In mathematics, a 3-sphere, glome or hypersphere is a higher-dimensional analogue of a sphere. In 4-dimensional Euclidean space, it is the set of points...
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{\displaystyle 2} -sphere, often simply called a sphere, is the boundary of a 3 {\displaystyle 3} -ball in three-dimensional space. The 3-sphere is the boundary...
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A sphere (from Greek σφαῖρα, sphaîra) is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. Formally, a sphere is the...
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homology sphere, first constructed by Henri Poincaré. Being a spherical 3-manifold, it is the only homology 3-sphere (besides the 3-sphere itself) with...
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In quantum mechanics and computing, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system (qubit)...
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Sphere (also called Sphere at the Venetian Resort) is a music and entertainment arena in Paradise, Nevada, United States, east of the Las Vegas Strip....
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Three-dimensional space (redirect from 3-dimensional)
points on the unit 3-sphere centered at the origin. This 3-sphere is an example of a 3-manifold: a space which is 'looks locally' like 3-D space. In precise...
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topological embedding of a two-dimensional sphere in three-dimensional space. Together with its inside, it is a topological 3-ball, the Alexander horned ball, and...
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3D rotation group (redirect from Projective 3-sphere)
SO(3) is a Lie group called Spin(3). The group Spin(3) is isomorphic to the special unitary group SU(2); it is also diffeomorphic to the unit 3-sphere S3...
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Special unitary group (redirect from SU(3))
norm 1, and is thus diffeomorphic to the 3-sphere. Since unit quaternions can be used to represent rotations in 3-dimensional space (up to sign), there is...
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The Sphere (officially Große Kugelkaryatide N.Y., also known as Sphere at Plaza Fountain, WTC Sphere or Koenig Sphere) is a monumental cast bronze sculpture...
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A Dyson sphere is a hypothetical megastructure that encompasses a star and captures a large percentage of its solar power output. The concept is a thought...
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Tetrahedron (redirect from Twelve-point sphere)
For any tetrahedron there exists a sphere (called the circumsphere) on which all four vertices lie, and another sphere (the insphere) tangent to the tetrahedron's...
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Sphere packing in a sphere is a three-dimensional packing problem with the objective of packing a given number of equal spheres inside a unit sphere. It...
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Hopf fibration (section Fibrations between spheres)
bundle or Hopf map) describes a 3-sphere (a hypersphere in four-dimensional space) in terms of circles and an ordinary sphere. Discovered by Heinz Hopf in...
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armillary sphere (variations are known as spherical astrolabe, armilla, or armil) is a model of objects in the sky (on the celestial sphere), consisting...
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shape of the universe. Just as a sphere looks like a plane (a tangent plane) to a small and close enough observer, all 3-manifolds look like our universe...
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center of the circle, the surface is a degenerate torus, a double-covered sphere. If the revolved curve is not a circle, the surface is called a toroid,...
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Versor (section Presentation on 3- and 2-spheres)
with quaternion multiplication forms a group, and the set of versors is a 3-sphere in the 4-dimensional quaternion algebra. Hamilton denoted the versor of...
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represents a reflection hyperplane on 3-dimensional surfaces: the 3-sphere, Euclidean 3-space, and hyperbolic 3-space. Coxeter named them after Édouard...
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theorem) states that a finite group acting on the 3-sphere is conjugate to a group of isometries of the 3-sphere. The conjecture was posed by Heinz Hopf in 1926...
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mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other. They are examples...
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Ball (mathematics) (redirect from Solid sphere)
bounded by a sphere; it is also called a solid sphere. It may be a closed ball (including the boundary points that constitute the sphere) or an open ball...
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locally modeled by a region of a 3-sphere S3. Negative curvature – a drawn triangle's angles add up to less than 180°; such 3-dimensional space is locally...
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In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane (also called the closed complex plane): the...
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Poincaré conjecture (category 3-manifolds)
/ˌpwæ̃kɑːˈreɪ/, French: [pwɛ̃kaʁe]) is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional...
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exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean n-sphere. That is, M is a sphere from...
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(Australia and Europe) in 2008. A remake, titled Odin Sphere Leifthrasir, was released on PlayStation 3, PlayStation 4, and PlayStation Vita in 2016: Atlus...
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Tesseract (redirect from Order-3-3 square honeycomb)
{4}}=2} edge lengths. An axis-aligned tesseract inscribed in a unit-radius 3-sphere has vertices with coordinates ( ± 1 2 , ± 1 2 , ± 1 2 , ± 1 2 ) . {\displaystyle...
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give a group structure on the 3-sphere S3 isomorphic to the groups Spin(3) and SU(2), i.e. the universal cover group of SO(3). The positive and negative...
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