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A 2D orthogonal projection of a 5-cube. 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 the usual three spatial dimensions and the fourth dimension of time used in relativistic physics. [1]
The base space of Kaluza–Klein theory need not be four-dimensional spacetime; it can be any Riemannian manifold, or even a supersymmetric manifold or orbifold or even a noncommutative space. The construction can be outlined, roughly, as follows. [30] One starts by considering a principal fiber bundle P with gauge group G over a manifold M.
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.
In physics, Randall–Sundrum models (RS) (also called 5-dimensional warped geometry theory) are models that describe the world in terms of a warped-geometry higher-dimensional universe, or more concretely as a 5-dimensional anti-de Sitter space where the elementary particles (except the graviton) are localized on a (3 + 1)-dimensional brane or branes.
For any natural number , an -sphere of radius is defined as the set of points in (+) -dimensional Euclidean space that are at distance from some fixed point , where may be any positive real number and where may be any point in (+) -dimensional space.
The set of all one-dimensional linear subspaces of a (n+1)-dimensional linear space is, by definition, a n-dimensional projective space. And the affine subspace A is embedded into the projective space as a proper subset. However, the projective space itself is homogeneous.
In 1998/99, Merab Gogberashvili published on arXiv a number of articles where he showed that if the Universe is considered as a thin shell (a mathematical synonym for "brane") expanding in 5-dimensional space then there is a possibility to obtain one scale for particle theory corresponding to the 5-dimensional cosmological constant and Universe ...
A 5-polytope is a closed five-dimensional figure with vertices, edges, faces, and cells, and 4-faces.A vertex is a point where five or more edges meet. An edge is a line segment where four or more faces meet, and a face is a polygon where three or more cells meet.