Newton numbers for overlapping circular discs (Q2754995)

The authors consider the maximum possible number \(N(d)\) of neighbours of a disc in a family of unit circular discs in the plane where \(d\) represents the infimum of the distances between any two circle centers. They determine \(N(d)\) for \(1<d \leq 2\). They also determine the maximum positive number \(D_n\) such that \(N(d)\geq n\) for \(d\leq D_n\) (\(6\leq n \leq 18\)) and present the extremal configurations.