# 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 $|r|$, 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 = $\mathrm{tan}c$.

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 |