geometry-topology / Discrete Geometry, Coverings

Optimal Partial Plank Coverings

Given planks of fixed total width, how should they be placed to cover as much of a convex body's volume as possible? Karoly Bezdek asked whether, for a Euclidean ball, the optimum is a single plank centred at the origin. It is, and the paper also settles every planar convex body.

15Significance / 100
1Frontier events
0Verification tasks
0Recorded attempts

Temporal state

Current frontier

No reconciled state yet.

Append-only history

Frontier timeline

geometry-topologyJul 29, 2026Significance 15/100Registry: unreviewed

Optimal Partial Plank Coverings

Prior state unknownproved

Given planks of fixed total width, how should they be placed to cover as much of a convex body's volume as possible? Karoly Bezdek asked whether, for a Euclidean ball, the optimum is a single plank centred at the origin. It is, and the paper also settles every planar convex body.

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Research memory

Claims and attempts

Scoped claims

Source authenticated

Given planks of fixed total width, how should they be placed to cover as much of a convex body's volume as possible? Karoly Bezdek asked whether, for a Euclidean ball, the optimum is a single plank centred at the origin. It is, and the paper also settles every planar convex body.

Recorded attempts

Evidence graph

Connected research record

No public relationships recorded yet.