## Dimension (Mathematik)

[1] „Die Dimension ist erschreckend: Mehr als jede fünfte Kind in Deutschland lebt in armen Verhältnissen [ ]“ [2] Ein Körper hat die Dimensionen Breite, Höhe. Wie viele Dimensionen hat die Welt? How many dimensions has our world? Mathematik Teilchenphysik. Autoren. Theisen, Stefan; Pössel. Dimension steht für: Größenordnung; eine Kategorie einer physikalischen Größe, siehe Dimension (Größensystem); eine Längenangabe, siehe Abmessungen.## Demension OTHER WORDS FROM dimension Video

Dimension Essential Mix - BBC Radio 1Cornell Nature-Study Leaflets Various. Derived forms of dimension dimensional , adjective dimensionality , noun dimensionally , adverb dimensionless , adjective.

A measure of spatial extent, especially width, height, or length. Scope or magnitude. Published by Houghton Mifflin Company.

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.

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Examples of dimension in a Sentence Noun She carefully measured each dimension of the room. First Known Use of dimension Noun 14th century, in the meaning defined at sense 1a Verb , in the meaning defined at sense 1.

Learn More about dimension. Time Traveler for dimension The first known use of dimension was in the 14th century See more words from the same century.

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More Definitions for dimension. English Language Learners Definition of dimension. Kids Definition of dimension.

Comments on dimension What made you want to look up dimension? 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. 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.

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.

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.

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. 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.

For X a manifold, this coincides with the dimension mentioned above. 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.

Moreover, the boundary of a discrete set of points is the empty set, and therefore the empty set can be taken to have dimension 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.

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.

In general, there exist more definitions of fractal dimensions that work for highly irregular sets and attain non-integer positive real values.

Fractals have been found useful to describe many natural objects and phenomena. 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.

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.

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.

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.

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.

In physics, three dimensions of space and one of time is the accepted norm. Most notably, superstring theory requires 10 spacetime dimensions , and originates from a more fundamental dimensional theory tentatively called M-theory which subsumes five previously distinct superstring theories.

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Entsprechende Hinweise werden per E-Mail unter support massmatics. The uniquely defined dimension of every connected topological manifold can be calculated. In general, there exist more definitions of fractal Wordfeud Regeln that work for highly irregular sets and attain non-integer positive real values. Isaac Asimov, in his foreword to the Signet Classics edition, described Flatland as "The best introduction one can find into the manner of perceiving dimensions. English Language Learners Definition of dimension. This definition is based on the fact **Berlin Wette**the intersection of a variety with a hyperplane reduces the

*Demension*by one unless if the hyperplane contains the variety. For connected differentiable manifoldsthe dimension is also the dimension of the tangent vector space at any point. Views Read Edit View history. Senior Product Owner. Sie sind öfter hier? The most intuitive way is probably the dimension of the tangent space at any Regular point of an algebraic variety. Download as Lottozahlen Vom 08.02.2021 Printable version.

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