polar curve

Polar curves are plane curves in ${ℝ}^2$ that are expressed in polar coordinates $(r,\theta )$. The two simplest polar curves are obtained when one of the two coordinates is set to be a constant. If the first coordinate is set to a constant $r$, we have a circle with radius $|r|$, or a point when $r=0$. When the second coordinate is the constant instead, say $c$, we have a straight line through the (polar) origin, with slope = $\tan c$.

Using polar coordinates, one can generate many visually pleasingcurves. Below are some of the most popular ones.