1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    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

    [tex]u=-\frac{<a',w'>}{<w',w>}[/tex].

    The points of a line of striction are the "central points" of the ruled surface.
     
    Last edited: Mar 14, 2007
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Parallel of Least Radius
  1. Least Squares (Replies: 1)

  2. Least squares (Replies: 8)

  3. Least Squares (Replies: 3)

  4. Radius of Divergence (Replies: 8)

Loading...