# 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} }

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…

## 8 Citations

### Constant diameter and constant width of spherical convex bodies

- Materials ScienceAequationes mathematicae
- 2020

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}…

### Diameter, width and thickness of spherical reduced convex bodies with an application to Wulff shapes

- Materials ScienceBeiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
- 2019

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}…

### Diameter of reduced spherical convex bodies

- Mathematics
- 2018

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…

### Several problems on reduced spherical polygons of thickness less than {\pi}/2

- Mathematics
- 2022

: The present paper aims to solve some problems proposed by Lassak about the reduced spherical polygons. The main result is to show that the regular spherical n -gon has the minimal perimeter among…

### Spherical Geometry—A Survey on Width and Thickness of Convex Bodies

- MathematicsSurveys in Geometry I
- 2022

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…

### Constant diameter and constant width of spherical convex bodies

- MathematicsAequationes mathematicae
- 2020

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…

### Diameter, width and thickness of spherical reduced convex bodies with an application to Wulff shapes

- Mathematics
- 2019

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…

### Application of spherical convex bodies to Wulff shape

- Mathematics
- 2019

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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