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!

Parametrising a surface

  1. Oct 30, 2008 #1
    Hi there!

    I´ve come upon the following problem: I want to determine the set of all lines of the following surface:

    [tex]x_1^2+x_2^2-x_3^2=1[/tex]

    Here´s my idea: if one could determine one line parametrised by an angle and a radius, one could define the whole surface as rotation of this line over the x_3-axis. One can write every point of the surface as [tex]rcos\phi,rsin\phi,\sqrt{r^2-1}[/tex] where r is supposed to be the vector of any circle, got by a slice, parallel to the x_1x_2-plane

    We then go to the otherside of the x_1x_2-plane, to get (by symmetry) onother circle with radius of the same length. If we define another point on it, it will be of the form [tex]rcos\psi,rsin\psi,-\sqrt{r^2-1}[/tex].

    I claim (by intuition) that the phase difference between the angles will be constant for every line, but I cannot prove it :(

    Can someone please help me, or give me a hint?

    Thanks a lot in advance, Marin
     
  2. jcsd
  3. Oct 31, 2008 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi Marin! :smile:

    Hint: find the lines that go through (1,0,0). :wink:
     
  4. Nov 1, 2008 #3
    thanks, tiny-tim, it works :) But waht about my claim "the phase difference between the angles will be constant for every line" ? How can I find out if it is right?
     
  5. Nov 1, 2008 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi Marin! :smile:

    I honestly can't see the difficulty …

    just calculate where the line through (1,0,0) meets the two planes z = ±a constant. :wink:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Parametrising a surface
Loading...