Radon's theorem

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Published on January 27, 2025 12:32:34 PM ● Video Link: https://www.youtube.com/watch?v=DKZ99Y97RvQ

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In geometry, Radon's theorem on convex sets, published by Johann Radon in 1921, states that:
Any set of d + 2 points in R^(d) can be partitioned into two sets whose convex hulls intersect.
A point in the intersection of these convex hulls is called a Radon point of the set.For example, in the case d = 2, any set of four points in the Euclidean plane can be partitioned in one of two ways. It may form a triple and a singleton, where the convex hull of the triple (a triangle) contains the singleton; alternatively, it may form two pairs of points that form the endpoints of two intersecting line segments.

Source: https://en.wikipedia.org/wiki/Radon's_theorem
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