Fermat's Spiral and the Line Between Yin and Yang
2010
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.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
14
References
6
Citations
NaN
KQI