Statements (17)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:Euclidean_space
|
| gptkbp:field |
convex geometry
|
| gptkbp:generalizes |
convex combination
|
| https://www.w3.org/2000/01/rdf-schema#label |
Carathéodory's theorem
|
| gptkbp:namedAfter |
gptkb:Constantin_Carathéodory
|
| gptkbp:publicationYear |
1907
|
| gptkbp:publishedIn |
gptkb:Mathematische_Annalen
|
| gptkbp:relatedTo |
gptkb:Helly's_theorem
gptkb:Radon's_theorem convex hull |
| gptkbp:sentence |
If a point x of Rd lies in the convex hull of a set P, then x can be written as the convex combination of at most d+1 points in P.
|
| gptkbp:usedIn |
gptkb:combinatorial_geometry
optimization |
| gptkbp:bfsParent |
gptkb:Herglotz-Riesz_representation_theorem
gptkb:Convex_Analysis |
| gptkbp:bfsLayer |
6
|