The Real Projective Plane
E412208
The Real Projective Plane is a classic mathematical monograph by H. S. M. Coxeter that systematically develops the geometry and topology of the real projective plane, emphasizing its axiomatic foundations and non-Euclidean properties.
All labels observed (1)
| Label | Occurrences |
|---|---|
| The Real Projective Plane canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4105487 — 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 Real Projective Plane Context triple: [H. S. M. Coxeter, notableWork, The Real Projective Plane]
-
A.
Veblen axioms for projective geometry
The Veblen axioms for projective geometry are a foundational set of incidence-based axioms introduced by Oswald Veblen to rigorously formalize the structure of projective spaces.
-
B.
Smale’s paradox
Smale’s paradox is a result in differential topology showing that a sphere can be turned inside out in three-dimensional space through smooth deformations without tearing or creasing, challenging intuitive notions of geometry.
-
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.
Euler’s polyhedron formula
Euler’s polyhedron formula is a fundamental result in topology and geometry that relates the numbers of vertices, edges, and faces of a convex polyhedron through the equation V − E + F = 2.
-
E.
Clebsch diagonal surfaces
Clebsch diagonal surfaces are classical 19th-century algebraic surfaces in projective three-space, famous as the first explicit smooth cubic surface with all 27 lines defined over the real numbers.
- 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 Real Projective Plane Target entity description: The Real Projective Plane is a classic mathematical monograph by H. S. M. Coxeter that systematically develops the geometry and topology of the real projective plane, emphasizing its axiomatic foundations and non-Euclidean properties.
-
A.
Veblen axioms for projective geometry
The Veblen axioms for projective geometry are a foundational set of incidence-based axioms introduced by Oswald Veblen to rigorously formalize the structure of projective spaces.
-
B.
Smale’s paradox
Smale’s paradox is a result in differential topology showing that a sphere can be turned inside out in three-dimensional space through smooth deformations without tearing or creasing, challenging intuitive notions of geometry.
-
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.
Euler’s polyhedron formula
Euler’s polyhedron formula is a fundamental result in topology and geometry that relates the numbers of vertices, edges, and faces of a convex polyhedron through the equation V − E + F = 2.
-
E.
Clebsch diagonal surfaces
Clebsch diagonal surfaces are classical 19th-century algebraic surfaces in projective three-space, famous as the first explicit smooth cubic surface with all 27 lines defined over the real numbers.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ |
| approach |
axiomatic
ⓘ
geometric ⓘ rigorous ⓘ |
| audience |
advanced undergraduates in mathematics
ⓘ
graduate students in mathematics ⓘ research mathematicians interested in geometry ⓘ |
| author | H. S. M. Coxeter ⓘ |
| category |
geometry books
ⓘ
mathematics books ⓘ topology books ⓘ |
| contains |
axiomatic treatment of incidence geometry
ⓘ
discussion of coordinate systems for the projective plane ⓘ discussion of duality in projective geometry ⓘ examples of non-orientable surfaces ⓘ figures illustrating projective configurations ⓘ topological description of the real projective plane ⓘ treatment of lines and points in the projective plane ⓘ |
| emphasis |
systematic development of the geometry of the real projective plane
ⓘ
systematic development of the topology of the real projective plane ⓘ |
| field |
mathematics
ⓘ
projective geometry ⓘ topology ⓘ |
| focus |
axiomatic foundations of projective geometry
ⓘ
non-Euclidean properties of the projective plane ⓘ |
| hasAuthorFullName |
Harold Scott MacDonald Coxeter
ⓘ
linked to:
H. S. M. Coxeter
|
| hasMainTopic |
properties of lines and points in projective geometry
ⓘ
structure of the real projective plane ⓘ topological model of the projective plane ⓘ |
| influenced | later textbooks on projective geometry ⓘ |
| isAbout |
geometric models of the projective plane
ⓘ
two-dimensional real projective space ⓘ |
| language | English ⓘ |
| notableFor |
clear exposition of the real projective plane
ⓘ
integration of geometric and topological viewpoints ⓘ |
| relatedTo |
homogeneous coordinates
ⓘ
incidence geometry ⓘ non-Euclidean geometry ⓘ projective transformations ⓘ real projective space ⓘ |
| subject | real projective plane ⓘ |
| teaches |
basic properties of non-orientable surfaces
ⓘ
concept of duality between points and lines ⓘ concept of projective equivalence ⓘ |
| usedIn |
self-study by mathematicians
ⓘ
university courses on projective 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: The Real Projective Plane Description of subject: The Real Projective Plane is a classic mathematical monograph by H. S. M. Coxeter that systematically develops the geometry and topology of the real projective plane, emphasizing its axiomatic foundations and non-Euclidean properties.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.