lastwords

manifold

1-16
English German
manifold adj. mannigfach
  mannigfaltig
  mehrfach
  vielfach
  vielfältig
to manifold vt. vervielfältigen
manifold subst. die Mannigfaltigkeit f
  die Sammelleitung f
manifold subst. der Krümmer m
  der Rohrverteiler m
  der Verteiler m
manifold subst. das Sammelrohr n
  das Verteilerrohr n
  das Verteilerstück n
manifold paper subst.   das Durchschlagpapier n
manifoldness subst. die Mannigfaltigkeit f
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Manifold aus Wikipedia. Zum Beitrag

Manifold - Wikipedia, the free encyclopedia a.new,#quickbar a.new{color:#ba0000} /* cache key: enwiki:resourceloader:filter:minify-css:5:f2a9127573a22335c2a9102b208c73e7 */ Manifold From Wikipedia, the free encyclopedia Jump to: , For other uses, see Manifold (disambiguation). The sphere (surface of a ball) is a two-dimensional manifold since it can be represented by a collection of two-dimensional maps. In mathematics (specifically in differential geometry and topology), a manifold is a topological space that on a small enough scale resembles the Euclidean space of a specific dimension, called the dimension of the manifold. Thus, a line and a circle are one-dimensional manifolds, a plane and sphere (the surface of a ball) are two-dimensional manifolds, and so on into high-dimensional space. More formally, every point of an n-dimensional manifold has a neighborhood homeomorphic to an open subset of the n-dimensional space Rn. Although manifolds resemble Euclidean spaces near each point ("locally"), the global structure of a manifold may be more complicated. For example, any point on the usual two-dimensional surface of a sphere is surrounded by a circular region that can be flattened to a circular region of the plane, as in a geographical map. However, the sphere differs from the plane "in the large": in the language of topology, they are not homeomorphic. The structure of a manifold is encoded by a collection of charts that form an atlas, in analogy with an atlas consisting of charts of the surface of the Earth. The concept of manifolds is central to many parts of geometry and modern mathematical physics because it allows more complicated structures to be expressed and understood in terms of the relatively well-understood properties of simpler spaces. For example, a manifold is typically endowed with a differentiable structure that allows one to do calculus and a Riemannian metric that allows one to measure distances and angles. Symplectic manifolds serve as the phase spaces in the Hamiltonian formalism of classical mechanics, while four-dimensional Lorentzian manifolds model space-time in general relativity.

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1.1 Circlemehr

Manifold aus Wikipedia. Zum Beitrag


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