Cylindrical coordinates

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Cylindrical coordinates refers to a three-dimensional coordinate system used to describe the location of a point in space based on the distance from the origin in the x-y plane , the angle measured in the x-y plane between the point and the x axis , the distance perpendicular to the x-y plane:

In a sense, cylindrical coordinates are polar coordinates with a third dimension added: correspond to the polar coordinates for . This is in contrast to spherical coordinates, where is replaced by an angle, just like x and y are in polar coordinates.

The equations converting the parameters are as follows:

In cylindrical coordinates, the Jacobian is so that .