Covering a reduced spherical body by a disk
DOI:
https://doi.org/10.37863/umzh.v72i10.6029Keywords:
spherical convex body, spherical geometry, hemisphere, lune, width, thickness, diskAbstract
UDC 514
In this paper, the following theorems are proved: (1) every spherical convex body W of constant width Δ(W)≥π2 may be covered by a disk of radius Δ(W)+arcsin(2√33cosΔ(W)2)−π2; (2) every reduced spherical convex body R of thickness Δ(R)<π2 may be covered by a disk of radius arctan(√2tanΔ(R)2).
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