Definitions for n-sphere
This page provides all possible meanings and translations of the word n-sphere
In mathematics, an n-sphere is a generalization of the surface of an ordinary sphere to a n-dimensional space. For any natural number n, an n-sphere of radius r is defined as the set of points in-dimensional Euclidean space which are at distance r from a central point, where the radius r may be any positive real number. Thus, the n-sphere centred at the origin is defined by: It is an n-dimensional manifold in Euclidean-space. In particular:: Spheres of dimension n > 2 are sometimes called hyperspheres, with 3-spheres sometimes known as glomes. The n-sphere of unit radius centered at the origin is called the unit n-sphere, denoted S. The unit n-sphere is often referred to as the n-sphere. An n-sphere is the surface or boundary of an-dimensional ball, and is an n-dimensional manifold. For n ≥ 2, the n-spheres are the simply connected n-dimensional manifolds of constant, positive curvature. The n-spheres admit several other topological descriptions: for example, they can be constructed by gluing two n-dimensional Euclidean spaces together, by identifying the boundary of an n-cube with a point, or by forming the suspension of an-sphere.
Sample Sentences & Example Usage
The power of man has grown in every sphere, except over himself.
In the economics sphere, the regime seems to lack any real strategic vision.
Repentance may begin instantly, but reformation often requires a sphere of years.
The U.S. and Qatar are partners economically just as we are in the security sphere.
Everybody loves a comeback story, and Aqua Sphere could stand to benefit considerably.
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