In Euclidean space, given any two points, the vector connecting them can be characterized by length (distance) and direction (bearing). Now I am only interested in the bearing part. And I found it is inconvenient to analyze the bearing property because in Euclidean space distance is always involved in the analysis.
Is there a space I can map the Euclidean space to so that I can analyze the bearing between any two points better? Say some kind of projection space or something, I don't know. Any suggestions?
Here is an example. Consider a triangle in Euclidean space. What I am interested is the shape, i.e., interior angles of the triangle. I don't care the scale, i.e., length of the sides. How can I map this triangle into another space where I need not care the distance?