Fermat’s Spiral and the Line Between Yin and Yang
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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, ..