Abstract
A zone of half-width w on the unit sphere S 2 in Euclidean 3-space is the parallel domain of radius w of a great circle. L. Fejes Tóth raised the following question in [6]: what is the minimal w n such that one can cover S 2 with n zones of half-width w n ? This question can be considered as a spherical relative of the famous plank problem of Tarski. We prove lower bounds for the minimum half-width w n for all n ≧ 5.
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Fodor, F., Vígh, V. & Zarnócz, T. Covering the sphere by equal zones. Acta Math. Hungar. 149, 478–489 (2016). https://doi.org/10.1007/s10474-016-0613-2
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DOI: https://doi.org/10.1007/s10474-016-0613-2