Results 1 to 2 of 2

Math Help - prove paraboloid is umbilic by unit vectors

  1. #1
    Newbie
    Joined
    Apr 2013
    From
    Los Angeles
    Posts
    10

    prove paraboloid is umbilic by unit vectors

    Prove that the point p=(0,0,0) on the paraboloid z= x + y is umbilic by computing k() for all unit vectors ∈ T_p(M)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Mar 2010
    From
    Beijing, China
    Posts
    293
    Thanks
    23

    Re: prove paraboloid is umbilic by unit vectors

    let u=(cost, sint, 0) be a tangent vector of the surface at 0, since 0 is a critical point.
    The curve cut by the normal plain through u is ( s cost, s sint, s^2), its tangent vector is T=(cost, sint, 2s), accelerator is A=( 0, 0, 2),
    since |T|=1 at 0, so A(0) is the curvature vector, and its length 2 is the curvature. It is constant for all t.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: February 15th 2013, 02:01 PM
  2. What are unit vectors used for and how?
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 19th 2011, 04:28 AM
  3. [SOLVED] Unit Vectors
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: April 23rd 2011, 01:00 PM
  4. Calculating parallel vectors to paraboloid
    Posted in the Calculus Forum
    Replies: 0
    Last Post: March 5th 2009, 06:10 PM
  5. unit vectors
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 4th 2008, 04:03 PM

Search Tags


/mathhelpforum @mathhelpforum