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# 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.

Defines:

lemniscate, rhodonea, cardioid, limacon

Related:

AreaOfPlaneRegion, CassiniOval

Synonym:

lima\c{c}on

Type of Math Object:

Example

Major Section:

Reference

Parent:

Groups audience:

## Mathematics Subject Classification

53A04*no label found*51-01

*no label found*

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## Comments

## rhodonea curve

An error on http://planetmath.org/PolarCurve.html:

A rhodonea curve with two inner loops is labeled

"r = sin(t)." The label should read "r = sin(t/2)"

David Shively

frankshiv@yahoo.com