I'm pretty sure this is a graph theory problem :
I'm trying to figure out a formula for the number of triangles that can be created from n distinct points in the (Euclidean) Plane such that no 2 lines cross each other (if a formula is possible).
For my purposes, we can assume that no 3 points are on the same line, and of course, we can assume n > 2. Also, points, and lines, can be used for more than 1 triangle, but, as mentioned, lines cannot cross.
Is there a formula for this?
Also, a related question : Given those n points, and the triangles formed by them, is there a formula to find the number of distinct segments forming those triangles? (So, for 2 triangles that share 1 side, there are 5 segments, etc.)
Thanks in advance!