Hypersphere
In mathematics, an n-sphere is a generalization of the surface of an ordinary sphere to a n-dimensional space. For any natural number n, an n-sphere of radius r is defined as the set of points in (n + 1)-dimensional Euclidean space which are at distance r from a central point, where the radius r may be any positive real number. Thus, the n-sphere centred at the origin is defined by:
S^n = \left\{ x \in \mathbb{R}^{n+1} : \|x\| = r\right\}.
It is an n-dimensional manifold in Euclidean (n + 1)-space.
In particular::
a 0-sphere is the pair of points at the ends of a (one-dimensional) line segment,
a 1-sphere is the circle, which is the one-dimensional circumference of a (two-dimensional) disk in the plane,
a 2-sphere is the two-dimensional surface of a (three-dimensional) ball in three-dimensional space.
Spheres of dimension n > 2 are sometimes called hyperspheres, with 3-spheres sometimes known as glomes. The n-sphere of unit radius centered at the origin is called the unit n-sphere, denoted Sn. The unit n-sphere is often referred to as the n-sphere.
An n-sphere is the surface or boundary of an (n + 1)-dimensional ball, and is an n-dimensional manifold. For n ≥ 2, the n-spheres are the simply connected n-dimensional manifolds of constant, positive curvature. The n-spheres admit several other topological descriptions: for example, they can be constructed by gluing two n-dimensional Euclidean spaces together, by identifying the boundary of an n-cube with a point, or (inductively) by forming the suspension of an (n − 1)-sphere.

This is an excerpt from the article Hypersphere from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.
The article Hypersphere at en.wikipedia.org was accessed 2,251 times in the last 30 days. (as of: 12/23/2013)
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Hypersphere -- from Wolfram MathWorld
Hypersphere. DOWNLOAD Mathematica Notebook EXPLORE THIS TOPIC IN the MathWorld Classroom. The n -Hypersphere (often simply called the n -sphere ) ...
mathworld.wolfram.com/Hypersphere.html
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About the Hypersphere
In mathematics, a Hypersphere is a sphere having more than three dimensions. Since the early twentieth century, physicists have used this idea of a  ...
www.hypersphere.com/hs/abouths.html
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Problem 311: The Volume of a Hypersphere - Space Math @ NASA
89. The Volume of a Hypersphere. This spherical propellant tank is an important component of testing for the Altair lunar lander, an integral part of.
spacemath.gsfc.nasa.gov/weekly/6Page89.pdf
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n-sphere - Wikipedia, the free encyclopedia
In mathematics, an n-sphere is a generalization of the surface of an ordinary sphere to a n-dimensional space. For any natural number n, an n-sphere of radius r ...
en.wikipedia.org/wiki/N-sphere
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The HyperSphere
The mathematical objects that live on the sphere in four dimensional space -- the Hypersphere -- are both beautiful and interesting. The four dimensional sphere ...
groups.csail.mit.edu/mac/users/rfrankel/fourd/FourDArt.html
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The volume and surface area of an n-dimensional hypersphere
An n-dimensional Hypersphere of radius R consists of the locus of points such ... To compute the volume of this Hypersphere, we simply integrate the infinitesimal.
scipp.ucsc.edu/~haber/ph116A/volume_11.pdf
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Hypersphere
Feb 23, 2006 ... Visualizing a Hypersphere. There's lots to be found on the internet on the subject of higher-dimensional spheres. There are all kinds of ...
web.meson.org/hypersphere/
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Play Hyper Sphere Online at 2DPlay for Free
Game Controls for Hyper Sphere. Use the ARROW KEYS to move the hyper sphere and collect the power crystals to complete the levels. Don't forget to submit ...
www.2dplay.com/hyper-sphere/hyper-sphere-play.htm
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Hypersphere
About the system. The Hypersphere HS-5k system for continuous surveillance represents a disruptive innovation for two major fast- growing industries ...
www.hipersfera.hr/
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Hyper Sphere - Free Online Action Games from AddictingGames
Hyper Sphere : Rolling balls isn't so hard. But when bots are after you, it gets tough! Checkpoints keep you sane. Free Online Action Games from ...
www.addictinggames.com/action-games/hypersphere.jsp
Search results for "Hypersphere"
Google: approx. 312.000
Hypersphere in science
The number of lattice points in a k-dimensional hypersphere ...
The number of lattice points in a k-dimensional Hypersphere (1965) ... Volume: Report (University of Illinois at Urbana-Champaign. Dept. of Computer Science) ...
The number of lattice points in a k-dimensional hypersphere, (Illinois ...
The number of lattice points in a k-dimensional Hypersphere, (Illinois. University. Dept. of Computer Science. Report) Unknown Binding – January 1, 1965.
[PDF]Clustering on the Unit Hypersphere using von Mises-Fisher ...
University of Texas at Austin. Austin, TX 78712, USA ... such data is L2 normalized so that it lies on the surface of a unit Hypersphere. Popular models such as ...
Dr Morné MC Lamont
2008: PhD (Statistics) – Stellenbosch University, South Africa ... Kernel Fisher Discriminant Analysis by using the Smallest Enclosing Hypersphere”, in Advances ...
Regression for compositional data by using distributions defined on ...
May 6, 2011 ... University ... transformation and then modelled using distributions defined on the Hypersphere. ... Janice Scealy, Australian National University.
Weighted Hyper-sphere SVM for Hypertext Classification - Springer
Weighted Hyper-sphere SVM for Hypertext Classification ... Intel China Research Center, 8/F, Peking University, Department of Machine Intelligence; 4.
Hypersphere Exotica - Scientific American
Aug 10, 2009 ... Hypersphere Exotica: Kervaire Invariant Problem Has a Solution! ... William Browder of Princeton University later removed that ambiguity, ...
Hypersphere Packing -- from Wolfram MathWorld
Hypersphere Packing ... of the densest known non-lattice packings of Hyperspheres in dimensions up ... Cambridge, England: Cambridge University Press, pp.
[PDF]5 A Bayesian Approach to Hypersphere Estimation - UvA DARE
Downloaded from UvA-DARE, the institutional repository of the University of ... An early step on the way to a Hypersphere estimator is a circle estimator. A circle ...
[PDF]Brownian dynamics simulations on a hypersphere in 4 ... - Scitation
Department of Physical Chemistry, Uppsala University, Box 532, S-751 21 Uppsala, ... address the question how to generate a random walk on the 3-sphere, ...
Books on the term Hypersphere
Minisum Hyperspheres
Minisum Hyperspheres
Mark-Christoph Körner, 2011
In this text we consider the following variant of the Weber problem: Minisum Hypersphere problem. Let D = {A 1 ,...,A M} ⊆ Rn be a set of fixed points with positive weights ωm > 0 for all m = 1,...,M. Given a norm · in Rn, find a minimizer of f : G ...
HYPERSPHERE, ... A JOURNEY AT THE SPEED OF GEOMETRY Revised Edition,
HYPERSPHERE, ... A JOURNEY AT THE SPEED OF GEOMETRY Revised Edition,
2013
Robert B Cronkhite, a member of the British Interplanetary Society, The H.G. Wells Society, and The United States Naval Institute has after over 12 years of theoretical dissertation, experimentation and provocative results, has the basis of Hypergeometric Mechanics profoundly operating as mechanism. No more is geometry esoteric or mere abstraction,...
Neural Information Processing: 13th International ...
Neural Information Processing: 13th International ...
Irwin King, 2006
We repeat the same procedure for these points and keep adding Hyperspheres until we have covered all points from class k. We repeat the whole procedure for all other classes. The algorithm may be briefly described as follows: Algorithm ...
Full Color Illustrations of the Fourth Dimension, Volume 2: Hypercube- and Hypersphere-Based Objects
Full Color Illustrations of the Fourth Dimension, Volume 2: Hypercube- and Hypersphere-Based Objects
Chris McMullen, 2009
Chris McMullen is a physics instructor at Northwestern State University of Louisiana. He earned his Ph.D. in phenomenological high-energy physics (particle physics) from Oklahoma State University in 2002. Originally from California, he earned his Master's degree from California State University, Northridge, where his thesis was in the field of...
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
John Shawe-Taylor, Nello Cristianini, 2004
John Shawe-Taylor, Nello Cristianini. 7.1 The smallest enclosing Hypersphere In Chapter 1 novelty-detection was cited as one of the pattern analysis algorithms that we aimed to develop in the course of this book. A novelty- detection algorithm ...
Minisum Hyperspheres (Springer Optimization and Its Applications)
Minisum Hyperspheres (Springer Optimization and Its Applications)
Mark-Christoph Körner, 2011
This book presents a self-contained introduction to the theory of minisum Hyperspheres. This specialized research area within the larger field of geometric optimization is full of interesting and open problems.This work provides an overview of the history of minisum Hyperspheres as well as describes the best techniques for developing and solving mi...
Conformal Differential Geometry and Its Generalizations
Conformal Differential Geometry and Its Generalizations
Maks A. Akivis, Vladislav V. Goldberg, 2011
(1.1.1) i=1 i=1 We will call the set of numbers so,si and 5"“ the polyspherical (or (n + 2)spherical) coordinates of the Hypersphere S C R". If n = 3, the numbers so, s1, 32, 33, and s4 are called the pentaspherical coordinates of the sphere S in ...
Geometry, Relativity and the Fourth Dimension (Dover Books on Mathematics)
Geometry, Relativity and the Fourth Dimension (Dover Books on Mathematics)
1977
This is a highly readable, popular exposition of the fourth dimension and the structure of the universe. A remarkable pictorial discussion of the curved space-time we call home, it achieves even greater impact through the use of 141 excellent illustrations. This is the first sustained visual account of many important topics in relativity theory tha...
Artificial Neural Nets and Genetic Algorithms: Proceedings ...
Artificial Neural Nets and Genetic Algorithms: Proceedings ...
Vera Kurkova, 2001
Using the just constructed Hypersphere we find a pattern g = {gl,...,gn) within the Hypersphere that is nearest to the pattern h . The final radius r is then recalculated according to formula hi+8i (1) The number of patterns within the Hypersphere ...
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Blog posts on the term
Hypersphere
Visualizing a 4D hypersphere - - Jon Aquino’s Mental Garden
My coworker Chris Brewer created a visualization that allows you to experience a 4D sphere (or Hypersphere ) by zooming around a 3D space. Set Viewing Distanc…
jona.ca/blog/visualizing-a-4d-hypersphere
HYPERSPHERE.... Now On Sale!
Company Name - Amsterdam, NY. Company Message
www.cronkhitetechnion.com/blog/2013/11/02/HYPERSPHERE-Now-On-Sale.aspx
Surface Areas and Volumes of Hyperspheres | Rob Hubbard's Blog
I noticed that the formulae for the sizes of the surface (or rather, boundary) and volume (interior) of circles, spheres and Hyperspheres seem to have discontinuities (or 'jumps') in the index of $latex \pi$. However, this is only a result of simplifying a uniform formula for particular cases. The indices I prefer for the boundary…
rhubbarb.wordpress.com/2013/10/03/hyperspheres/
Reasoning in Higher Dimensions: Hyperspheres | on Topology
In my last post on higher dimensions, I alluded to the fact that I don't agree completely with certain notions about higher dimensions. Specifically, I disagree with the idea that the intuition that you take for granted in low dimensions is necessarily ill-equipped to serve you in higher dimensions. Low-dimensional intuition is ill-equipped for many…
ontopo.wordpress.com/2009/03/03/reasoning-in-higher-dimensions-hyperspheres/
Hyper Sphere
Hyper Sphere. Release your hijacked space ship by controlling the hyper sphere to destroy the effected virus throu
www.smallgamesonline.com/play-5444.html
Hypersphere Exotica: Kervaire Invariant Problem Has a Solution! - Scientific American
www.scientificamerican.com/article/hypersphere-exotica/
Hypersphere-2010.png | Melka blog
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hypersphere « Peeter Joot's Blog.
Posts about Hypersphere written by Peeter Joot
peeterjoot.wordpress.com/tag/hypersphere/
hypersphere: definition of hypersphere in Oxford dictionary (British & World English)
Definition of Hypersphere in British and World English in Oxford dictionary. Meaning, pronunciation and example sentences. English to English reference content.
www.oxforddictionaries.com/definition/english/hypersphere
Dámhsgoil Neamhachais na hErend: Chasing the Hyper Sphere in Real Space Geometry
This is an outline of a computational process designed to develop a method of creating a hyper sphere in Real Space geometry. It has the potential when fully resolved to make an impact on the most cutting edge aspects of Physics, namely the current search for a theory of everything.
damhsgoilneamhachaisnaherend.blogspot.com/2013/11/chasing-hyper-sphere-in-real-space.html
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