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Ordered geometry

Ordered geometry is a form of geometry featuring the concept of intermediacy (or "betweenness") but, like projective geometry, omitting the basic notion of measurement. Ordered geometry is a fundamental geometry forming a common framework for affine, Euclidean, absolute, and hyperbolic geometry (but not for projective geometry).

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History

Moritz PaschPeanoHilbertVeblenEuclid
5 related topics

Results

Sylvester–Gallai theoremGaussBolyaiLobachevskyParallelism
7 related topics

Primitive concepts

Primitive notionsPointsTernary relation
3 related topics

Definitions

Set3-spaceTetrahedron
3 related topics

Topics to explore

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Overview

History

Primitive concepts

Definitions

Axioms of ordered geometry

Results

Advanced semantic analysis

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Map overview Semantic statistics

Ordered geometry

Nodes35
Edges34
Triples35
Avg. degree1.94
Density0.057143
Components1

How this topic connects Entity context

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Ordered geometry

Top relations

related to Axioms of ordered geometry · 22
Ordered geometry → AB, ABC, AFB, All, Axiom, BCD, CAB, CBA, CD, CEA, DE, Dedekind's Axiom, For, Hilbert's, If, If AB, If ABC, OrIf ABC, Pambuccian, Pasch
related to Parallelism · 7
Ordered geometry → Ar, Bolyai, Gauss, Given, Lobachevsky, So, Theorem
is a · 2
Ordered geometry → form of geometry featuring the concept of intermediacy, fundamental geometry forming a common framework for affine
related to Primitive concepts · 2
Ordered geometry → ABC, The
related to Sylvester's problem of collinear points · 2
Ordered geometry → Gallai, The Sylvester

Important terminology Word statistics

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Important terminology

points geometry ordered line parallelism abc ab point plane set two one axioms collinear exists projective measurement affine euclidean absolute

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Ordered geometryis aform of geometry featuring the concept of intermediacy0.90text
Ordered geometryis afundamental geometry forming a common framework for affine0.90text
Ordered geometryrelated to Axioms of ordered geometryThere0.60section
Ordered geometryrelated to Axioms of ordered geometryIf0.60section
Ordered geometryrelated to Axioms of ordered geometryABC0.60section
Ordered geometryrelated to Axioms of ordered geometryCBA0.60section
Ordered geometryrelated to Axioms of ordered geometryCAB0.60section
Ordered geometryrelated to Axioms of ordered geometryAB0.60section
Ordered geometryrelated to Axioms of ordered geometryCD0.60section
Ordered geometryrelated to Axioms of ordered geometryIf AB0.60section
Ordered geometryrelated to Axioms of ordered geometryAxiom0.60section
Ordered geometryrelated to Axioms of ordered geometryPasch0.60section

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