Non-Euclidean Geometry

E412207

branch of mathematics geometry

Non-Euclidean Geometry is a branch of mathematics that studies geometrical systems in which Euclid’s parallel postulate does not hold, leading to alternative models of space such as hyperbolic and elliptic geometry.

Try in SPARQL Jump to: Surface forms Disambiguation Statements Elicitation Referenced by

All labels observed (3)

Label	Occurrences
Lobachevskian geometry	2
Imaginary Geometry	1
Non-Euclidean Geometry canonical	1

How this entity was disambiguated

This entity first appeared as the object of triple T4105486 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Non-Euclidean Geometry
Context triple: [H. S. M. Coxeter, notableWork, Non-Euclidean Geometry]

A. Lorentzian geometry
Lorentzian geometry is the branch of differential geometry that studies manifolds equipped with metrics of Lorentzian signature, providing the mathematical framework for general relativity and spacetime physics.
B. The Foundations of Geometry
The Foundations of Geometry is a seminal mathematical text by Oswald Veblen that rigorously develops the axiomatic basis of geometry in a modern, logical framework.
C. Neue Geometrie des Raumes
Neue Geometrie des Raumes is a foundational 19th-century mathematical work by Julius Plücker that develops projective and line geometry in three-dimensional space.
D. Geometry
Geometry is René Descartes’ foundational work that introduced analytic geometry, uniting algebra and Euclidean geometry through the use of coordinates.
E. Erlangen Program
The Erlangen Program is Felix Klein’s influential 1872 framework that classifies and studies geometries based on their underlying symmetry groups and transformation properties.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Non-Euclidean Geometry
Target entity description: Non-Euclidean Geometry is a branch of mathematics that studies geometrical systems in which Euclid’s parallel postulate does not hold, leading to alternative models of space such as hyperbolic and elliptic geometry.

A. Lorentzian geometry
Lorentzian geometry is the branch of differential geometry that studies manifolds equipped with metrics of Lorentzian signature, providing the mathematical framework for general relativity and spacetime physics.
B. The Foundations of Geometry
The Foundations of Geometry is a seminal mathematical text by Oswald Veblen that rigorously develops the axiomatic basis of geometry in a modern, logical framework.
C. Neue Geometrie des Raumes
Neue Geometrie des Raumes is a foundational 19th-century mathematical work by Julius Plücker that develops projective and line geometry in three-dimensional space.
D. Geometry
Geometry is René Descartes’ foundational work that introduced analytic geometry, uniting algebra and Euclidean geometry through the use of coordinates.
E. Erlangen Program
The Erlangen Program is Felix Klein’s influential 1872 framework that classifies and studies geometries based on their underlying symmetry groups and transformation properties.
F. None of above. chosen

Statements (48)

Predicate	Object
instanceOf	branch of mathematics ⓘ geometry ⓘ
basedOn	alternative parallel axioms ⓘ
contrastsWith	Euclidean geometry ⓘ
definedBy	rejection of Euclid's parallel postulate ⓘ
developedBy	Bernhard Riemann ⓘ Carl Friedrich Gauss ⓘ Eugenio Beltrami ⓘ Felix Klein ⓘ János Bolyai ⓘ Nikolai Lobachevsky ⓘ
fieldOfStudy	mathematics ⓘ
formalizedBy	axiomatic systems ⓘ
generalizes	Euclidean geometry to curved spaces ⓘ
hasApplicationIn	computer graphics ⓘ cosmology ⓘ general relativity ⓘ navigation on curved surfaces ⓘ theoretical physics ⓘ topology ⓘ
hasKeyProperty	sum of angles in a triangle may differ from 180 degrees ⓘ
hasKeyResult	existence of consistent geometries with different parallel axioms ⓘ independence of Euclid's parallel postulate from other axioms ⓘ
hasModel	Beltrami–Klein model ⓘ Poincaré disk model ⓘ Poincaré upper half-plane model ⓘ surface form: Poincaré half-plane model sphere as a model of elliptic geometry ⓘ
hasSubfield	hyperbolic trigonometry ⓘ spherical trigonometry ⓘ
historicalRoot	19th-century mathematics ⓘ
includes	Non-Euclidean Geometry self-linksurface differs ⓘ surface form: Lobachevskian geometry Riemannian manifolds ⓘ surface form: Riemannian geometry elliptic geometry ⓘ hyperbolic geometry ⓘ projective models of geometry ⓘ
influenced	axiomatic method in mathematics ⓘ modern concept of space-time ⓘ
relatedTo	Riemannian manifolds ⓘ curved space ⓘ differential geometry ⓘ group theory via isometries ⓘ projective geometry ⓘ
studies	geometrical systems where Euclid's fifth postulate does not hold ⓘ
taughtIn	university mathematics curricula ⓘ
usesConcept	curvature ⓘ geodesic ⓘ metric space ⓘ models of geometry ⓘ

How these facts were elicited

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

H. S. M. Coxeter → notableWork → Non-Euclidean Geometry ⓘ

Nikolai Lobachevsky → notableWork → Non-Euclidean Geometry ⓘ

this entity surface form: Imaginary Geometry

Nikolai Lobachevsky → knownFor → Non-Euclidean Geometry ⓘ

this entity surface form: Lobachevskian geometry

Non-Euclidean Geometry → includes → Non-Euclidean Geometry self-linksurface differs ⓘ

subject surface form: Non-Euclidean geometry