curl (vector) proof

In vector calculus in three-dimensional space, curl (also named: rotor) is a vector operator that shows a vector field's "rotation"; that is, the direction of the axis of rotation and the magnitude of the rotation. It can also be described as the circulation density.

"Rotation" and "circulation" represents variations of the vector function with respect to position, regardless of any variation over time.

A vector field which has zero curl everywhere is called irrotational.

The alternative terminology rotor and alternative notation are often used (especially in many European countries) for curl and .

This is purely a mathematics problem. Why not put it into the maths forum?