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Curvature and Tangential angle

  1. Jun 30, 2010 #1
    In Differential Geometry by Heinrich Guggenheimer (if you have the book, the proof I am asking about is Theorem 2-19), he gives the angle between a chord through points s and s' and the tangent at s, as the integral of the curvature (with respect to arc length) from s' to s. I'm not sure how he got this, because I thought that the integral of curvature gave the angle between the tangent and the x-axis. Or maybe I'm not understanding something.
  2. jcsd
  3. Jun 30, 2010 #2
    It should be the angle between the tangents at the endpoints. (You can, of course, calculate the slope of the chord thereon).
  4. Jul 3, 2010 #3
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