John ellipsoid
E890445
The John ellipsoid is the unique maximum-volume ellipsoid contained within a convex body, fundamental in convex geometry and functional analysis.
All labels observed (2)
| Label | Occurrences |
|---|---|
| John ellipsoid canonical | 2 |
| for centrally symmetric convex bodies, the John ellipsoid is the ellipsoid of maximal volume centered at the origin | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10881123 — 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: John ellipsoid Context triple: [Fritz John, notableWork, John ellipsoid]
-
A.
Roche ellipsoid
A Roche ellipsoid is an equilibrium shape assumed by a self-gravitating fluid body that is tidally distorted by a nearby massive companion, important in the study of close binary systems and tidal interactions.
-
B.
Ellipsoids
"Ellipsoids" is a sculptural series by German artist Isa Genzken that explores geometric abstraction through elongated, aerodynamic forms often associated with modern architecture and industrial design.
-
C.
Bessel ellipsoid
The Bessel ellipsoid is a historical reference ellipsoid of the Earth defined in the 19th century for geodetic and cartographic purposes, particularly in Europe.
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D.
Jacobi ellipsoid
A Jacobi ellipsoid is a rotating, self-gravitating fluid body in equilibrium that takes on a triaxial ellipsoidal shape due to its rapid spin.
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E.
Maclaurin spheroid
A Maclaurin spheroid is an oblate, rotationally symmetric ellipsoidal figure used in astrophysics and geophysics to model the equilibrium shape of a uniformly rotating, self-gravitating fluid body.
- 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: John ellipsoid Target entity description: The John ellipsoid is the unique maximum-volume ellipsoid contained within a convex body, fundamental in convex geometry and functional analysis.
-
A.
Roche ellipsoid
A Roche ellipsoid is an equilibrium shape assumed by a self-gravitating fluid body that is tidally distorted by a nearby massive companion, important in the study of close binary systems and tidal interactions.
-
B.
Ellipsoids
"Ellipsoids" is a sculptural series by German artist Isa Genzken that explores geometric abstraction through elongated, aerodynamic forms often associated with modern architecture and industrial design.
-
C.
Bessel ellipsoid
The Bessel ellipsoid is a historical reference ellipsoid of the Earth defined in the 19th century for geodetic and cartographic purposes, particularly in Europe.
-
D.
Jacobi ellipsoid
A Jacobi ellipsoid is a rotating, self-gravitating fluid body in equilibrium that takes on a triaxial ellipsoidal shape due to its rapid spin.
-
E.
Maclaurin spheroid
A Maclaurin spheroid is an oblate, rotationally symmetric ellipsoidal figure used in astrophysics and geophysics to model the equilibrium shape of a uniformly rotating, self-gravitating fluid body.
- F. None of above. chosen
Statements (36)
| Predicate | Object |
|---|---|
| instanceOf |
concept in convex geometry
ⓘ
ellipsoid ⓘ geometric object ⓘ |
| alsoKnownAs |
maximal volume inscribed ellipsoid
ⓘ
maximum-volume inscribed ellipsoid ⓘ |
| appearsIn |
Fritz John’s paper “Extremum problems with inequalities as subsidiary conditions”
ⓘ
linked to:
Fritz John conditions
|
| appliesTo |
centrally symmetric convex bodies
ⓘ
finite-dimensional normed spaces ⓘ |
| category | inscribed ellipsoid ⓘ |
| characterizedBy | contact points with the boundary of the convex body satisfying certain balance conditions ⓘ |
| contrastWith |
Löwner ellipsoid, the minimum-volume ellipsoid containing the convex body
ⓘ
linked to:
Löwner ellipsoid
|
| definedOn | convex body ⓘ |
| dimension | defined in any finite dimension n ≥ 2 ⓘ |
| field |
Banach space theory
ⓘ
convex geometry ⓘ functional analysis ⓘ |
| introducedBy | Fritz John ⓘ |
| introducedIn | 1948 ⓘ |
| invariantUnder | affine transformations of the ambient space (up to image of the transformation) ⓘ |
| is | unique maximum-volume ellipsoid contained in a convex body ⓘ |
| namedAfter | Fritz John ⓘ |
| property |
has maximal volume among all ellipsoids contained in the convex body
ⓘ
is contained in the convex body ⓘ |
| relatedTo |
Banach–Mazur compactum
ⓘ
John’s theorem ⓘ Löwner ellipsoid ⓘ isotropic position of convex bodies ⓘ |
| role |
provides canonical inner ellipsoid associated with a convex body
ⓘ
tool for deriving inequalities in convex geometry ⓘ |
| specialCase |
for centrally symmetric convex bodies, the John ellipsoid is the ellipsoid of maximal volume centered at the origin
ⓘ
linked to:
John ellipsoid
|
| uniqueness | there is exactly one John ellipsoid for each convex body ⓘ |
| usedFor |
bounding norms and operator ideals in Banach spaces
ⓘ
studying stability of isoperimetric-type inequalities ⓘ |
| usedIn |
approximation of convex bodies by ellipsoids
ⓘ
geometric functional analysis ⓘ study of Banach–Mazur distance ⓘ |
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: John ellipsoid Description of subject: The John ellipsoid is the unique maximum-volume ellipsoid contained within a convex body, fundamental in convex geometry and functional analysis.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
John ellipsoid
→
specialCase
→
for centrally symmetric convex bodies, the John ellipsoid is the ellipsoid of maximal volume centered at the origin
ⓘ
linked to: John ellipsoid