Theorem

Radon's Theorem

Geometry

Radon's Theorem states that any set of d plus two points in d-dimensional space can be partitioned into two disjoint subsets whose convex hulls share at least one common point. Named for Johann Radon, it is a foundational result of convex geometry, and its repeated application gives one of the standard proofs of Helly's Theorem.

Facts

Statement

Any set of d+2 points in R^d can be partitioned into two sets whose convex hulls intersect. 1

Proof Year

1921 1

Classification

Statement Form

Existence Theorem 1

Connections

Has Statement Form

Existence Theorem

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

In Branch

Geometry

Source Radon's theorem (Wikipedia)

Proved By

Johann Radon

Source Radon's theorem (Wikipedia)

Sources

1. Radon's theorem (Wikipedia)

Radon's theorem section
Any set of d + 2 points in Rd can be partitioned into two sets whose convex hulls intersect.
Introduction, publication
published by Johann Radon in 1921
In Branch: Geometry, Lead sentence
In geometry, Radon's theorem on convex sets, published by Johann Radon in 1921, states that:Any set of d + 2 points in Rd can be p
Proved By: Johann Radon, Lead paragraph
In geometry, Radon's theorem on convex sets, published by Johann Radon in 1921, states that:Any set of d + 2 points in Rd can be partitioned

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Radon's Theorem

Has Statement Form

In Branch

Proved By