Geodesic
Sectorial Covers for Curves of Constant Length
Canadian mathematical bulletin, Tome 16 (1973) no. 3, pp. 367-375

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DOI

In answer to a question raised by Leo Moser, A. Meir proved some years ago that every plane arc of unit length lies in some closed semidisk of radius 1⁄2. His elegant, unpublished argument is reproduced here with his kind permission. 
Wetzel, John E. Sectorial Covers for Curves of Constant Length. Canadian mathematical bulletin, Tome 16 (1973) no. 3, pp. 367-375. doi: 10.4153/CMB-1973-058-8
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     title = {Sectorial {Covers} for {Curves} of {Constant} {Length}},
     journal = {Canadian mathematical bulletin},
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     year = {1973},
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     number = {3},
     doi = {10.4153/CMB-1973-058-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1973-058-8/}
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