Hyperplane separation theorem

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Overview

Geometry Disjoint Convex sets Euclidean space Closed

13 related topics

Counterexamples and uniqueness

Horn angle Unit disk Convex polyhedron

3 related topics

Use in collision detection

Collision detection Face Normal

3 related topics

Statements and proof

Counterexamples and uniqueness Relative interior

2 related topics

Key facts & relationships

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Conjectured by: Hermann Minkowski
Field: Convex geometry · Topological vector spaces · Collision detection
Generalizations: Hahn–Banach separation theorem
Open problem: No
Type: Theorem

Topics to explore

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Overview

Geometry
Disjoint Disjoint sets
Convex sets Convex set
Euclidean space
Closed Closed set
Compact Compact set
Hyperplane
Projections Projection (set theory)
Hermann Minkowski
Hahn–Banach separation theorem Hahn–Banach theorem
Topological vector spaces
Supporting hyperplane theorem
Support-vector machines Support-vector machine

Statements and proof

Counterexamples and uniqueness Hyperplane separation theorem
Relative interior

Case with possible intersections

Boundary Boundary (topology)

Counterexamples and uniqueness

More variants

Farkas' lemma

Use in collision detection

Collision detection
Face Face (geometry)
Normal Surface normal

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Map overview Semantic statistics

Nodes30

Edges29

Triples16

Avg. degree1.93

Density0.066667

Components1

How this topic connects Entity context

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Hyperplane separation theorem

Top relations

Field · 3

Hyperplane separation theorem → Collision detection, Convex geometry, Topological vector spaces

related to Statements and proof · 3

Hyperplane separation theorem → Hyperplane, Let, Then

related to Use in collision detection · 3

Hyperplane separation theorem → In, Separating, Two

related to More variants · 2

Hyperplane separation theorem → Farkas, More

Conjectured by · 1

Hyperplane separation theorem → Hermann Minkowski

Generalizations · 1

Hyperplane separation theorem → Hahn–Banach separation theorem

Open problem · 1

Hyperplane separation theorem → No

Type · 1

Hyperplane separation theorem → Theorem

is a · 1

Hyperplane separation theorem → theorem about disjoint convex sets in n-dimensional Euclidean space

Important terminology Word statistics

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Important terminology

displaystyle hyperplane theorem convex separation disjoint separating sets closed two compact open langle rangle vector exist axis points since version

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Hyperplane separation theorem	Conjectured by	Hermann Minkowski	1.00	infobox
Hyperplane separation theorem	Field	Convex geometry	1.00	infobox
Hyperplane separation theorem	Field	Topological vector spaces	1.00	infobox
Hyperplane separation theorem	Field	Collision detection	1.00	infobox
Hyperplane separation theorem	Generalizations	Hahn–Banach separation theorem	1.00	infobox
Hyperplane separation theorem	Open problem	No	1.00	infobox
Hyperplane separation theorem	Type	Theorem	1.00	infobox
Hyperplane separation theorem	is a	theorem about disjoint convex sets in n-dimensional Euclidean space	0.90	text
Hyperplane separation theorem	related to More variants	Farkas	0.60	section
Hyperplane separation theorem	related to More variants	More	0.60	section
Hyperplane separation theorem	related to Statements and proof	Hyperplane	0.60	section
Hyperplane separation theorem	related to Statements and proof	Let	0.60	section

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Min side: 3