What does n-sphere mean?

Definitions for n-sphere
n-sphere

This dictionary definitions page includes all the possible meanings, example usage and translations of the word n-sphere.


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Wikipedia

  1. N-sphere

    In mathematics, an n-sphere or a hypersphere is a topological space that is homeomorphic to a standard n-sphere, which is the set of points in (n + 1)-dimensional Euclidean space that are situated at a constant distance r from a fixed point, called the center. It is the generalization of an ordinary sphere in the ordinary three-dimensional space. The "radius" of a sphere is the constant distance of its points to the center. When the sphere has unit radius, it is usual to call it the unit n-sphere or simply the n-sphere for brevity. In terms of the standard norm, the n-sphere is defined as S n = { x ∈ R n + 1 : ‖ x ‖ = 1 } , {\displaystyle S^{n}=\left\{x\in \mathbb {R} ^{n+1}:\left\|x\right\|=1\right\},} and an n-sphere of radius r can be defined as S n ( r ) = { x ∈ R n + 1 : ‖ x ‖ = r } . {\displaystyle S^{n}(r)=\left\{x\in \mathbb {R} ^{n+1}:\left\|x\right\|=r\right\}.} The dimension of n-sphere is n, and must not be confused with the dimension (n + 1) of the Euclidean space in which it is naturally embedded. An n-sphere is the surface or boundary of an (n + 1)-dimensional ball.

Wikidata

  1. 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.

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Numerology

  1. Chaldean Numerology

    The numerical value of n-sphere in Chaldean Numerology is: 6

  2. Pythagorean Numerology

    The numerical value of n-sphere in Pythagorean Numerology is: 4

Examples of n-sphere in a Sentence

  1. Liz Rosenberg:

    Energy and( Islamic Revolutionary Guard Corps) sanctions from April and May provoked a very powerful Iranian response and tipped this confrontation and tensions into a more military sphere. Now the pressure levers are military pressure levers, so the key parties in the escalation relationship are the Islamic Revolutionary Guard Corps and The US military.

  2. Petro Poroshenko:

    It's difficult to find any sphere where reforms have not been launched. Definitely if you launch reform in such a big number of spheres, you make a mistake.

  3. Nick Merrill:

    This is someone who has spent nearly two decades in public service, and is widely known for her integrity and tireless work ethic, after the birth of her son, she took maternity leave. The IG had questions about the details of her leave, Huma answered. Anything beyond that injected into the public sphere is unfounded and from partisans in Congress with a clear agenda. These emails serve to reinforce that these allegations are baseless. It's not surprising, but it is disappointing.

  4. Mvemba Phezo Dizolele:

    This is happening in the context of Russia trying to carve its own sphere of influence in Africa.

  5. Steve Vladeck:

    Every time a member of Congress does something in the foreign policy sphere that's at odds with the president, someone trots out the Logan Act.

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"n-sphere." Definitions.net. STANDS4 LLC, 2024. Web. 19 Mar. 2024. <https://www.definitions.net/definition/n-sphere>.

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