# 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…
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In this paper we show that a spherical convex body C is of constant diameter τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}
• M. Lassak
• Materials Science
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After a few claims about lunes and convex sets on the d-dimensional sphere Sd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}
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The intersection $L$ of two different non-opposite hemispheres of the unit sphere $S^2$ is called a lune. By $\Delta (L)$ we denote the distance of the centers of the semicircles bounding $L$. By the
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We present a survey on the geometry of convex bodies on the d-dimensional sphere S. We concentrate on the results based on the notion of the width of a convex body C ⊂ S determined by a supporting
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In this paper we show that a spherical convex body C is of constant diameter $$\tau$$ τ if and only if C is of constant width $$\tau$$ τ , for $$0<\tau <\pi$$ 0 < τ < π . Moreover, some
After a few claims about lunes and convex sets on the d -dimensional sphere $$S^d$$ S d we present some relationships between the diameter, width and thickness of reduced convex bodies and bodies of
We present some relationships between the diameter, width and thickness of a reduced convex body on the $d$-dimensional sphere. We apply the obtained properties to recognize if a Wulff shape in the

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