Covering a reduced spherical body by a disk

M. Musielak

doi:10.37863/umzh.v72i10.6029

M. Musielak Univ. Sci. and Technology, Bydgoszcz, Poland

DOI: https://doi.org/10.37863/umzh.v72i10.6029

Ключові слова: spherical convex body, spherical geometry, hemisphere, lune, width, thickness, disk

Анотація

UDC 514

Покриття редукованого сферичного тiла диском

У цій статті доведено такі теореми: (1) кожне редуковане сферичне тіло $W$ сталої ширини $\Delta (W) \geq \dfrac{\pi}{2}$ можна покрити диском радіуса $\Delta(W) + \arcsin \!\left(\dfrac{2\sqrt{3}}{3} \cos \dfrac{\Delta(W)}{2}\right) - \dfrac{\pi}{2};$ (2) кожне редуковане сферичне тіло $R$ товщини $\Delta(R)<\dfrac{\pi}{2}$ можна покрити диском радіуса $\arctan \!\left(\sqrt{2} \tan \dfrac{\Delta(R)}{2}\right)\!.$

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