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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 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…

Affine algebraic hypersurface, Overview & Smooth hypersurface

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Overview

Smooth hypersurface

Affine algebraic hypersurface

Projective algebraic hypersurface

Advanced semantic analysis

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Map overview Semantic statistics

Hypersurface

Nodes52
Edges51
Triples41
Avg. degree1.96
Density0.038462
Components1

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Hypersurface

Top relations

related to References · 12
Hypersurface → Beal, Differential Geometry Vol II, EMS Press, Encyclopedia, Foundations, Katsumi Nomizu, Mathematics, Shoshichi Kobayashi, Simionescu, The Visual Computer, Visualization, Wiley InterscienceP
is a · 6
Hypersurface → algebraic variety that may be defined by a single implicit equation of the form p, generalization of the concepts of hyperplane, hypersurface that is defined by a polynomial with real coefficients, level set, manifold or an algebraic variety of dimension n, real part of the hypersurface
related to Affine algebraic hypersurface · 5
Hypersurface → An, For, Generally, It, When
related to Projective algebraic hypersurface · 5
Hypersurface → As, Conversely, If, That, The
related to Smooth hypersurface · 5
Hypersurface → Brouwer, Every, In Rn, Jordan, Rn
related to Real and rational points · 4
Hypersurface → If, In, Often, The
related to Properties · 3
Hypersurface → Hilbert's Nullstellensatz, Hypersurfaces, One
see also · 1
Hypersurface → Affine

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Important terminology

space affine dimension algebraic projective points polynomial equation real displaystyle defined smooth manifold field may one generally hypersurfaces two euclidean

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Hypersurfaceis ageneralization of the concepts of hyperplane0.90text
Hypersurfaceis amanifold or an algebraic variety of dimension n0.90text
Hypersurfaceis alevel set0.90text
Hypersurfaceis aalgebraic variety that may be defined by a single implicit equation of the form p0.90text
Hypersurfaceis ahypersurface that is defined by a polynomial with real coefficients0.90text
Hypersurfaceis areal part of the hypersurface0.90text
Hypersurfacerelated to Affine algebraic hypersurfaceAn0.60section
Hypersurfacerelated to Affine algebraic hypersurfaceGenerally0.60section
Hypersurfacerelated to Affine algebraic hypersurfaceWhen0.60section
Hypersurfacerelated to Affine algebraic hypersurfaceIt0.60section
Hypersurfacerelated to Affine algebraic hypersurfaceFor0.60section
Hypersurfacerelated to Projective algebraic hypersurfaceAs0.60section

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    Min side: 3
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