On Tarski Plank Problem and its Discrete Analogues
Lenny Fukshansky · Scholarship - Claremont (Claremont Colleges) · 2008
In 1932 A. Tarski conjectured that if a convex body in R^N is covered by a finite collection of planks (strips of space between parallel hyperplanes), then the sum of widths of these planks must be at least the minimal width of the convex body. Tarski himself proved this conjecture for the case of a disc in R^2, and the general form of this conjecture was proved by T. Bang in 1951. Various generalizations of Tarski's problem have been studied by different authors more recently as well, for instance K. Ball in 1990 studied an interesting version of Tarski's problem in normed linear spaces. We will review some results in this area, and will also discuss certain discrete analogues of the Tarski plank problem.