Osculation Vertices in Arrangements of Curves
WASHINGTON UNIV SEATTLE DEPT OF MATHEMATICS
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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.
- Theoretical Mathematics