# polar curve

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.

 Title polar curve Canonical name PolarCurve Date of creation 2013-03-22 15:17:08 Last modified on 2013-03-22 15:17:08 Owner CWoo (3771) Last modified by CWoo (3771) Numerical id 6 Author CWoo (3771) Entry type Example Classification msc 53A04 Classification msc 51-01 Synonym limaçon Related topic AreaOfPlaneRegion Related topic CassiniOval Defines lemniscate Defines rhodonea Defines cardioid Defines limacon