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arXiv · 1806.04246

Covering a reduced spherical body by a disk

Michał Musielak
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Abstract

In this paper, the following two theorems are proved: $(1)$ every spherical convex body $W$ of constant width $Δ(W) \geq \fracπ{2}$ may be covered by a disk of radius $Δ(W) + \arcsin \left( \frac{2\sqrt{3}}{3} \cdot \cos \frac{Δ(W)}{2}\right) - \fracπ{2}$; $(2)$ every reduced spherical convex body $R$ of thickness $Δ(R)<\fracπ{2}$ may be covered by a disk of radius $\arctan \left( \sqrt{2} \cdot \tan \frac{Δ(R)}{2}\right)$.

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Michał Musielak. 2018-06-11. Covering a reduced spherical body by a disk. https://arxiv.org/abs/1806.04246

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