# Polar coordinates

The numbers and (see ) related to rectangular Cartesian coordinates and by the formulas:

where , . The coordinate lines are: concentric circles ( ) and rays ().

Figure: p073410a

The system of polar coordinates is an orthogonal system. To each point in the -plane (except the point for which and is undefined, i.e. can be any number ) corresponds a pair of numbers and vice versa. The distance between a point and (the pole) is called the polar radius, and the angle is called the polar angle. The Lamé coefficients (scale factors) are:

The surface element is:

The fundamental operations of vector analysis are:

The numbers and related to Cartesian rectangular coordinates and by the formulas:

where , , , , are called generalized polar coordinates. The coordinate lines are: ellipses () and rays ().

#### References

 [1] G.A. Korn, T.M. Korn, "Mathematical handbook for scientists and engineers" , McGraw-Hill (1961)