Abstract
In the 1930s, A.Tarski introduced his plank problem at a time when the field discrete geometry was about to born. It is quite remarkable that Tarski’s question and its variants continue to generate interest in the geometric and analytic aspects of coverings by cylinders in the present time as well. This chapter surveys plank theorems, covering convex bodies by cylinders, Kadets–Ohmann-type theorems and investigates partial coverings of balls by planks.
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Bezdek, K. (2013). Coverings by Cylinders. In: Lectures on Sphere Arrangements – the Discrete Geometric Side. Fields Institute Monographs, vol 32. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8118-8_7
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DOI: https://doi.org/10.1007/978-1-4614-8118-8_7
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