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Summary Of: Hypersphere

way to generate a random distribution on a hypersphere is to make a uniform one over a hypercube that includes the unit hypersphere... As the relative volume of the hypersphere to the hypercube decreases very rapidly with dimension it will only work for fairly small...

Encyclodia Page On: Hypersphere

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2-sphere wireframe as an orthogonal projection | | orthogonal projection | Just as a stereographic projection can project a sphere's surface to a plane, it can also project a 3-sphere's surface into 3-space. This image shows three coordinate directions projected to 3-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 <0,0,0,1> have an infinite radius (= straight line). | | stereographic projection | meridians | conformal | mathematics | sphere | dimension | natural number | Euclidean space | positive | real number | manifold | circle | ball | manifold | simply connected | manifold | Euclidean spaces | n-cube | suspension | natural number | Euclidean space | positive | real number | 1-sphere | circle | 2-sphere | 3-sphere | manifold | volume form | Hodge star operator | ball | closed | open | line segment | disk | circle | ball | sphere | 3-sphere | gamma function | double factorial | integration | spherical coordinates | point | line segment | disk | ball | continuous function | global maximum | hypercube | spherical coordinate system | volume element | Jacobian | area element | stereographic projection | unit circle | U(1) | circle group | real projective line | Riemann sphere | complex projective line | Sp(1) | octonions | quasigroup | octonions | Conformal geometry | Homology sphere | Homotopy groups of spheres | Homotopy sphere | Hyperbolic group | Hypersphere | Hypercube | Inversive geometry | Orthogonal group | Möbius transformation | Dover Publications | ISBN 978-0-486-66169-8 | Prentice Hall | ISBN 978-0-13-373770-7 | Weeks, Jeffrey R. | ISBN 978-0-8247-7437-0 | Eric W. Weisstein | MathWorld | Categories | 4-dimensional geometry | Multi-dimensional geometry |
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Hypersphere".