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 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