# cylindrical coordinates

*Cylindrical coordinates ^{}* are a system of coordinates for ${\mathbb{R}}^{3}$. Two of the coordinates correspond to the polar coordinates

^{}of ${\mathbb{R}}^{2}$, and the third coordinate corresponds with the $z$ axis. Thus, the coordinates are given by

$$\left(\begin{array}{c}\hfill x\hfill \\ \hfill y\hfill \\ \hfill z\hfill \end{array}\right)=\left(\begin{array}{c}\hfill r\mathrm{cos}\theta \hfill \\ \hfill r\mathrm{sin}\theta \hfill \\ \hfill z\hfill \end{array}\right),$$ |

where $r$ is the distance^{} from $(0,0,0)$ to $(x,y,0)$ and $\theta $ is the azimuthal angle defined for $\theta \in [0,2\pi )$.

Just as with polar coordinates, one can convert from Cartesian coordinates^{} to cylindrical coordinates for any point not lying on the $z$ axis via

$r(x,y)$ | $=$ | $\sqrt{{x}^{2}+{y}^{2}},$ | ||

$\theta (x,y)$ | $=$ | $\mathrm{arctan}(x,y),$ |

where $\mathrm{arctan}$ is defined here (http://planetmath.org/OperatornamearcTanWithTwoArguments).

Title | cylindrical coordinates |
---|---|

Canonical name | CylindricalCoordinates |

Date of creation | 2013-03-22 17:01:54 |

Last modified on | 2013-03-22 17:01:54 |

Owner | Wkbj79 (1863) |

Last modified by | Wkbj79 (1863) |

Numerical id | 6 |

Author | Wkbj79 (1863) |

Entry type | Definition |

Classification | msc 51M05 |

Related topic | PolarCoordinates |

Related topic | SphericalCoordinates |