mathematics, a hypersphere, 3-sphere, or glome is a 4-dimensional analogue of a sphere, and is the 3-dimensional n-sphere. In 4-dimensional Euclidean...

{\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...

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)...

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...

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....

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...

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

A Dyson sphere is a hypothetical megastructure that encompasses a star and captures a large percentage of its power output. The concept is a thought experiment...

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...

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...

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...

/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...

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

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...

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...

sculptor Arnaldo Pomodoro. In 1966, Pomodoro was commissioned to create a 3.5-meter sphere for Expo 67 in Montreal. The success of this sculpture propelled Pomodoro's...

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...

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...

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...

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...

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...

the 3-sphere S 3 {\displaystyle S^{3}} . All such manifolds are prime, orientable, and closed. Spherical 3-manifolds are sometimes called elliptic 3-manifolds...

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

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...

{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...

In differential topology, sphere eversion is the process of turning a sphere inside out in a three-dimensional space (the word eversion means "turning...