# 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) |

x_{0} | x-coordinate of the point coresponding to Co (dimensionless) |

C_{0} | Fixed Center of the 3-shere (dimensionless) |

x_{1} | x-coordinate of the point coresponding to C1 (dimensionless) |

C_{1} | Center of the 3-shere (dimensionless) |

x_{2} | x-coordinate of the point coresponding to C2 (dimensionless) |

C_{2} | Center of the 3-shere (dimensionless) |

x_{3} | x-coordinate of the point coresponding to C3 (dimensionless) |

C_{3} | Center of the 3-shere (dimensionless) |