n-sphere
Sign in to saveAlso known as n-dimensional sphere, hypersphere
thumb|2-sphere wireframe as an orthogonal projection right|thumb|Just as a stereographic projection can project a sphere's surface to a plane, it can also project a -sphere into -space. This image shows three coordinate directions projected to -space: parallels (red), meridians (blue), and hypermeridians (green). Due to the conformal property of the stereographic projection, the curves intersect each other orthogonally (in the yellow points) as in 4D. All of the curves are circles: the curves that intersect have an infinite radius (= straight line).
~26 min read
Encyclopedic overview
20 sectionsContents
- Description
- Cartesian coordinates
- ''n''-ball
- Topological description
- Volume and area
- Recurrences
- Spherical coordinates
- Spherical volume and area elements
- Polyspherical coordinates
- Stereographic projection
- Probability distributions
- Uniformly at random on the {{math|(''n'' − 1)}}-sphere
- Uniformly at random within the ''n''-ball
- Distribution of the first coordinate
- Specific spheres
- Octahedral sphere
- See also
- Notes
- References
- External links
thumb|2-sphere wireframe as an orthogonal projection right|thumb|Just as a stereographic projection can project a sphere's surface to a plane, it can also project a -sphere into -space. This image shows three coordinate directions projected to -space: parallels (red), meridians (blue), and hypermeridians (green). Due to the conformal property of the stereographic projection, the curves intersect each other orthogonally (in the yellow points) as in 4D. All of the curves are circles: the curves that intersect have an infinite radius (= straight line).
In mathematics, an -sphere or hypersphere is an -dimensional generalization of the -dimensional circle and -dimensional sphere to any non-negative integer .
Excerpted from Wikipedia’s “n-sphere” article, available under the CC BY-SA 4.0 licence.