Abstract
Abstract : One of the fundamental differences between arrangements of lines (or similar linear patterns) and arrangements of curves is the possibility of osculation vertices in arrangements of the latter kind. Bounds are obtained for the number of osculation vertices in three types of arrangements: Appollonian, that is such in which all vertices are osculation vertices; general arrangements of circles; arrangements of circles. The topic has connections to packing problems, as well as to graph theory and the theory of numbers.
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