronunciation and usage notes | Oxford Advanced Learner's Dictionary at OxfordLearnersDictionaries.com
dimension noun - Definition, pictures, pronunciation and usage notes | Oxford Advanced Learner's Dictionary at OxfordLearnersDictionaries.com
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Definition of dimension noun from the Oxford Advanced Learner's Dictionary
dimension noun OPAL WOPAL S /daɪˈmenʃn/, /dɪˈmenʃn/ /daɪˈmenʃn/, /dɪˈmenʃn/
jump to other results
enlarge image a measurement in space, for example how high, wide or long something isWe measured the dimensions of the kitchen.computer design tools that work in three dimensions see also fourth dimensionExtra ExamplesDespite the unit's compact dimensions, there's still plenty of room for expansion.It is important to measure the exact dimensions of the room.The fourth dimension, time, is also finite in extent.a model in three dimensionsa structure of considerable dimensionsThe images can be viewed in three dimensions using these special glasses.The rectangles are arranged with their longer dimension running from top to bottom.Topics Colours and Shapesc1, Maths and measurementc1Oxford Collocations Dictionaryadjectiveapproximateexactprecise…verb + dimensioncheckmeasurephrasesin two dimensionsin three dimensionsSee full entry
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[usually plural] the size and extent of a situationa problem of considerable dimensions
an aspect, or way of looking at or thinking about somethingHer job added a new dimension to her life.We should also consider the social dimension of unemployment.Extra ExamplesCommunication via the internet gives an important international dimension to the project.Her illness adds an extra dimension to the problem.In looking at population ageing we will consider two distinct dimensions.The affair had a different dimension now.The crisis acquired a new dimension.There is a wider dimension to the question.the spiritual dimension to our livesOxford Collocations Dictionaryadjectiveaddedadditionaldifferent…verb + dimensionaddbringgive (something)…prepositiondimension toSee full entry Word Originlate Middle English (in sense (1)): via Old French from Latin dimensio(n-), from dimetiri ‘measure out’. Sense (2) dates from the 1920s.See dimension in the Oxford Advanced American DictionarySee dimension in the Oxford Learner's Dictionary of Academic EnglishCheck pronunciation:
dimension
Other results
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the fourth dimension noun
Nearby words
dime noun
dime novel noun
dimension noun
dimensional adjective
-dimensional combining form
boost
verb
From the Topic
Change, cause and effect
B2
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