# Category: Dimension

Exterior dimension
In geometry, exterior dimension is a type of dimension that can be used to characterize the scaling behavior of "fat fractals".A fat fractal is defined to be a subset of Euclidean space such that, for
Dimensional metrology
Dimensional metrology is the science of using physical measurement equipment to quantify the physical size, form, characteristics, and relational distance from any given feature.
Global dimension
In ring theory and homological algebra, the global dimension (or global homological dimension; sometimes just called homological dimension) of a ring A denoted gl dim A, is a non-negative integer or i
Dimension of an algebraic variety
In mathematics and specifically in algebraic geometry, the dimension of an algebraic variety may be defined in various equivalent ways. Some of these definitions are of geometric nature, while some ot
Matroid rank
In the mathematical theory of matroids, the rank of a matroid is the maximum size of an independent set in the matroid. The rank of a subset S of elements of the matroid is, similarly, the maximum siz
Extra dimensions
In physics, extra dimensions are proposed additional space or time dimensions beyond the (3 + 1) typical of observed spacetime, such as the first attempts based on the Kaluza–Klein theory. Among theor
Complex dimension
In mathematics, complex dimension usually refers to the dimension of a complex manifold or a complex algebraic variety. These are spaces in which the local neighborhoods of points (or of non-singular
Krull dimension
In commutative algebra, the Krull dimension of a commutative ring R, named after Wolfgang Krull, is the supremum of the lengths of all chains of prime ideals. The Krull dimension need not be finite ev
String theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these str
Degrees of freedom (physics and chemistry)
In physics and chemistry, a degree of freedom is an independent physical parameter in the formal description of the state of a physical system. The set of all states of a system is known as the system
Multiple time dimensions
The possibility that there might be more than one dimension of time has occasionally been discussed in physics and philosophy. Similar ideas appear in folklore and fantasy literature.
One-dimensional space
In physics and mathematics, a sequence of n numbers can specify a location in n-dimensional space. When n = 1, the set of all such locations is called a one-dimensional space. An example of a one-dime
Poppy-seed bagel theorem
In physics, the poppy-seed bagel theorem concerns interacting particles (e.g., electrons) confined to a bounded surface (or body) when the particles repel each other pairwise with a magnitude that is
2 1/2-dimensional manufacturing
2+1⁄2-dimensional manufacturing , also known as 2+1⁄2-D, is a conventional way of describing a process for obtaining an object where the third dimension is somehow dependent from the transversal cross
Curse of dimensionality
The curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces that do not occur in low-dimensional settings such as the three-dimensi
Dimension
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 dimen
Degrees of freedom
Degrees of freedom (often abbreviated df or DOF) refers to the number of independent variables or parameters of a thermodynamic system. In various scientific fields, the word "freedom" is used to desc
Schauder dimension
No description available.
Regular sequence
In commutative algebra, a regular sequence is a sequence of elements of a commutative ring which are as independent as possible, in a precise sense. This is the algebraic analogue of the geometric not
Five-dimensional space
A five-dimensional space is a space with five dimensions. In mathematics, a sequence of N numbers can represent a location in an N-dimensional space. If interpreted physically, that is one more than t
Flatland
Flatland: A Romance of Many Dimensions is a satirical novella by the English schoolmaster Edwin Abbott Abbott, first published in 1884 by Seeley & Co. of London. Written pseudonymously by "A Square",
Fourth dimension in art
New possibilities opened up by the concept of four-dimensional space (and difficulties involved in trying to visualize it) helped inspire many modern artists in the first half of the twentieth century
Vapnik–Chervonenkis dimension
In Vapnik–Chervonenkis theory, the Vapnik–Chervonenkis (VC) dimension is a measure of the capacity (complexity, expressive power, richness, or flexibility) of a set of functions that can be learned by
2.5D
2.5D (two-and-a-half dimensional, alternatively pseudo-3D or three-quarter) perspective refers to one of two things: * Gameplay or movement in a video game or virtual reality environment that is rest
Kodaira dimension
In algebraic geometry, the Kodaira dimension κ(X) measures the size of the canonical model of a projective variety X. Igor Shafarevich, in a seminar introduced an important numerical invariant of surf
Eight-dimensional space
In mathematics, a sequence of n real numbers can be understood as a location in n-dimensional space. When n = 8, the set of all such locations is called 8-dimensional space. Often such spaces are stud
Dimension theory (algebra)
In mathematics, dimension theory is the study in terms of commutative algebra of the notion dimension of an algebraic variety (and by extension that of a scheme). The need of a theory for such an appa
Abscissa and ordinate
In common usage, the abscissa refers to the (x) coordinate and the ordinate refers to the (y) coordinate of a standard two-dimensional graph. The distance of a point from the y-axis, scaled with the x
Dimension (vector space)
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. It is sometimes called Hamel dimension (after Georg Hamel) or al
Interdimensional being
An interdimensional being (also extra-dimensional, intra-dimensional) suggests an entity that can "time-travel and move out of the physical body into a spiritual one". The NASA website has a somewhat
Gelfand–Kirillov dimension
In algebra, the Gelfand–Kirillov dimension (or GK dimension) of a right module M over a k-algebra A is: where the supremum is taken over all finite-dimensional subspaces and . An algebra is said to ha
Euclidean plane
In mathematics, the Euclidean plane is a Euclidean space of dimension two. That is, a geometric setting in which two real quantities are required to determine the position of each point (element of th
Codimension
In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, to submanifolds in manifolds, and suitable subsets of algebraic varieties. For affine and projective a
Interdimensional
No description available.
Minkowski content
The Minkowski content (named after Hermann Minkowski), or the boundary measure, of a set is a basic concept that uses concepts from geometry and measure theory to generalize the notions of length of a
Zero-dimensional space
In mathematics, a zero-dimensional topological space (or nildimensional space) is a topological space that has dimension zero with respect to one of several inequivalent notions of assigning a dimensi
Six-dimensional space
Six-dimensional space is any space that has six dimensions, six degrees of freedom, and that needs six pieces of data, or coordinates, to specify a location in this space. There are an infinite number
Isoperimetric dimension
In mathematics, the isoperimetric dimension of a manifold is a notion of dimension that tries to capture how the large-scale behavior of the manifold resembles that of a Euclidean space (unlike the to
Relative canonical model
In the mathematical field of algebraic geometry, the relative canonical model of a singular variety of a mathematical object where is a particular canonical variety that maps to , which simplifies the
Concentration dimension
In mathematics — specifically, in probability theory — the concentration dimension of a Banach space-valued random variable is a numerical measure of how "spread out" the random variable is compared t
Relative dimension
In mathematics, specifically linear algebra and geometry, relative dimension is the dual notion to codimension. In linear algebra, given a quotient map , the difference dim V − dim Q is the relative d
Kaplan–Yorke conjecture
In applied mathematics, the Kaplan–Yorke conjecture concerns the dimension of an attractor, using Lyapunov exponents. By arranging the Lyapunov exponents in order from largest to smallest , let j be t
Seven-dimensional space
In mathematics, a sequence of n real numbers can be understood as a location in n-dimensional space. When n = 7, the set of all such locations is called 7-dimensional space. Often such a space is stud
Fourth dimension in literature
The idea of a fourth dimension has been a factor in the evolution of modern art, but use of concepts relating to higher dimensions has been little discussed by academics in the literary world. From th
Four-dimensional space
A four-dimensional space (4D) is a mathematical extension of the concept of three-dimensional or 3D space. Three-dimensional space is the simplest possible abstraction of the observation that one only