Covering a reduced spherical body by a disk

• Date: 2020
• Main Author: Musielak, M.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2020
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/6029
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 514 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...