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Elliptic geometry

Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect. However, unlike in spherical geometry, two lines are usually assumed to intersect at a single point (rather than two). Because of this, the elliptic geometry…

Products, Elliptic space (the 3D case) & Two dimensions

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Overview

Definitions

Two dimensions

Elliptic space (the 3D case)

Higher-dimensional spaces

Self-consistency

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Map overview Semantic statistics

Elliptic geometry

Nodes56
Edges55
Triples107
Avg. degree1.96
Density0.035714
Components1

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Elliptic geometry

Top relations

related to References · 53
Elliptic geometry → Abuse, AK Peters, Alan, Alfred North Whitehead, Alfred Tarski, America, American Mathematical Society ISBN, An Incomplete Guide, Beardon, Book VI Chapter, Boris Odehnal, California Press, Coxeter, Decision Method, Delphenich, Discrete Groups, Eduard Study, Elementary Algebra, Elliptic, EMS Press
related to Elliptic plane · 18
Elliptic geometry → Arthur Cayley, As, Bernhard Riemann, Desargues, Euclidean, Felix Klein, Given, Kepler, No, OL, On, OP, POQ, Riemannian, The, This, Thus, With
related to Comparison with Euclidean geometry · 8
Elliptic geometry → Elements, Euclid's, Euclidean, For, In, In Euclidean, Postulate, Therefore
related to Elliptic space (the 3D case) · 7
Elliptic geometry → As, Elliptic, Note, One, The, These, This
related to Self-consistency · 7
Elliptic geometry → Because, Euclidean, Gödel's, It, Tarski, Therefore, This
related to Projective elliptic geometry · 5
Elliptic geometry → Distance, In, Rn, The, This
related to Definitions · 4
Elliptic geometry → As, Elliptic, In, The
related to External links · 4
Elliptic geometry → Elliptic, Media, Wikimedia Commons, Wiktionary-logo-en-v2
is a · 1
Elliptic geometry → example of a geometry in which Euclid's parallel postulate does not hold

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Important terminology

elliptic geometry space points lines line euclidean spherical plane two distance point intersect model great one example projective sphere parallel

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Elliptic geometryis aexample of a geometry in which Euclid's parallel postulate does not hold0.90text
Elliptic geometryrelated to Comparison with Euclidean geometryIn Euclidean0.60section
Elliptic geometryrelated to Comparison with Euclidean geometryIn0.60section
Elliptic geometryrelated to Comparison with Euclidean geometryFor0.60section
Elliptic geometryrelated to Comparison with Euclidean geometryEuclidean0.60section
Elliptic geometryrelated to Comparison with Euclidean geometryEuclid's0.60section
Elliptic geometryrelated to Comparison with Euclidean geometryPostulate0.60section
Elliptic geometryrelated to Comparison with Euclidean geometryTherefore0.60section
Elliptic geometryrelated to Comparison with Euclidean geometryElements0.60section
Elliptic geometryrelated to DefinitionsElliptic0.60section
Elliptic geometryrelated to DefinitionsThe0.60section
Elliptic geometryrelated to DefinitionsAs0.60section

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