The Geometry of Geodesics
E855792
The Geometry of Geodesics is a foundational mathematical monograph that systematically develops the theory of geodesics and metric geometry, particularly in non-Riemannian settings.
All labels observed (1)
| Label | Occurrences |
|---|---|
| The Geometry of Geodesics canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10313524 — 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: The Geometry of Geodesics Context triple: [Herbert Busemann, notableWork, The Geometry of Geodesics]
-
A.
On the Principles of Geometry
"On the Principles of Geometry" is Nikolai Lobachevsky’s foundational work that introduced non-Euclidean (hyperbolic) geometry, challenging the universality of Euclid’s parallel postulate.
-
B.
Vorlesungen über Geometrie
Vorlesungen über Geometrie is a foundational 19th-century textbook on geometry authored by German mathematician Alfred Clebsch.
-
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.
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.
-
E.
On the Curvature of Space
"On the Curvature of Space" is a pioneering 1922 paper by Alexander Friedmann that introduced non-static, expanding-universe solutions to Einstein’s field equations, laying the theoretical foundation for modern cosmology.
- 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: The Geometry of Geodesics Target entity description: The Geometry of Geodesics is a foundational mathematical monograph that systematically develops the theory of geodesics and metric geometry, particularly in non-Riemannian settings.
-
A.
On the Principles of Geometry
"On the Principles of Geometry" is Nikolai Lobachevsky’s foundational work that introduced non-Euclidean (hyperbolic) geometry, challenging the universality of Euclid’s parallel postulate.
-
B.
Vorlesungen über Geometrie
Vorlesungen über Geometrie is a foundational 19th-century textbook on geometry authored by German mathematician Alfred Clebsch.
-
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.
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.
-
E.
On the Curvature of Space
"On the Curvature of Space" is a pioneering 1922 paper by Alexander Friedmann that introduced non-static, expanding-universe solutions to Einstein’s field equations, laying the theoretical foundation for modern cosmology.
- F. None of above. chosen
Statements (29)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ |
| contributesTo | foundations of modern metric geometry ⓘ |
| develops |
general theory of geodesics in metric spaces
ⓘ
tools for studying geodesics without smooth structure ⓘ |
| emphasizes | non-Riemannian settings ⓘ |
| focusesOn |
foundations of metric geometry
ⓘ
systematic development of geodesic theory ⓘ |
| hasField |
differential geometry
ⓘ
geometry ⓘ mathematics ⓘ metric geometry ⓘ |
| hasGenre | research monograph ⓘ |
| hasStyle | rigorous mathematical exposition ⓘ |
| hasTopic |
completeness in metric geometry
ⓘ
curves of minimal length ⓘ distance functions ⓘ existence of geodesics ⓘ geodesics ⓘ global properties of geodesics ⓘ length spaces ⓘ local properties of geodesics ⓘ metric spaces ⓘ metric structures beyond Riemannian manifolds ⓘ non-Riemannian geometry ⓘ uniqueness of geodesics ⓘ variational methods in geometry ⓘ |
| intendedFor |
advanced graduate students in mathematics
ⓘ
research mathematicians ⓘ |
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: The Geometry of Geodesics Description of subject: The Geometry of Geodesics is a foundational mathematical monograph that systematically develops the theory of geodesics and metric geometry, particularly in non-Riemannian settings.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.