Name
Abstract | ||
|---|---|---|
Let D denote a disk of unit area. We call a set A subset of 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 beta in D a 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 the unique yin-yang line in the class of smooth curves algebraic in polar coordinates. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.4169/000298910X521652 | AMERICAN MATHEMATICAL MONTHLY |
Keywords | Field | DocType |
polar coordinate | Reflection symmetry,Spiral,Combinatorics,Concentric,Algebraic number,Smooth curves,Mathematical analysis,Polar coordinate system,Fermat's Last Theorem,Congruence (geometry),Mathematics | Journal |
Volume | Issue | ISSN |
117 | 9 | 0002-9890 |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Taras O. Banakh | 1 | 9 | 7.24 |
| Oleg Verbitsky | 2 | 191 | 27.50 |
| Yaroslav Vorobets | 3 | 11 | 1.72 |