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Radius of curvature formula derivation

  1. Sep 4, 2005 #1
    for a curve defined by y=f(x) the radius of curvature is defined as
    [f""(x)/(1+f"(x))] power 3/2. I need a good neat & understandable derivation for that. can any body show a web.
  2. jcsd
  3. Sep 4, 2005 #2
    Differential Geometry of Curves

    I don't like the format of the forum reply, so click on the following link to view your derivative: DGC.
  4. Sep 4, 2005 #3
    Well first understand that curvature for a vector function is given by:


    Now, let r = xi + f(x)j and simplify. To prove the first formula [itex]\kappa[/itex], use the following fact and compute r' x r''. The answer should be clear from there.


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