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.
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) |