1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Differential Gemoetry

  1. Jan 31, 2009 #1
    Describe the one sheeted hyperboloid as a ruled surface, that is find vector functions [itex]\vec{z},\vec{p}:\mathbf{R} \rightarrow \mathbf{R}^{3} [/itex] such that

    [itex]\vec{x}(u,\nu)=\vec{z}(u)+\nu \vec{p}(u)[/itex] parameterises the hyperboloid.

    Hint:Let [itex]\vec{z}(u)[/itex] parameterise the circle [itex]x^2+y^2=1[/itex]in the [itex]z=0[/itex] plane.

    So far I've established [itex]\vec{z}(u)= \left[ \begin {array}{c} \cos \left( u \right) \\\noalign{\medskip}
    \sin \left( u \right) \\\noalign{\medskip}0\end {array} \right] [/itex] which is pretty obvious. Any ideas on what to do next? Thanks in advance
     
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted