Maximum area covered by planks of fixed total width
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For a planar convex body K and 0<W<width(K), can any finite collection of planks with total width at most W cover more area of K than the best single plank of width W?
Why it matters and what counts as progress
Why it matters: This extends plank covering from the question of covering the whole body to an optimal partial-area problem.
What counts as progress: A single-plank optimality theorem for every planar convex body, extending the known triangle cases, or a body and plank family violating it.
How the problem developed
- 29 Jul 2026 · Proof [1]
Egor Bakaev and Alexander Polyanskii Answered the planar question affirmatively for every convex body, with an optimal covering by one plank.
AI contribution
Optimal partial plank coverings
For any planar convex body K and 0<W<width(K), one plank of width W covers at least as much area of K as any finite family of planks whose total width is at most W. The assessed AI-associated result is this planar reduction.
Sources
Website timeline
Publication dates and editorial changes.
Bakaev and Polyanskii report one-plank optimality in the plane