Tarski's plank problem

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In mathematics, Tarski's plank problem is a question about coverings of convex regions in n-dimensional Euclidean space by "planks": regions between two hyperplanes. Tarski asked if the sum of the widths of the planks must be at least the minimum width of the convex region. The question was answered affirmatively by Thøger Bang (1950, 1951).

[edit] References

• Bang, Thøger (1950), “On covering by parallel-strips.”, Mat. Tidsskr. B.: 49-53, MR0038085 
• Bang, Thøger (1951), “A solution of the "plank problem"”, Proc. Amer. Math. Soc. 2: 990-993, MR0046672, <http://links.jstor.org/sici?sici=0002-9939%28195112%292%3A6%3C990%3AASOT%22P%3E2.0.CO%3B2-E>