Non-Euclidean Geometry
E412207
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.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Lobachevskian geometry | 4 |
| non-Euclidean 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 half-plane model ⓘ
linked to:
Poincaré upper half-plane model
sphere as a model of elliptic geometry ⓘ |
| hasSubfield |
hyperbolic trigonometry
ⓘ
spherical trigonometry ⓘ |
| historicalRoot | 19th-century mathematics ⓘ |
| includes |
Lobachevskian geometry
ⓘ
linked to:
Non-Euclidean Geometry
Riemannian geometry ⓘ
linked to:
Riemannian manifolds
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
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Non-Euclidean Geometry Description of subject: 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.
Referenced by (8)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Non-Euclidean Geometry
linked to: Non-Euclidean Geometry
subject linked to:
Non-Euclidean Geometry
linked to: Non-Euclidean Geometry
linked to: Non-Euclidean Geometry
linked to: Non-Euclidean Geometry
linked to: Non-Euclidean Geometry
linked to: Non-Euclidean Geometry