Results 1 to 2 of 2

Math Help - The Shortest curve

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    1

    The Shortest curve

    want to prove that the lone segment[P,Q] is the shortest curve going from P to Q. Consider a piecewise differentiable curve y ,[IMG]file:///C:/DOCUME%7E1/libguest/LOCALS%7E1/Temp/moz-screenshot.jpg[/IMG] going from P to Q. We want to show that the euclidean length (y) is greater than or equal to the euclidean length ([P,Q]) of the line segment [P,Q].

    a. First consider the case where P= (X0,Y0) and Q= (X0,Y1) sit on the same vertical line of equation X= X0. Show hat the euclidean length is greater than or equal to
    lY1-Y0 l = euclidean length([P,Q])




    This problem has been racking my brains. Any help will greatly be appreciated




























    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,583
    Thanks
    1418
    That is a standard "Calculus of Variations" problem.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. shortest path
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: January 5th 2009, 11:03 AM
  2. xyz^2=5 shortest distance
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 27th 2008, 11:34 AM
  3. z=xy+1 shortest distance
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 28th 2007, 07:22 PM
  4. shortest distance
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: December 18th 2006, 08:48 AM
  5. The Shortest Time
    Posted in the Algebra Forum
    Replies: 2
    Last Post: September 8th 2005, 07:03 PM

Search Tags


/mathhelpforum @mathhelpforum