Fermat's Spiral and the Line Between Yin and Yang Academic Article uri icon


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

published proceedings


author list (cited authors)

  • Banakh, T., Verbitsky, O., & Vorobets, Y.

citation count

  • 2

complete list of authors

  • Banakh, Taras||Verbitsky, Oleg||Vorobets, Yaroslav

publication date

  • November 2010