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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
• 1-sphere, 2-sphere, n-sphere
• tesseract, polychoron, simplex
• Pauli matrices
• Hopf bundle, Riemann sphere
• Poincaré sphere 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 …
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 …
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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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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 …
Unit sphere - Wikipedia
In mathematics, a unit sphere is a sphere of unit radius: the set of points at Euclidean distance 1 from some center point in three-dimensional space. More generally, the unit -sphere is an …
SPHERES - Wikipedia
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3-sphère — Wikipédia
En mathématiques, et plus précisément en géométrie, une 3-sphère est l'analogue d'une sphère en dimension quatre. C'est l'ensemble des points équidistants d'un point central fixé dans un …
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 …
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 …
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 …
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 …
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 …
Exploring the 3-Sphere: A Beginner's Guide to Higher Dimensions
Jun 4, 2014 · There are a lot of different aspects of S^3 and it's not clear what kind of understanding you're after. I would like to learn what is the current understanding of the …
Three spheres - Encyclopedia of Buddhism
In the Mahayana tradition, the "three spheres" are subject, object and action. For example, consider a child looking a toy: When the three spheres are conceptualized (seen as inherently …
3-Sphere - SpringerLink
Jan 1, 2014 · We focus on four types of spheres. Three of the four types are pictured in Figure 1.1 below — from left-to-right we see models of a 0-sphere (two points), a 1-sphere (circle), and a …
Moon Music - Wikipedia
Moon Music (full title Music of the Spheres Vol. II: Moon Music) is the tenth studio album by British rock band Coldplay. [2] Released on 4 October 2024 by Parlophone in the United Kingdom …
Crowned Anglerfish | Fisch Wiki | Fandom
The Crowned Anglerfish is a Secret fish that can be caught in the third area of Mariana's Veil, Abyssal Zenith. When reeling, a -95% progress speed decrease is inflicted, moving erratically …
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