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Tarski's Plank Problem

Given a circular table of diameter 9 feet, which is the minimal number of planks (each 1 foot wide and length greater than 9 feet) needed in order to completely cover the tabletop? Nine parallel planks suffice, but is there a covering using fewer planks if suitably oriented?

This proposition is tantamount to showing that a radial projection is area-preserving (King 1994).

It was solved by an ingenious argument of Bang (1950, 1951).

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References

Aharoni, R.; Holzman, R.; Krivelevich, M.; and Meshulam, R. "Fractional Planks." Disc. Comput. Geom. 27, 585-602, 2002.Bang, T. "On Covering by Parallel-Strips." Mat. Tidsskr. B, 49-53, 1950.Bang, T. "A Solution to the 'Plank Problem.' " Proc. Amer. Math. Soc. 2, 990-993, 1951.King, J. L. "Three Problems in Search of a Measure." Amer. Math. Monthly 101, 609-628, 1994.Tarski, A. "Further Remarks about the Degree of Equivalence of Polygons." [Polish]. Odbitka Z. Parametru. 2, 310-314, 1932.

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Tarski's Plank Problem

Cite this as:

Weisstein, Eric W. "Tarski's Plank Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TarskisPlankProblem.html