Kreis und Kugel
E853122
"Kreis und Kugel" is a foundational mathematical work by Wilhelm Blaschke that develops the theory of circles and spheres within the field of differential and convex geometry.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Kreis und Kugel canonical | 3 |
How this entity was disambiguated
This entity first appeared as the object of triple T10269900 — 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: Kreis und Kugel Context triple: [Wilhelm Blaschke, notableWork, Kreis und Kugel]
-
A.
Sphere
Sphere is a British publishing imprint known for releasing a wide range of commercial fiction and non-fiction titles.
-
B.
Sphere
"Sphere" is a 1998 science fiction thriller film directed by Barry Levinson, based on Michael Crichton's novel about a team of scientists investigating a mysterious spacecraft on the ocean floor.
-
C.
Steinmetz solid
The Steinmetz solid is a three-dimensional geometric shape formed by the intersection of two or more cylinders at right angles, often studied in calculus and solid geometry for its interesting volume and symmetry properties.
-
D.
Several Circles
Several Circles is an abstract painting by Wassily Kandinsky that explores pure geometric forms and color relationships through a dynamic composition of overlapping circles.
-
E.
SPHERE
SPHERE is a high-contrast imaging instrument on the Very Large Telescope designed primarily for directly observing and characterizing exoplanets and circumstellar disks.
- 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: Kreis und Kugel Target entity description: "Kreis und Kugel" is a foundational mathematical work by Wilhelm Blaschke that develops the theory of circles and spheres within the field of differential and convex geometry.
-
A.
Sphere
Sphere is a British publishing imprint known for releasing a wide range of commercial fiction and non-fiction titles.
-
B.
Sphere
"Sphere" is a 1998 science fiction thriller film directed by Barry Levinson, based on Michael Crichton's novel about a team of scientists investigating a mysterious spacecraft on the ocean floor.
-
C.
Steinmetz solid
The Steinmetz solid is a three-dimensional geometric shape formed by the intersection of two or more cylinders at right angles, often studied in calculus and solid geometry for its interesting volume and symmetry properties.
-
D.
Several Circles
Several Circles is an abstract painting by Wassily Kandinsky that explores pure geometric forms and color relationships through a dynamic composition of overlapping circles.
-
E.
SPHERE
SPHERE is a high-contrast imaging instrument on the Very Large Telescope designed primarily for directly observing and characterizing exoplanets and circumstellar disks.
- F. None of above. chosen
Statements (41)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ |
| author | Wilhelm Blaschke ⓘ |
| contributionTo |
development of differential geometry of curves and surfaces
ⓘ
foundations of convex geometry ⓘ |
| countryOfOrigin | Germany ⓘ |
| field |
convex geometry
ⓘ
differential geometry ⓘ mathematics ⓘ |
| genre |
mathematics textbook
ⓘ
scientific literature ⓘ |
| hasAuthor | Wilhelm Blaschke ⓘ |
| hasSubject |
Euclidean geometry
ⓘ
analytic geometry of circles ⓘ analytic geometry of spheres ⓘ classical geometry ⓘ classical theorems about circles ⓘ classical theorems about spheres ⓘ curves on spheres ⓘ geometric constructions ⓘ geometric inequalities ⓘ metric properties of circles ⓘ metric properties of spheres ⓘ surface geometry ⓘ symmetry of geometric figures ⓘ transformations in geometry ⓘ |
| influenced |
20th-century geometry
ⓘ
theory of convex bodies ⓘ |
| language | German ⓘ |
| originalLanguage | German ⓘ |
| title | Kreis und Kugel ⓘ |
| topic |
circles
ⓘ
convex bodies ⓘ curvature ⓘ differential geometric methods ⓘ geometry of circles ⓘ geometry of spheres ⓘ spheres ⓘ |
| usedIn |
advanced mathematics education
ⓘ
research in convex geometry ⓘ research in differential 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: Kreis und Kugel Description of subject: "Kreis und Kugel" is a foundational mathematical work by Wilhelm Blaschke that develops the theory of circles and spheres within the field of differential and convex geometry.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.