Perhaps a one-form might best be described by telling what it does.
A vector and a one-form in a dot product form a scalar.
A vector of 5 and a one-form of 4 dot product to a scalar of 20.
If we choose to use blue line graph paper, then we can make the choice to draw an arrow devil have a length of 5 blue lines. I told once we are told that the 1 – form is for, will do something like put equally spaced marks Honda Vector such that there are four Marc’s between adjacent blue lines. After this is done we will see 20 marks on the vector.
You should notice that we have two different scalenes in the story. Our first scaling was created by the blue lines of the graph paper. Our second scaling was done by markings related to the blue lines. Maybe the blue lines were inches and we make a choice for the markings to be centimeters.
If we are just working on the line we are working with the simplest possible case, and it’s a good place to start. If we rotate our perspective through an angle, taking us off the line, we will have curvature.
In fact, for our one-form to serve in the calculation of distance, we will need to replace the number with the one-form of the function. It was a function all along; we have to change the angle to become aware the function. (Hint: if you only work with 0 degrees and 90 degrees, the fact that it’s a function can remain hidden.)
Vectoreverything 