# Difference between revisions of "Spherical coordinates"

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− | '''Spherical coordinates''' are a way to describe the location of a point in three-dimensional space based on | + | '''Spherical coordinates''' are a way to describe the location of a point in three-dimensional space based on <math>r</math>, the distance from the origin (where <math>x=y=z=0</math>); <math>\theta</math>, the angle between the point and the x-z plane (in the positive x direction); and <math>\phi</math>, the angle between the point and the z axis (in the positive z direction). Thus, each point is described by: <math>(r, \theta, \phi)</math>. |

− | In a sense, | + | In a sense, spherical coordinates are coordinates on a [[sphere]] just like [[polar coordinates]] are coordinates on a [[circle]]. |

The equations converting the parameters are as follows: | The equations converting the parameters are as follows: | ||

:<math>r^2 = x^2 + y^2 + z^2</math> | :<math>r^2 = x^2 + y^2 + z^2</math> | ||

− | :x=r | + | :<math>x = r \sin{\theta} \cos{\phi}</math> |

− | :y=r | + | :<math>y = r \cos{\theta} \sin{\phi} |

− | :z=r | + | :<math>z = r \cos{\phi}</math> |

+ | The Jacobian in spherical polar coordinates is <math>r^2 \sin{\theta}</math> so that <math>\text{d}x \, \text{d}y \, \text{d}z = r^2 \sin{\theta} \, \text{d}r \, \text{d} \theta \, \text{d} \phi</math>. | ||

[[Category:Mathematics]] | [[Category:Mathematics]] | ||

[[Category:Geometry]] | [[Category:Geometry]] |

## Latest revision as of 14:13, 14 December 2016

**Spherical coordinates** are a way to describe the location of a point in three-dimensional space based on , the distance from the origin (where ); , the angle between the point and the x-z plane (in the positive x direction); and , the angle between the point and the z axis (in the positive z direction). Thus, each point is described by: .

In a sense, spherical coordinates are coordinates on a sphere just like polar coordinates are coordinates on a circle.

The equations converting the parameters are as follows:

The Jacobian in spherical polar coordinates is so that .