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Abstract

Suppose d > 2, n > d+1, and we have a set P of n points in d-dimensional Euclidean space. Then P contains a subset Q of d points such that for any p ∈ P, the convex hull of Q∪{p} does not contain the origin in its interior. We also show that for non-empty, finite point sets A1, ..., Ad+1 in ℝd, if the origin is contained in the convex hull of Ai ∪ Aj for all 1≤i

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