Visualization of k-forms

See xournal 054.
The key point int this file is that covectors are interpreted as:

grid lines
length measurement devices (linear)
equations (if we take the measurement device and ask ourselves about what vectors have length equal to zero)

Covectors or 1-forms in a 2D vector space can be seen like grid lines, in the same way that vectors can be seen like arrows.
In general, they are devices to "measure" vectors, in a linear way. It can be seen that they correspond to families of parallel $(n - 1)$ -planes, and the measurement is given by the number of crossings. This is the natural pairing between vectors and covectors.

On the other hand, a 2-form is a measurement device for 2-vectors (bivectors in Geometric Algebra). In $R^{3}$ they can visualized as flows of straight lines, and the measurement is given, again, by the crossing number. In general they are families of $(n - 2)$ -planes.

The wedge product of two 1-forms is a 2-form, and it has an interpretation in this context: it corresponds to the family of $(n - 2)$ -lines given by the intersection of the two families of $(n - 2)$ -planes.