For (n + 1)-dimensional Euclidean space the hypersphere (n-sphere) of radius r and center c is the set of all points that are at the same distance r from point c:
where is euclidean metric for (n+1)-dimensional space
Examples:
- For 2-dimensional Euclidean space the hypersphere is circle (1-sphere),
- For 3-dimensional Euclidean space the hypersphere is sphere (2-sphere).
- For 4-dimensional Euclidean space the hypersphere is glome (3-sphere).