|
gptkbp:instanceOf
|
gptkb:mathematical_concept
|
|
gptkbp:application
|
gptkb:Physics
gptkb:Probability_theory
gptkb:Mathematical_analysis
gptkb:Computational_geometry
Economics
Optimization
|
|
gptkbp:dimensions
|
n-dimensional (in Euclidean space)
|
|
gptkbp:example
|
gptkb:Polygon
gptkb:Simplex
gptkb:Cube
Ball
|
|
gptkbp:field
|
gptkb:geometry
gptkb:Convex_geometry
|
|
gptkbp:heldBy
|
gptkb:Convex_set
Compact set
Set with non-empty interior
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Convex body
|
|
gptkbp:important_theorem
|
gptkb:Carathéodory's_theorem
gptkb:Helly's_theorem
gptkb:Radon's_theorem
gptkb:Minkowski's_existence_theorem
gptkb:Blaschke_selection_theorem
gptkb:Brunn–Minkowski_theorem
gptkb:Krein–Milman_theorem
|
|
gptkbp:namedFor
|
Mathematicians in 19th century
|
|
gptkbp:property
|
Closed under convex combinations
Bounded
Non-empty interior
Every line segment between two points in the body lies entirely within the body
|
|
gptkbp:relatedConcept
|
gptkb:Minkowski_sum
John ellipsoid
Convex hull
Support function
|
|
gptkbp:studiedBy
|
gptkb:Discrete_geometry
Functional analysis
|
|
gptkbp:bfsParent
|
gptkb:Minkowski's_second_theorem
|
|
gptkbp:bfsLayer
|
7
|