Here's the familiar yin-yang figure in a circle of radius 1.
If you continue subdividing the diameter of the large circle into
semicircles, this wavy line approaches the diameter as a limit.
It's tempting to say that this wavy line then has a length
of 2, but of course, its length is still π. Starting at the top and
moving downward, any path (mix and match) also has length π.
- idea from “Wheels, Life and other Mathematical Amusements“,
by Martin Gardner, pg 54
