# N-Sphere

In mathematics, a rose (also known as a bouquet of n circles) is a topological space obtained by gluing together a collection of circles along a single point. The hairy ball theorem of algebraic topology (sometimes called the hedgehog theorem in Europe) states that there is no nonvanishing continuous tangent vector field on even-dimensional n-spheres. 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-dimensional Euclidean space which are at distance r from a central point, where the . May 27,  · Mathematica» The #1 tool for creating Demonstrations and anything technical. Wolfram|Alpha» Explore anything with the first computational knowledge engine. Retain more nitrogen for plant uptake with this nitrogen fertilizer manager. Learn how NutriSphere-N® contributes to a higher yield here. In homotopy theory, spheres and Eilenberg–MacLane spaces are two very different types of basic spaces from which all spaces can be built. In higher dimensions, the great circles on the n-sphere are the intersection of the n-sphere with 2-planes that pass through the origin in the Euclidean space R n + 1. An n -ball is a ball in n -dimensional Euclidean space. The volume of a unit n-ball is an important expression that occurs in formulas throughout mathematics; it generalizes the notion of the volume enclosed by a sphere in 3-dimensional space. Jun 01,  · This is a wonderful question. I am very happy about the A2A. The short answer is that, yes, there are plenty of ways to do it. Allow me to describe two. [math] n [/math]-sphere as an extended Euclidean space. Any [math] n [/math]-sphere can be. nSphere offers the next great technology platform for consumer data collection and interaction. Millions of consumer data points and our proprietary mobile engagement platform allow us to initiate high-impact consumer marketing. In mathematics, the n-sphere is the generalization of the ordinary sphere to an 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 .

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## 9 thoughts on “ N-Sphere ”

1. Zulujinn says:
For any natural numbern, an n-sphere of radius ris defined as the set of points in (n + 1)-dimensional Euclidean spacewhich are at distance rfrom a central point, where the radius rmay be any positivereal number. Thus, the n-sphere centred at the origin is defined by: It is an n-dimensional manifoldin Euclidean (n + 1)-space.
2. Aradal says:
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3. Shaktigore says:
Jun 03,  · (mathematics) Used to form nouns indicating a sphere of x dimensions n-sphere· Designating a spherical field or object. sarcosphere; chromosphere· Designating a global system or layer of the Earth or another planet. biosphere; hydrosphere (figuratively) Designating a particular realm or interest of a group of people, object, etc.; its spatial or.
4. Shazragore says:
In mathematics, an n-sphere is a topological space that is homeomorphic to a standard n-sphere, which is the set of points in -dimensional Euclidean space, that are situated at a constant distance r of a fixed point, called the center. It is the generalization of an ordinary sphere in the ordinary three-dimensional space. The "radius" of a sphere is the constant distance of its points to the.
5. Nam says:
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6. Fauzilkree says:
Jul 30,  · Sphere. A sphere is defined as the set of all points in three-dimensional Euclidean space that are located at a distance (the "radius") from a given point (the "center"). Twice the radius is called the diameter, and pairs of points on the sphere on opposite sides of a diameter are called antipodes. Unfortunately, geometers and topologists adopt incompatible conventions for the meaning of.
7. Faujinn says:
[X,Y,Z] = sphere returns the x-, y-, and z- coordinates of a sphere without drawing it. The returned sphere has a radius equal to 1 and consists of by faces. The function returns the x-, y-, and z- coordinates as three by matrices.
8. Arashilkree says:
The n-sphere of unit radius centered at the origin is denoted S n and is often referred to as "the" n-sphere. Note that the ordinary sphere is a 2-sphere, because it is a 2-dimensional surface (which is embedded in 3-dimensional space). The surface area of the unit (n-1)-sphere is.
9. Jujinn says:
N-sphere synonyms, N-sphere pronunciation, N-sphere translation, English dictionary definition of N-sphere. n. Any of a set of objects resulting from the generalization of a two-dimensional circle and a three-dimensional sphere to n dimensions. In n -dimensional.