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A Basic Differential Geometry Question

  1. Feb 7, 2013 #1
    Suppose x(t) is a curve in ℝ^2 satisfying x*x'=0 where * is the dot product. Show that x(t) is a circle.

    The hint says find the derivative of ||x(t)||^2 which is zero and doesn't tell me much.

    I was hoping for x*x= r, r a constant.
  2. jcsd
  3. Feb 7, 2013 #2


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    If the derivative of a function is constant zero. What can you tell about the original function?
  4. Feb 7, 2013 #3
    Oh my gosh I can't believe I even posted this question haha!..its a constant of course
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