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Parallel of Least Radius

  1. Mar 13, 2007 #1
    1. The problem statement, all variables and given/known data
    Show that on of the hyperboloid of revolution x^2+y^2-z^2=1, the parallel of least radius is the line of striction, ...

    What's the parallel of least radius?
  2. jcsd
  3. Mar 14, 2007 #2


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    The "parallel of least radius" is the line, parallel to an axis, that is shortest from one point on the hyperboloid to another.

    Now, clear up my confusion: what is a "line of striction"?
  4. Mar 14, 2007 #3
    Given a ruled surface x(t,v)=a(t)+vw(t), a line of striction is a curve b(t) such that <b'(t),w'(t)>=0 for all t and b lies on the trace of x, ie b(t)=a(t)+u(t)w(t) for some real valued function u(t). It be can then shown that u(t) is given by


    The points of a line of striction are the "central points" of the ruled surface.
    Last edited: Mar 14, 2007
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