I am taking the geometry approach. We know from intuition that more than three legs on a chair will make it unstable if any of the legs have a different length than the others. So by "wobble" I mean the possibility that at least one of the legs will be in the air when one or more legs are made shorter/longer than others. Also, the "surface" must be perfectly flat.
A three legged chair is unaffected by any amount of change we make to its legs. So to prove this I started out connecting lines between each legs (diagonals). So far I haven't made any progress.
For a triangle there are no diagonals. Is it enough to show that all the legs must be in the same plane for the chair to be stable?