• DOI:10.1007/s11253-021-01875-5
• Corpus ID: 54505508

Covering of a Reduced Spherical Body by a Disk

@article{Musielak2018CoveringOA,
  title={Covering of a Reduced Spherical Body by a Disk},
  author={Michał Musielak},
  journal={Ukrainian Mathematical Journal},
  year={2018},
  volume={72},
  pages={1613 - 1624}
}

• M. Musielak
• Published 11 June 2018
• Mathematics
• Ukrainian Mathematical Journal

We prove the following theorems: (1) every spherical convex body W of constant width ΔW≥π2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \varDelta (W)\ge \frac{\uppi}{2} $$\end{document} can be covered by a disk of radius ΔW+arcsin233cosΔW2−π2;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \varDelta (W)+\arcsin \left(\frac{2\sqrt{3}}{3}\cos \frac{\varDelta (W)}{2}\right)-\frac{\uppi}{2}; $$\end{document} (2) every reduced spherical convex body R of thickness ΔR<π2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \varDelta (R)<\frac{\uppi}{2} $$\end{document} can be covered by a disk of radius arctan 2tanΔR2.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left(\sqrt{2}\tan \frac{\varDelta (R)}{2}\right). $$\end{document}