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Article


Title

Diameter of reduced spherical convex bodies

Authors

Year of publication

2018

Published in

Fasciculi Mathematici

Journal year: 2018 | Journal number: nr 61

Article type

scientific article

Publication language

english

Keywords
EN
  • spherical convex body
  • spherical geometry
  • hemisphere
  • lune
  • width
  • constant width
  • thickness
  • diameter
Abstract

EN The intersection L of two different non-opposite hemispheres of the unit sphere S2 is called a lune. By Δ(L) we denote the distance of the centers of the semicircles bounding L. By the thickness Δ(C) of a convex body CS2 we mean the minimal value of Δ(L) over all lunes LC. We call a convex body RS2 reduced provided Δ(Z) < Δ(R) for every convex body Z being a proper subset of R. Our aim is to estimate the diameter of R, where Δ(R) < π/2, in terms of its thickness.

Pages (from - to)

103 - 108

DOI

10.1515/fascmath-2018-0020

License type

CC BY-NC-ND (attribution - noncommercial - no derivatives)

Full text of article

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Access level to full text

public

Points of MNiSW / journal

10.0

Points of MNiSW / journal in years 2017-2021

10.0

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