Abel's theorem in problems and solutions - School of Mathematics

70 Chapter 2
turn around the point if: a) b) c)
where d) where is the conjugate
of
DEFINITION. Suppose that a continuous curve C with the equation
does not pass through the point We thus say that the
curve C turns times around the point if the curve with equation
turns times around the point (Figure 23).
FIGURE 23
Consequently to define the number of turns of a curve around the
point we have to look at the rotation of the vector i.e.,
the vector joining points and (cf., 221).
259. How many times do the curves described in Problem 256 turn
around the point
260. Let and be the equations of two curves and
not passing through the point Let the variations of the argument
along these curves be equal, respectively, to and What is the
variation of the argument along the curve C with the equation if: a)
b)