Linked from

The 12 pages that link to Carathéodory's theorem, each with the reason it gives.

• Convex setRelated: It limits how many points are needed to witness membership in a convex hull.

• Convex hullRelated: It limits how many original points are needed to represent any hull point.

• Convex geometryRelated: It bounds how many points are needed to represent a point in a convex hull.

• Extreme pointRelated: It bounds how many extreme points may be needed to represent points in finite-dimensional hulls.

• ConvexityRelated: It gives a finite bound on how many points are needed to witness convex-hull membership.

• Convex combinationRelated: It limits the number of nonzero weights needed in a convex combination.

• Helly's theoremRelated: It shares the dimension threshold and underlies related convexity arguments.

• Radon's theoremRelated: It gives a complementary bound on how many points are needed to represent a convex-hull point.

• Krein–Milman theoremCompared with: It gives finite convex representations under finite-dimensional assumptions, unlike the closed-hull conclusion here.

• Tverberg's theoremRelated: It supplies a complementary bound on how many points witness convex-hull membership.

• Borel–Carathéodory theoremCompared with: The shared surname can obscure that this disk estimate is a separate result.

• Shapley–Folkman lemmaRelated: Its dimension-based sparsity principle is closely related to the lemma’s bound on exceptional summands.