# Cylindrical coordinates

From AMS Glossary

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## cylindrical coordinates

(

*Also called*cylindrical polar coordinates, circular cylindrical coordinates.) A system of curvilinear coordinates in which the position of a point in space is determined by 1) its perpendicular distance from a given line, 2) its distance from a selected reference plane perpendicular to this line, and 3) its angular distance from a selected reference line when projected onto this plane.The coordinates thus form the elements of a cylinder, and, in the usual notation, are written

*r*, θ, and*z*, where*r*is the radial distance from the cylinder's*z*axis, and θ is the angular position from a reference line in a cylindrical cross section normal to the*z*axis. The relations between the cylindrical coordinates and the rectangular Cartesian coordinates (*x*, y,*z*) are*x*=*r*cos θ,*y*=*r*sin θ,*z*=*z*.*See also*polar coordinates.