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manifolds

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or n-manifold for short, is a topological space with the property that each point has a neighborhood that is homeomorphic to an open subset of n-dimensional Euclidean space.
One-dimensional manifolds include lines and circles, but not figure eights. Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, and also the Klein bottle and real projective plane.
The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows complicated structures to be described in terms of well-understood topological properties of simpler spaces. Manifolds naturally arise as solution sets of systems of equations and as graphs of functions. The concept has applications in computer-graphics and augmented-reality given the need to associate pictures with coordinates (e.g. CT scans).
Manifolds can be equipped with additional structure. One important class of manifolds are differentiable manifolds; their differentiable structure allows calculus to be done. A Riemannian metric on a manifold allows distances and angles to be measured. Symplectic manifolds serve as the phase spaces in the Hamiltonian formalism of classical mechanics, while four-dimensional Lorentzian manifolds model spacetime in general relativity.
The study of manifolds requires working knowledge of calculus and topology.

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  1. M

    Balancing U/Floor heating manifolds

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  2. H

    Underfloor heating

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    • Forum: Plumbing Jobs | The Job-board
  3. D

    pipe size?

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  4. M

    Under floor heating help needed

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  5. J

    Wth underfloor heating manifold

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  6. A

    ufh zones

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    • Forum: Plumbing Zone
  7. I

    Manifolds?

    Hi All Firstly, brilliant forum with lots of advice.....great work. I've just become a registered user of this forum and thought I'd see if anyone had used these for domestic supply? If so, any advice/gotcha's that you could share would be greatly appreciated. Ta!
  8. O

    DIY job what do you think ???

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  9. B

    Manifolds

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  10. T

    manifolds and twin entry IMI yorky valves

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  11. I

    Flow and Return Temps at the UFH Manifolds

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  12. K

    22mm to 10mm CH Manifolds

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  13. I

    Microbore Manifolds

    Where are the manifolds normally located, near the boiler, under the airing cupbaord??? I believe there are normally two. one you upstairs and one down stairs. :confused::confused::confused:
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