n-sphere


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n-sphere

[′en ‚sfir]
(mathematics)
The set of all points in (n +1)-dimensional euclidean space whose distance from the origin is unity, where n is a positive integer.
References in periodicals archive ?
Let f : ([S.sub.n], [[kappa].sub.n]) [right arrow] ([S.sub.n], [[kappa].sub.n]) be a ([[kappa].sub.n], [[kappa].sub.n])-continuous map where ([S.sub.n], [[kappa].sub.n]) is digital n-sphere, n [member of] {1,2} and [[kappa].sub.1] = 4, [[kappa].sub.2] = 6.
Let [S.sub.n] be a digital n-sphere where n [member of] {1,2}.
Calculation of the radius of the circumscribed n-sphere
In this section a general formula to calculate the radius [R.sub.2] of the circumscribed n-sphere is derived.
Assume Vol(M) [is greater than or equal to]v(n, r) where r [is greater than] 0 and v(n, r) is the volume of the r-ball in the standard n-sphere [S.sup.n], then there is D [is less than] [Pi] depending on n, k and r so that if d(M) [is greater than or equal to] D, then M is homeomorphic to [S.sup.n].