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.