A note and a short survey on supporting lines of compact convex sets in   the plane
  After surveying some known properties of compact convex sets in the plane, we give a two rigorous proofs of the general feeling that supporting lines can be slide-turned slowly and continuously. Targeting a wide readership, our treatment is elementary on purpose. 
G\'abor Cz\'edli and L\'aszl\'o L. Stach\'o
math.CO math.MG