3-sphere radius

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

rRadius (dimensionless)
x0x-coordinate of the point coresponding to Co (dimensionless)
C0Fixed Center of the 3-shere (dimensionless)
x1x-coordinate of the point coresponding to C1 (dimensionless)
C1Center of the 3-shere (dimensionless)
x2x-coordinate of the point coresponding to C2 (dimensionless)
C2Center of the 3-shere (dimensionless)
x3x-coordinate of the point coresponding to C3 (dimensionless)
C3Center of the 3-shere (dimensionless)