In mathematics, the pyjama problem asks whether the plane can be covered by a finite number of rotated copies of a repeating pattern of stripes ("pyjama stripes"), no matter how thin the stripes are. The problem was posed in 2006 by Alex Iosevich, Mihail Kolountzakis, and Máté Matolcsi. A preliminary version appeared on arXiv.org on 26 November 2006. It was answered in the affirmative by Freddie Manners in 2015, using an analogy with Furstenberg’s ×2, ×3 Theorem.
Quantitative bounds Let be the pyjama stripe of width . Noah Kravitz and James Leng proved that rotations of about the origin are sufficient to cover , hence obtaining an explicit upper bound for the pyjama problem. It remains an open problem to obtain lower bounds for the pyjama problem beyond the trivial volume preserving bound of .
See also Affine plank problem, on covering a constant body by stripes of small total relative width Tarski's plank problem, on covering bounded sets by stripes
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