Analogy

Dog on Leash Complex Analysis
  • tree
  • origin
  • man and dog return to starting point
  • z traverses a simple closed curve C
  • position of man
  • f(z) as z traverses C
  • position of dog
  • f(z)+g(z) as z traverses C
  • dog cannot reach tree
  • |g(z)| < |f(z)| for z on C
  • man and dog walk around tree
  • winding number of f and f+g
  • same number of times about origin are equal