Radon's Theorem

Theorem

Let $S$ be a set of $n + 2$ points in a real Euclidean space $\R^n$ of $n$ dimensions.

Then $S$ can be partitioned into $2$ subsets whose convex hulls have at least one point in their intersection.

Such a point of intersection is known as a Radon point of $S$.

Proof

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Also see

• Definition:Radon Point

Source of Name

This entry was named for Johann Karl August Radon.

Historical Note

Radon's Theorem was proved by Johann Karl August Radon in $1921$.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Radon's theorem