Tarski's plank problem revisited

TL;DR

This paper surveys the historical and ongoing research on Tarski's plank problem in discrete geometry, highlighting its significance and unresolved questions in geometric coverings.

Contribution

It provides a comprehensive overview of Tarski's plank problem, its variants, and open research problems in the field of discrete geometry.

Findings

Continued interest in Tarski's plank problem over decades

Identification of key open problems in geometric coverings

Summary of recent developments and research directions

Abstract

In the 1930's, 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 planks in the present time as well. The paper is a survey type with a list of open research problems.