A two-dimensional space is a mathematical space with two dimensions, meaning points have two degrees of freedom: their locations can be locally described...

three-dimensional Euclidean space, that is, the Euclidean space of dimension three, which models physical space. More general three-dimensional spaces are...

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...

plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional space R 3 {\displaystyle...

are one-dimensional spaces but are usually referred to by more specific terms. Any field K {\displaystyle K} is a one-dimensional vector space over itself...

that two finite-dimensional vector spaces are equal, the following criterion can be used: if V {\displaystyle V} is a finite-dimensional vector space and...

Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible...

A five-dimensional (5D) space is a space with five dimensions. 5D Euclidean geometry designated by the mathematical sign: E {\displaystyle \mathbb {E}...

In mathematics, a zero-dimensional topological space (or nildimensional space) is a topological space that has dimension zero with respect to one of several...

A two-dimensional gas is a collection of objects constrained to move in a planar or other two-dimensional space in a gaseous state. The objects can be:...

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...

Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's Elements, it was the three-dimensional space...

dimensions), a line (one dimension) and three-dimensional space. When working exclusively in two-dimensional Euclidean space, the definite article is...

A two-dimensional shape or two-dimensional figure (also: 2D shape or 2D figure) may lie on a more general curved surface (a two-dimensional space). Some...

A two-dimensional liquid (2D liquid) is a collection of objects constrained to move in a planar space or other two-dimensional space in a liquid state...

also refer to a seven-dimensional manifold such as a 7-sphere, or a variety of other geometric constructions. Seven-dimensional spaces have a number of special...

a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. Just as the perimeter of the...

space of a manifold is a generalization of tangent lines to curves in two-dimensional space and tangent planes to surfaces in three-dimensional space...

4-dimensional vector space over the reals, 2-dimensional over the complex numbers, isomorphic to tessarines. multicomplex numbers: 2n-dimensional vector...

Bravais lattices. This was corrected to 14 by A. Bravais in 1848. In two-dimensional space, there are four crystal systems (oblique, rectangular, square, hexagonal)...

real world four-dimensional space geometrically by projecting that space into a five-dimensional superspace with the fifth dimension corresponding to...

plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional space R 3 {\displaystyle...

transformations on a space. In a real two dimensional space, conformal geometry is precisely the geometry of Riemann surfaces. In space higher than two dimensions...

referred to as topology, a surface is a two-dimensional manifold. Some surfaces arise as the boundaries of three-dimensional solid figures; for example, the sphere...

covering dimension of the disk is thus two. More generally, the n-dimensional Euclidean space E n {\displaystyle \mathbb {E} ^{n}} has covering dimension n....

cross-sections. The boundary of a cross-section in three-dimensional space that is parallel to two of the axes, that is, parallel to the plane determined...

parent space. In an n-dimensional space, there are k-flats of every dimension k from 0 to n; flats one dimension lower than the parent space, (n − 1)-flats...

dimension is an infinite cardinal. Finite-dimensional vector spaces occur naturally in geometry and related areas. Infinite-dimensional vector spaces...

function f defined on the plane to a function Rf defined on the (two-dimensional) space of lines in the plane, whose value at a particular line is equal...

A two-dimensional conformal field theory is a quantum field theory on a Euclidean two-dimensional space, that is invariant under local conformal transformations...