We prove the following theorems: (1) every spherical convex body W of constant width \( \varDelta (W)\ge \frac{\uppi}{2} \) can be covered by a disk of radius \( \varDelta (W)+\arcsin \left(\frac{2\sqrt{3}}{3}\cos \frac{\varDelta (W)}{2}\right)-\frac{\uppi}{2}; \) (2) every reduced spherical convex body R of thickness \( \varDelta (R)<\frac{\uppi}{2} \) can be covered by a disk of radius arctan \( \left(\sqrt{2}\tan \frac{\varDelta (R)}{2}\right). \)
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 10, pp. 1400–1409, October, 2020. Ukrainian DOI: 10.37863/umzh.v72i10.6029.
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Musielak, M. Covering of a Reduced Spherical Body by a Disk. Ukr Math J 72, 1613–1624 (2021). https://doi.org/10.1007/s11253-021-01875-5
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DOI: https://doi.org/10.1007/s11253-021-01875-5