A Remark on the Odd Area of Unit Disks

Abstract

Let $F$ be a family of $n$ unit disks in $\mathbb{R}^2$ with $n$ being odd. We use $\mbox{OA}(F)$ to denote the area of the set of points that is covered by an odd number of disks. The purpose of this note is to disprove the conjecture $\mbox{OA}(F) \geq π$ which was suggested in the literature and to present some examples.