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## Description

In mathematics, a 3-sphere is a higher-dimensional analogue of a sphere. It consists of the set of points equidistant from a fixed central point in 4-dimensional Euclidean space. Just as an ordinary sphere (or 2-sphere) is a two-dimensional surface that forms the boundary of a ball in three dimensions, a 3-sphere is an object with three dimensions that forms the boundary of a ball in four dimensions.
In coordinates, a 3-sphere with center (C0, C1, C2, C3) and radius r is the set of all points (x0, x1, x2, x3) in real, 4-dimensional space.

Related formulas

## Variables

 r Radius (dimensionless) x0 x-coordinate of the point coresponding to Co (dimensionless) C0 Fixed Center of the 3-shere (dimensionless) x1 x-coordinate of the point coresponding to C1 (dimensionless) C1 Center of the 3-shere (dimensionless) x2 x-coordinate of the point coresponding to C2 (dimensionless) C2 Center of the 3-shere (dimensionless) x3 x-coordinate of the point coresponding to C3 (dimensionless) C3 Center of the 3-shere (dimensionless)