@article{Musielak_2020, title={Covering a reduced spherical body by a disk}, volume={72}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/6029}, DOI={10.37863/umzh.v72i10.6029}, abstractNote={<p>UDC 514</p> <p>In this paper, the following theorems are proved: (1) every spherical convex body $W$ of constant width $\Delta (W) \geq \dfrac{\pi}{2}$ may be covered by a disk of radius $\Delta(W) + \arcsin \!\left(\dfrac{2\sqrt{3 }{3} \cos \dfrac{\Delta(W)}{2}\right) - \dfrac{\pi}{2};$ (2) every reduced spherical convex body $R$ of thickness $\Delta(R)&lt;\dfrac{\pi}{2}$ may be covered by a disk of radius $\arctan \!\left(\sqrt{2} \tan \dfrac{\Delta(R)}{2}\right)\!.$</p> <p>&nbsp;</p&gt;}, number={10}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Musielak, M.}, year={2020}, month={Oct.}, pages={1400 - 1409} }