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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.
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.
a 3-sphere, an n-sphere whose surface is three-dimensional; three spheres inequality, a bound of a harmonic function on a sphere; Religion
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.
When one sphere at the end is lifted and released, it strikes the stationary spheres, compressing them and thereby transmitting a pressure wave through the stationary spheres, which creates a force that pushes the last sphere upward. The last sphere swings back and strikes the stationary spheres, repeating the effect in the opposite direction.
Technically, Hopf found a many-to-one continuous function (or "map") from the 3-sphere onto the 2-sphere such that each distinct point of the 2-sphere is mapped from a distinct great circle of the 3-sphere . [1] Thus the 3-sphere is composed of fibers, where each fiber is a circle — one for each point of the 2-sphere.
For the first 3 experiments the period was about 15 minutes and for the next 14 experiments the period was half of that, about 7.5 minutes. The period changed because after the third experiment Cavendish put in a stiffer wire. The torsion coefficient could be calculated from this and the mass and dimensions of the balance.