I've just started looking at the axioms of 3D Geometry. The first one that I encountered is this one:
"Three non collinear points define a plane" or " Given three non collinear points, only one plane goes through them"
I know that it is an axiom and it is taken to be true but I don't understand the intuition behind it. I understand that if I take one point or any number of collinear points, then I can draw infinite planes just by rotating around the line that connects these points, but why do we need 3 non collinear points to define a plane, why not more? And why, given three non collinear points, does only one plane go through them? Why not two or three?