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The 3-sphere is homeomorphic to the one-point compactification of R 3. In general, any topological space that is homeomorphic to the 3-sphere is called a topological 3-sphere. The homology groups of the 3-sphere are as follows: H 0 (S 3, Z) and H 3 (S 3, Z) are both infinite cyclic, while H i (S 3, Z) = {} for all other indices i.
Gaspar Schott's sketch of Otto von Guericke's Magdeburg hemispheres experiment Small 4 in. hemispheres, 1870s. The Magdeburg hemispheres are a pair of large copper hemispheres with mating rims that were used in a famous 1654 experiment to demonstrate the power of atmospheric pressure.
Furthermore, if two points on the 3-sphere map to the same point on the 2-sphere, i.e., if p(z 0, z 1) = p(w 0, w 1), then (w 0, w 1) must equal (λ z 0, λ z 1) for some complex number λ with |λ| 2 = 1. The converse is also true; any two points on the 3-sphere that differ by a common complex factor λ map to the same point on the 2-sphere.
Faraday employed a 7 in. diameter by 10.5 in. tall pewter pail on a wooden stool,(B) [1] but modern demonstrations often use a hollow metal sphere with a hole in the top, [10] or a cylinder of metal screen, [9] [12] mounted on an insulating stand. Its outside surface is connected by a wire to a sensitive electric charge detector.
In the 2003 film The Hulk, a model of the Gamma Sphere, built at Lawrence Berkeley National Laboratory as a detector of gamma rays, is used as the powerful source of gamma rays. [52] The Hulk ends up hurling it through the iconic dome of the Advanced Light Source, which was designed by Arthur Brown Jr. around 1940 for the 184-inch cyclotron.
a 3-sphere, an n-sphere whose surface is three-dimensional; three spheres inequality, a bound of a harmonic function on a sphere; Religion
The Sudanese Möbius strip was constructed as a minimal surface bounded by a great circle in a 3-sphere, but there is also a unique complete (boundaryless) minimal surface immersed in Euclidean space that has the topology of an open Möbius strip. It is called the Meeks Möbius strip, [64] after its 1982 description by William Hamilton Meeks ...
In the mathematical field of geometric topology, the Poincaré conjecture (UK: / ˈ p w æ̃ k ær eɪ /, [2] US: / ˌ p w æ̃ k ɑː ˈ r eɪ /, [3] [4] French: [pwɛ̃kaʁe]) is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space.