Tarski's Plank Problem - Nomenclature

Nomenclature

The name for the problem, specifically for the sets of points between parallel hyperplanes, comes from the visualisation of the problem in R2. Here, hyperplanes are just straight lines and so planks become the space between two parallel lines. Thus the planks can be thought of as (infinitely long) planks of wood, and the question becomes how many planks does one need to completely cover a convex tabletop of minimal width w? Bang's theorem shows that, for example, a circular table of diameter d feet can't be covered by less than d planks of wood of width one foot each.