Developer NSphere Inc Applications

NSphere Inc Apps Support

  • Developer NSphere Inc
  • Developer ID 473724704
  • Total Downloads 75,348
  • Web survey.com

Who is NSphere Inc?

In mathematics, an n-sphere or hypersphere is an n-dimensional generalization of the 1-dimensional circle and 2-dimensional sphere to any non-negative integer n. The n-sphere is the setting for n-dimensional spherical geometry. Considered extrinsically, as a hypersurface embedded in (n + 1)-dimensional Euclidean space, an n-sphere is the locus of points at equal distance (the radius) from a given center point. Its interior, consisting of all points closer to the center than the radius, is an (n + 1)-dimensional ball. In particular: The 0-sphere is the pair of points at the ends of a line segment (1-ball). The 1-sphere is a circle, the circumference of a disk (2-ball) in the two-dimensional plane. The 2-sphere, often simply called a sphere, is the boundary of a 3-ball in three-dimensional space. The 3-sphere is the boundary of a 4-ball in four-dimensional space. The (n – 1)-sphere is the boundary of an n-ball. Given a Cartesian coordinate system, the unit n-sphere of radius 1 can be 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\}.} Considered intrinsically, when n ≥ 1, the n-sphere is a Riemannian manifold of positive constant curvature, and is orientable. The geodesics of the n-sphere are called great circles. The stereographic projection maps the n-sphere onto n-space with a single adjoined point at infinity; under the metric thereby defined, R n ∪ { ∞ } {\displaystyle \mathbb {R} ^{n}\cup \{\infty \}} is a model for the n-sphere. In the more general setting of topology, any topological space that is homeomorphic to the unit n-sphere is called an n-sphere. Under inverse stereographic projection, the n-sphere is the one-point compactification of n-space. The n-spheres admit several other topological descriptions: for example, they can be constructed by gluing two n-dimensional spaces together, by identifying the boundary of an n-cube with a point, or (inductively) by forming the suspension of an (n − 1)-sphere. When n ≥ 2 it is simply connected; the 1-sphere (circle) is not simply connected; the 0-sphere is not even connected, consisting of two discrete points.

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