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See all on Wikipedia3-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
Mathematicians consider a sphere to be a two-dimensional closed surface embedded in three-dimensional Euclidean space. They draw a distinction between a sphere and a ball, which is a solid figure, a three-dimensional …
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
The Poincaré homology sphere (also known as Poincaré dodecahedral space) is a particular example of a homology sphere, first constructed by Henri Poincaré. Being a spherical 3 …
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What are all these "visualizations" of the 3-sphere?
There are an uncountable number of 2 2 -spheres, each existing at a unique point along the w w -axis, which "glue" together to give us a 3 3 -manifold (the 3 3 -sphere) embedded in R4 R 4.
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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 …
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 …
What does the 3-sphere look like? - Mathematics Stack Exchange
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 …
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 …
Hierarchy of angels - Wikipedia
Pseudo-Dionysius (On the Celestial Hierarchy) and Thomas Aquinas (Summa Theologiae) drew on passages from the New Testament, specifically Ephesians 1:21 and Colossians 1:16, to develop a schema of three Hierarchies, Spheres …
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 …
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 …
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 …
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; …
3-Sphere | SpringerLink
Jan 1, 2014 · But what does it mean to say spheres constructed inside universes of dimensions three and four? And how can we think about and understand such spheres without getting …
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 …
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 …
Blue Sphere | Sonic Wiki Zone | Fandom
Blue Sphere is a collection of Special Stages in the same style and engine of those featured in Sonic 3 & Knuckles. The title screen with single Blue Sphere stage code, from Sonic & …
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 …
3.5e Spheres - D&D Wiki
Spheres [] Related to Tome of Fiends (3.5e Sourcebook)/Spheres and Feats 3.5e Sphere Preload Air Bone Bubbles Carnage Chaos Cold Control Death Dominion Fire Frostbite Genasi, Tirr …
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