# Forms¶

Forms are used in many contexts of relativity. It might be difficult to visualize a general n-form, 1-form, on the other hand, carries a simple geometrical meaning even to physicists.

1-form can be viewed as the dual space of vectors. In many textbooks, vectors are named as contravariant vectors. In any case, **vectors are visualized using arrows**.

By definition, contraction of 1-form \(\tilde \omega\) and a vector \(v^a\) should result in a number. In the field of relativity, we talk about real fields, so

A 1-form maps a vector to a real number. From this point of view, 1-form is a set of contour lines. Given this set of contour lines, it maps an arrow to a number.