  Let $D$ denote a disk of unit area. We call a subset $A$ of $D$ perfect if it
has measure 1/2 and, with respect to any axial symmetry of $D$, the maximal
symmetric subset of $A$ has measure 1/4. We call a curve $\beta$ in $D$ an
yin-yang line if
  $\beta$ splits $D$ into two congruent perfect sets,
  $\beta$ crosses each concentric circle of $D$ twice,
  $\beta$ crosses each radius of $D$ once.
  We prove that Fermat's spiral is a unique yin-yang line in the class of
smooth curves algebraic in polar coordinates.
