Wetzel’s sector covers unit arcs
© 2020, Akadémiai Kiadó, Budapest, Hungary. We settle J. Wetzel’s 1970’s conjecture and show that a 30 ∘ circular sector of unit radius can accommodate every planar arc of unit length. Leo Moser asked in 1966 for the (convex) region with the smallest area in the plane that can accommodate each arc o...
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| Format: | Article |
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2020
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| Online Access: | https://repository.li.mahidol.ac.th/handle/123456789/57998 |
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| Institution: | Mahidol University |
| Summary: | © 2020, Akadémiai Kiadó, Budapest, Hungary. We settle J. Wetzel’s 1970’s conjecture and show that a 30 ∘ circular sector of unit radius can accommodate every planar arc of unit length. Leo Moser asked in 1966 for the (convex) region with the smallest area 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. |
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