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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. When the rims were sealed with grease and the air was pumped out, the sphere contained a vacuum and could not be pulled apart by teams of horses. Once the valve was opened ...
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.
a 3-sphere, an n-sphere whose surface is three-dimensional; three spheres inequality, a bound of a harmonic function on a sphere; Religion
A giant sphere 700 m (2,300 ft) underground with thousands of light-detecting tubes will be sealed in a 12-storey cylindrical pool of water in coming months for an experiment that will shine new ...
In physics, specifically classical mechanics, the three-body problem is to take the initial positions and velocities (or momenta) of three point masses that orbit each other in space and calculate their subsequent trajectories using Newton's laws of motion and Newton's law of universal gravitation.
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.
The director of the experiment, Art McDonald, was co-awarded the Nobel Prize in Physics in 2015 for the experiment's contribution to the discovery of neutrino oscillation. [ 1 ] The underground laboratory has been enlarged into a permanent facility and now operates multiple experiments as SNOLAB .
Parallel transport of polarization vectors along such sphere gives rise to Thomas precession, which is analogous to the rotation of the swing plane of Foucault pendulum due to parallel transport along a sphere S 2 in 3-dimensional Euclidean space. [17] In physics, the evolution of such systems is determined by geometric phases.