# Spherical coordinates

The numbers which are related to the Cartesian coordinates by the formulas

where , , .

Figure: s086660a

The coordinate surfaces are (see Fig.): concentric spheres with centre ; half-planes that pass through the axis ; circular cones with vertex and axis . The system of spherical coordinates is orthogonal.

The Lamé coefficients are

The element of surface area is

The volume element is

The basic operations of vector calculus are

The numbers , called generalized spherical coordinates, are related to the Cartesian coordinates by the formulas

where , , , , . The coordinate surface are: ellipsoids , half-planes and elliptical cones .