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Umbilic points

  1. May 12, 2009 #1
    who can help me with this:

    on an ellipsoid most points are not umbilic, but there are some special places that are. Discuss how to find these points and their connection to lines of curvature.
     
  2. jcsd
  3. May 13, 2009 #2

    HallsofIvy

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    Staff Emeritus
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    What is the definition of "umbilic point"?
     
  4. May 13, 2009 #3
    an umbilic point is where the directional curvature is the same in all directions. for example, all points on a sphere are umbilic. I know the ellipsoid has four umbilic points but I need help in finding them.
     
  5. May 13, 2009 #4

    Mark44

    Staff: Mentor

    This umbilic concept is new to me, but based on your description, I would think that an ellipsoid could have as many as six such points: at the ends of each of the three axes, in the case where all three "radii" are unequal.
     
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