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Polar Graphs, Limaçons, Lemniscates, ...

Circles:
\[ r = r \] \[ r = a * cos \theta \] \[ r = a * sin \theta \]

Cardioids & Limaçons:
\[ r = a + b * cos \theta \] \[ r = a + b * sin \theta \]

Lemniscates:
\[ r = \sqrt{a^2 * cos (2 \theta)} \] \[ r = \sqrt{-a^2 * cos (2 \theta)} \] \[ r = \sqrt{a^2 * sin (2 \theta)} \] \[ r = \sqrt{-a^2 * sin (2 \theta)} \]

Rose curves:
\[ r = a * cos (n\theta) \]

Archimedes's spiral:
\[ r = a \theta \]