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).
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. Monthly101,
609-628, 1994.Tarski, A. "Further Remarks about the Degree of Equivalence
of Polygons." [Polish]. Odbitka Z. Parametru.2, 310-314, 1932.
