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a 3-sphere, an n-sphere whose surface is three-dimensional; three spheres inequality, a bound of a harmonic function on a sphere

The noosphere (alternate spelling noösphere) is a philosophical concept developed and popularized by the biogeochemist Vladimir Vernadsky and philosopher and Jesuit priest Pierre …

A glome, also known as a 3-sphere, is the set of all points in 4D space that are a certain distance away from a given point. This distance is known as the radius. While a glome can be thought …

In mathematics, a ball is the solid figure bounded by a sphere; it is also called a solid sphere. [1] It may be a closed ball (including the boundary points that constitute the sphere) or an open ball …

Oct 4, 2021 · A 3-sphere cannot fit into 3-dimensional euclidean space, just as a 2-sphere cannot be cut from a piece of paper. So while you can't just "look at it", here are two nice …

It is a 3-dimensional manifold homeomorphic to the Alexandroff compactification of the usual tridimensional space R 3, written S 3. In other words, the hypersphere minus one point is …

In mathematics, a 3-sphere, glome or hypersphere is a higher-dimensional analogue of a sphere. It may be embedded in 4-dimensional Euclidean space as the set of points equidistant from a …

數學中，三維球面（英文常寫作3-sphere）是球面在高維空間中的類比客體。 它由四維 歐幾里得空間 中與一固定中心點等距離的所有點所組成。 尋常的球面（或者說 二維球面 ）是一個二維 …

What is the 3-sphere? According to that Wikipedia page, the 3-sphere is the "higher-dimensional analogue of a sphere". A (regular) sphere is the boundary of a 3D ball, where a ball is a solid …

Une 3-sphère est une exemple de variété (différentielle) de dimension 3. Les 3-sphères sont aussi fréquemment appelées des hypersphères, mais ce terme peut en général être utilisé pour …

3-dimensional compact manifold, defined as the points of unit norm in Euclidean 4-space

Sep 22, 2022 · The 3-sphere is a compact, connected, 3-dimensional manifold without boundary. It is also simply connected: any loop on the 3-sphere can be continuously shrunk to a point …

Jun 4, 2014 · I would like to learn what is the current understanding of the geometry of the 3-sphere and what are the common elements of the 2-sphere and the 3-sphere - e.g. equator; …

May 20, 2016 · The 3-sphere \({\Bbb S}^3\) is defined as a subset of unit vectors in \({\Bbb R}^4\) \[{\Bbb S}^3=\Big\{(x,y,z,w)\in{\Bbb R}^4\,\Big|\,x^2+y^2+z^2+w^2=1\Big\}.\]

The glome, also known as the 3-sphere, is the 4-dimensional equivalent of a 3D sphere. It consists of a curved 3-manifold that forms circular intersections with planes, and spherical …

De Sphere, voluit de Sphere at the Venetian Resort genoemd, is een bolvormig muziek- en entertainmentgebouw in de Amerikaanse stad Las Vegas, dicht bij de Las Vegas Strip en het …

Jan 1, 2014 · Within this chapter we developed an intuitive understanding of the zero-sphere S 0, one-sphere S 1, two-sphere S 2, and three-sphere S 3. Since it is impossible for us to literally …