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 β in D a yin-yang line if βsplits D into two congruent perfect sets, βcrosses each concentric circle of D twice, β 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.

author list (cited authors)

  • Taras Banakh, .., Oleg Verbitsky, .., & Yaroslav Vorobets, ..

citation count

  • 1

publication date

  • January 2010