Manifold

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:This page is about a higher mathematics topic. For other meanings of the word manifold, see manifold (disambiguation).

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In mathematics, a manifold is a topological space that looks locally like the Euclidean space Rn, and the Euclidean space indeed provides the simplest example of a manifold. The surface of a sphere such as the Earth provides a more complicated example. A general manifold can be obtained by bending and gluing together flat regions.

Related Topics:
Mathematics - Topological space - Locally - Euclidean space - Sphere

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Manifolds are used in mathematics to describe geometrical objects and they provide the natural arena to study differentiability. In physics, manifolds serve as the phase space in classical mechanics and four-dimensional pseudo-Riemannian manifolds are used to model the spacetime in general relativity. They also occur as configuration spaces. The torus is the configuration space of the double pendulum.

Related Topics:
Differentiability - Physics - Phase space - Classical mechanics - Dimension - Pseudo-Riemannian manifold - Spacetime - General relativity - Configuration space - Torus - Double pendulum

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