Manifold
In mathematics, a manifold of dimension n is a topological space that near each point resembles n-dimensional Euclidean space. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n. Lines and circles, but not figure eights, are one-dimensional manifolds. Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, which can all be realized in three dimensions, but also the Klein bottle and real projective plane which cannot.
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Famous quotes containing the word manifold:
“Odysseus saw the sirens; they were charming,
Blonde, with snub breasts and little neat posteriors,”
—John Streeter Manifold (b. 1915)
“The Lord wrote it all down on the little slate
Of the baby tortoise.
Outward and visible indication of the plan within,
The complex, manifold involvedness of an individual creature”
—D.H. (David Herbert)
“They had met, and included in their meeting the thrust of the manifold grass stems, the cry of the peewit, the wheel of the stars.”
—D.H. (David Herbert)