Osculation Vertices in Arrangements of Curves

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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Document Details

Document Type
Technical Report
Publication Date
May 01, 1972
Accession Number
AD0744704

Entities

People

  • Branko Gruenbaum
  • Paul Erodoes

Organizations

  • University of Washington

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Bodies
  • Boundaries
  • Convex Bodies
  • Crossings
  • Families (Human)
  • Graph Theory
  • Inequalities
  • Literature
  • Mathematics
  • Military Research
  • New York
  • Number Theory
  • Numbers
  • Prime Numbers
  • Theorems
  • Universities

Readers

  • Graph Algorithms and Convex Optimization.
  • Marine Propulsion Engineering and Naval Architecture