Wetzel's sector covers unit arcs
arXiv:1907.07351 · doi:10.13140/RG.2.2.24935.80807
Abstract
We settle J. Wetzel's 1970's conjecture and show that a 30{^\circ} circular sector of unit radius can accommodate every planar arc of unit length. Leo Moser asked in 1966 for the smallest (convex) region in the plane that can accommodate each arc of unit length. With area π/12, this sector is the smallest such set presently known. Moser's question has prompted a multitude of papers on related problems over the past 50 years, most remaining unanswered.
preprint (since 2017)