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Proved .
Abstract
We prove that three planks covering a convex body in the plane have total relative width at least one. The planks may have parallel directions or zero width. The proof reduces a hypothetical counterexample to the convex hull of at most six points. Varying the plank boundaries then forces six supporting inequalities, whose slopes satisfy a planar compatibility condition. A cubic identity in the three widths completes the proof. We also give nonparallel equality examples and describe several consequences for equality.
Citation
Brown Zaz. The affine plank theorem for three planks in the plane. 2026.
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