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There are two different definitions of the polar angle. In the plane, the polar angle theta is the counterclockwise angle from the x-axis at which a point in the xy-plane ...

A divergenceless field can be partitioned into a toroidal and a poloidal part. This separation is important in geo- and heliophysics, and in particular in dynamo theory and ...

The study of harmonic functions (also called potential functions).

A group of four elements, also called a quadruplet or tetrad.

The distance from the center of a circle to its perimeter, or from the center of a sphere to its surface. The radius is equal to half the diameter.

A function whose range is in the real numbers is said to be a real function, also called a real-valued function.

A scalar is a one-component quantity that is invariant under rotations of the coordinate system.

A map f:R^n|->R which assigns each x a scalar function f(x).

In an exterior algebra ^ V, a top-dimensional form has degree n where n=dimV. Any form of higher degree must be zero. For example, if V=R^4 then alpha=e_1 ^ e_2 ^ e_3 ^ e_4 ...

A group of three elements, also called a triad. A triple is therefore a 3-tuple.