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3-sphere - Wikipedia
In mathematics, a hypersphere or 3-sphere is a 4-dimensional analogue of a sphere, and is the 3-dimensional n-sphere. In 4-dimensional Euclidean space, it is the set of points equidistant from a fixed central point. The interior of a 3-sphere is a 4-ball. It is called a 3-sphere because topologically, the surface itself is 3 … See more
In coordinates, a 3-sphere with center (C0, C1, C2, C3) and radius r is the set of all points (x0, x1, x2, x3) in real, 4-dimensional space (R ) such that
The 3-sphere … See moreThere are several well-known constructions of the three-sphere. Here we describe gluing a pair of three-balls and then the one-point … See more
The four Euclidean coordinates for S are redundant since they are subject to the condition that x0 + x1 + x2 + x3 = 1. As a 3-dimensional manifold one should be able to parameterize … See more
Elementary properties
The 3-dimensional surface volume of a 3-sphere of radius r is
$${\displaystyle SV=2\pi ^{2}r^{3}\,}$$
while the 4 … See moreWhen considered as the set of unit quaternions, S inherits an important structure, namely that of quaternionic multiplication. … See more
In Edwin Abbott Abbott's Flatland, published in 1884, and in Sphereland, a 1965 sequel to Flatland by Dionys Burger, the 3-sphere is referred to as an oversphere, and a 4 … See more
Wikipedia text under CC-BY-SA license Three spheres - Wikipedia
• a 3-sphere, an n-sphere whose surface is three-dimensional
• three spheres inequality, a bound of a harmonic function on a sphereWikipedia · Text under CC-BY-SA licenseSphere - Wikipedia
S 3: a 3-sphere is a sphere in 4-dimensional Euclidean space. Spheres for n > 2 are sometimes called hyperspheres. The n-sphere of unit radius centered at the origin is denoted S n and is often referred to as "the" n-sphere. The ordinary …
Three Spheres II - Wikipedia
Three Spheres II is a lithograph print by the Dutch artist M. C. Escher first printed in April 1946. As the title implies, it depicts three spheres resting on a flat surface. The sphere on the left is …
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Dandelin spheres - Wikipedia
Consider the illustration, depicting a cone with apex S at the top. A plane e intersects the cone in a curve C (with blue interior). The following proof shall …
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Klerksdorp sphere - Wikipedia
Klerksdorp spheres are small objects, often spherical to disc-shaped, that have been collected by miners and rockhounds from 3-billion-year-old pyrophyllite deposits mined by Wonderstone …
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Homology sphere - Wikipedia
Being a spherical 3-manifold, it is the only homology 3-sphere (besides the 3-sphere itself) with a finite fundamental group. Its fundamental group is known as the binary icosahedral group and …
Geodesic polyhedron - Wikipedia
In Magnus Wenninger's Spherical models, polyhedra are given geodesic notation in the form {3,q+} b,c, where {3,q} is the Schläfli symbol for the regular polyhedron with triangular faces, …
Armillary sphere - Wikipedia
Jost Bürgi and Antonius Eisenhoit: Armillary sphere with astronomical clock, made in 1585 in Kassel, now at Nordiska Museet in Stockholm. An armillary sphere (variations are known as spherical astrolabe, armilla, or armil) is a …
Music of the Spheres (Coldplay album) - Wikipedia
Music of the Spheres (subtitled Vol.I: From Earth with Love) [1] is the ninth studio album by British rock band Coldplay, released on 15 October 2021 by Parlophone in the United Kingdom and …
Hairy ball theorem - Wikipedia
The hairy ball theorem of algebraic topology (sometimes called the hedgehog theorem in Europe) [1] states that there is no nonvanishing continuous tangent vector field on even-dimensional n-spheres. [2] [3] For the ordinary sphere, or …
What are all these "visualizations" of the 3-sphere?
There are an uncountable number of $2$-spheres, each existing at a unique point along the $w$-axis, which "glue" together to give us a $3$-manifold (the $3$-sphere) embedded in …
Music of the Spheres World Tour - Wikipedia
The Music of the Spheres World Tour is the ongoing eighth concert tour undertaken by British rock band Coldplay.It is being staged to promote their ninth and tenth studio albums, Music of …
3-sphere - MATHCURVE.COM
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 …
Exploring the 3-Sphere: A Beginner's Guide to Higher Dimensions
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; …
Three spheres: Significance and symbolism - Wisdom Library
Oct 29, 2024 · The Three Spheres in Buddhism encompass representations of spiritual attainment linked to the four immeasurables and detail the realms of existence: the Sphere of Sensuous …
Sphere - Simple English Wikipedia, the free encyclopedia
All points on the edge of the sphere are at the same distance from the center. The distance from the center is called the radius of the sphere. A real-world sphere is called a globe if it is large …
Three spheres - Encyclopedia of Buddhism
Three spheres (Skt. trimaṇḍala; T. 'khor gsum འཁོར་གསུམ་). In the Mahayana tradition, the "three spheres" are subject, object and action. For example, consider a child looking a toy: the child = …
3-sphere | EPFL Graph Search
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 …
The Hunt: Mega Edition 2025 | Fisch Wiki | Fandom
6 days ago · Ends in:March 24 2025 15:00:00 PST. Overview. The Hunt: Mega Edition was a minor event featuring Fisch's participation in the The Hunt: Mega Edition ROBLOX event for …
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