publication . Preprint . Article . Other literature type . 2018

Spherical bodies of constant width

Lassak, Marek; Musielak, Michał;
Open Access English
  • Published: 09 May 2018
Abstract
The intersection L of two different non-opposite hemispheres G and H of the d-dimensional unit sphere $$S^d$$ is called a lune. By the thickness of L we mean the distance of the centers of the $$(d-1)$$ -dimensional hemispheres bounding L. For a hemisphere G supporting a convex body $$C \subset S^d$$ we define $$\mathrm{width}_G(C)$$ as the thickness of the narrowest lune or lunes of the form $$G \cap H$$ containing C. If $$\mathrm{width}_G(C) =w$$ for every hemisphere G supporting C, we say that C is a body of constant width w. We present properties of these bodies. In particular, we prove that the diameter of any spherical body C of constant width w on $$S^d$$...
Subjects
free text keywords: Mathematics - Metric Geometry, 52A55, Applied Mathematics, General Mathematics, Discrete Mathematics and Combinatorics, Lune, Spherical body, Unit sphere, Combinatorics, Convex function, Mathematical analysis, Pi, Convex body, Mathematics

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publication . Preprint . Article . Other literature type . 2018

Spherical bodies of constant width

Lassak, Marek; Musielak, Michał;