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

172 Problems of Chapter 2
Let us now prove that We give first a not strictly exact,
but nice, proof called ‘the lady with her little dog’. From the result of
Problem 266 we obtain that if then
Note that Thus for
When covers once the circle of radius the point (the
‘lady’) covers the circle of radius R times. Since
the point (‘the little dog’) cannot remain farther than R/10
from the lady. But thus if the lady turns times around the point
along a circle of radius R, her dog is also obliged to go times around
the point (Figure 63). It follows that
FIGURE 63
A more exact proof of the equality can be obtained in the