A Short Proof of Ball's Plank Theorem
Formalization in Lean 4 of the paper 'A Short Proof of Ball's Plank Theorem' by Arseniy Akopyan and Alexander Polyanskii (arXiv:2609.36163). The paper gives a short proof of Keith Ball's 1991 theorem: if a centrally symmetric convex body in R^d is covered by finitely many planks, the sum of their relative widths with respect to the body is at least 1. The proof is based on a simple proof of a core theorem about linear functionals on R^n and an orthonormal basis. It also yields a short proof of Davenport's problem for centrally symmetric convex bodies (interior-disjointness of a homothet…
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