Why are divergence and curl called by those names?

[Vectronix]

Why is the divergence operation called the 'divergence?' What is the significance of this operation on a vector-valued function? And what about "the curl?" The curl seems self-explanatory (at least it does in electrodynamics), but I need someone to expound on 'the curl' as well.

 

[waht]

The divergence gives you flux density of a vector field. If it's positive in a region then the vector field spreads outward from itself. That's why it's called divergence.

And the curl is a sort of rotational density of a vector field. Curl is a vector whose magnitude is proportional to the strength of rotation of the vector field. Hence it's called curl.

 

[tiny-tim]

The divergence gives you flux density of a vector field. If it's positive in a region then the vector field spreads outward from itself. That's why it's called divergence.

Hi what! Hi Vectronix!

And, conversely, if the divergence is negative, then the field lines converge.

In particular, you get divergence round sources, and convergence round sinks.