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hypersurface
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Definitions of hypersurface in various dictionaries:
HYPERSURFACE - In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface. A hypersurface is a manifold or an algebraic...
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Possible Dictionary Clues |
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A n.-dimensional surface in a space (often a Euclidean space) of dimension n.1 |
Hypersurface description |
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In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface. A hypersurface is a manifold or an algebraic variety of dimension n 1, which is embedded in an ambient space of dimension n, generally a Euclidean space, an affine space or a projective space. * Hypersurfaces share, with surfaces in a three-dimensional space, the property of being defined by a single implicit equation, at least locally (near every point), and sometimes globally. * A hypersurface in a (Euclidean, affine, or projective) space of dimension two is a plane curve. In a space of dimension three, it is a surface. * For example, the equation* * * * * x * * 1 * * * 2 * * * + * * x * * 2 * * * 2 * * * + * * + * * x * * n * * * 2 * |