caa a22 4500 605508356 CHVBK 20210128100636.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s00010-013-0237-3 doi (NATIONALLICENCE)springer-10.1007/s00010-013-0237-3 Lassak Marek Institute of Mathematics and Physics, University of Technology and Life Sciences, al. prof. Kaliskiego 7, 85-789, Bydgoszcz, Poland aut Width of spherical convex bodies [Elektronische Daten] [Marek Lassak] For every hemisphere K supporting a convex body C on the sphere S d we define the width of C determined by K. We show that it is a continuous function of the position of K. We prove that the diameter of every convex body $${C \subset S^d}$$ C ⊂ S d equals the maximum of the widths of C provided the diameter of C is at most $${\frac{\pi}{2}}$$ π 2 . In a natural way, we define spherical bodies of constant width. We also consider the thickness Δ(C) of C, i.e., the minimum width of C. A convex body $${R \subset S^d}$$ R ⊂ S d is said to be reduced if Δ(Z) < Δ(R) for every convex body Z properly contained in R. For instance, bodies of constant width on S d and regular spherical odd-gons of thickness at most $${\frac{\pi}{2}}$$ π 2 on S 2 are reduced. We prove that every reduced smooth spherical convex body is of constant width. The Author(s), 2013 Spherical convex body nationallicence Spherical geometry nationallicence Hemisphere nationallicence Supporting hemisphere nationallicence Lune nationallicence Width nationallicence Constant width nationallicence Thickness nationallicence Diameter nationallicence Reduced body nationallicence Extreme point nationallicence Aequationes mathematicae Springer Basel 89/3(2015-06-01), 555-567 0001-9054 89:3<555 2015 89 10 https://doi.org/10.1007/s00010-013-0237-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00010-013-0237-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Lassak Marek Institute of Mathematics and Physics, University of Technology and Life Sciences, al. prof. Kaliskiego 7, 85-789, Bydgoszcz, Poland aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/3(2015-06-01), 555-567 0001-9054 89:3<555 2015 89 10