Width of spherical convex bodies
| LEADER | caa a22 4500 | ||
|---|---|---|---|
| 001 | 605508356 | ||
| 003 | CHVBK | ||
| 005 | 20210128100636.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20150601xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00010-013-0237-3 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-013-0237-3 | ||
| 100 | 1 | |a Lassak |D Marek |u Institute of Mathematics and Physics, University of Technology and Life Sciences, al. prof. Kaliskiego 7, 85-789, Bydgoszcz, Poland |4 aut | |
| 245 | 1 | 0 | |a Width of spherical convex bodies |h [Elektronische Daten] |c [Marek Lassak] |
| 520 | 3 | |a 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. | |
| 540 | |a The Author(s), 2013 | ||
| 690 | 7 | |a Spherical convex body |2 nationallicence | |
| 690 | 7 | |a Spherical geometry |2 nationallicence | |
| 690 | 7 | |a Hemisphere |2 nationallicence | |
| 690 | 7 | |a Supporting hemisphere |2 nationallicence | |
| 690 | 7 | |a Lune |2 nationallicence | |
| 690 | 7 | |a Width |2 nationallicence | |
| 690 | 7 | |a Constant width |2 nationallicence | |
| 690 | 7 | |a Thickness |2 nationallicence | |
| 690 | 7 | |a Diameter |2 nationallicence | |
| 690 | 7 | |a Reduced body |2 nationallicence | |
| 690 | 7 | |a Extreme point |2 nationallicence | |
| 773 | 0 | |t Aequationes mathematicae |d Springer Basel |g 89/3(2015-06-01), 555-567 |x 0001-9054 |q 89:3<555 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-013-0237-3 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00010-013-0237-3 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Lassak |D Marek |u Institute of Mathematics and Physics, University of Technology and Life Sciences, al. prof. Kaliskiego 7, 85-789, Bydgoszcz, Poland |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer Basel |g 89/3(2015-06-01), 555-567 |x 0001-9054 |q 89:3<555 |1 2015 |2 89 |o 10 | ||