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...

{\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...

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...

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...

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)...

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....

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...

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...

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...

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...

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...

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...

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...

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...

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...

armillary sphere (variations are known as spherical astrolabe, armilla, or armil) is a model of objects in the sky (on the celestial sphere), consisting...

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...

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,...

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...

represents a reflection hyperplane on 3-dimensional surfaces: the 3-sphere, Euclidean 3-space, and hyperbolic 3-space. Coxeter named them after Édouard...

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...

mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other. They are examples...

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...

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...

In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane (also called the closed complex plane): the...

/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...

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...

(Australia and Europe) in 2008. A remake, titled Odin Sphere Leifthrasir, was released on PlayStation 3, PlayStation 4, and PlayStation Vita in 2016: Atlus...

{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...

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...