@article {Banakh:2010-11-01T00:00:00:0002-9890:786,
author = "Banakh, Taras and Verbitsky, Oleg and Vorobets, Yaroslav",
title = "Fermat's Spiral and the Line Between Yin and Yang",
journal = "American Mathematical Monthly",
volume = "117",
number = "9",
year = "2010-11-01T00:00:00",
abstract = "Let *D* denote a disk of unit area. We call a set *A* ⊂ *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.",
pages = "786-800",
url = "http://www.ingentaconnect.com/content/maa/amm/2010/00000117/00000009/art00004",
doi = "doi:10.4169/000298910X521652"
}