Polar curves are plane curves in $\mathbb{R}^{2}$ 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 $\lvert r\rvert$, 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 pleasing curves. Below are some of the most popular ones.