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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 …
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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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 …
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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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 …
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 …
SPHERES - Wikipedia
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sphere - Wiktionary, the free dictionary
Feb 27, 2025 · sphere (third-person singular simple present spheres, present participle sphering, simple past and past participle sphered) (transitive) To place in a sphere, or among the …
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 …
Dandelin spheres - Encyclopedia of Mathematics
Mar 26, 2023 · For instance, let two spheres (also known as Dandelin spheres), inscribed in a circular cone, make contact with the surface of the cone along circles $c$ and $c'$ (see Fig.) …
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 …
Sonic the Hedgehog 3/Special stages - StrategyWiki
Jun 6, 2023 · There are seven special stages in the game, one for each Chaos Emerald you can collect. In the special stages, you must collect all the blue spheres while avoiding the red …
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 …
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 & …
3.5e Spheres - D&D Wiki
Jan 27, 2023 · 3.5e Spheres. From D&D Wiki. Jump to navigation Jump to search. Back to Main Page → 3.5e Homebrew → Complex Special Ability Components. Spheres . Related to Tome …
Āyatana - Wikipedia
In Buddhism, āyatana (Pāli; Sanskrit: आयतन) is a "center of experience" or "mental home," [1] which create one's experience. The term saḷāyatana (Pāli; Skt. ṣaḍāyatana) refers to six …
Maman (2015 song) - Wikipedia
2 days ago · "Maman" is a song by French singer Louane Emera. It was written by Yohann Malory and Tristan Salvati, with production handled by Dan Black. The single was released on 30 …
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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