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n-sphere
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- 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.
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"n-sphere Rhymes." Rhymes.com. STANDS4 LLC, 2024. Web. 26 Apr. 2024. <https://www.rhymes.com/rhyme/n-sphere>.
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