Recent content by johngalt007

  1. J

    Graduate How is the four vertex theorem for convex figures proved?

    Lavinia, just to make sure that both of us are talking about the same thing, let me state the theorem from Do Carmo: The Four-Vertex Theorem: A simple closed convex curve has at least four vertices. Actually, I can kind of see that for a convex curve this line L should divide the curve in two...
  2. J

    Graduate How is the four vertex theorem for convex figures proved?

    Lavinia, I have attached a scan of that page containing the proof in Do Carmo's book. I understand the lemma. I also understand the first para of the proof of the theorem. I am a bit lost after that. First, I don't understand this: By convexity, and since p, q, r are distinct points on C, the...
  3. J

    Graduate How is the four vertex theorem for convex figures proved?

    I just began to read Do Carmo's Differential Geometry book and having breezed through most of the chapter 1, I am finding it difficult to see how the four vertex theorem for a convex figure is proved? Could someone please provide a simple and easy to understand proof?
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