Directed packings of circles in the plane (original) (raw)

We consider sequential packings of families of circles in the plane whose curvatures are given as members of a sequence of non-negative real numbers. Each such packing gives rise to a sequence of circle centers that might diverge to infinity or remain bounded. We examine the behavior of the sequence of circle centers as a function of the growth rate of the sequence of curvatures. In several special cases we obtain explicit formulas for the coordinates of the limit, while in other cases we obtain accurate estimates.