Results 1 to 3 of 3

Math Help - Shortest distance

  1. #1
    Newbie
    Joined
    Sep 2012
    From
    North Carolina
    Posts
    22

    Shortest distance

    Hi every one

    There is a question that is bugging me since a while. I remember this to be very easy to do when I was studying Calculus, but since this was many years ago, I cant recall how to do.

    I tried to figure it myself, but no luck

    I looked in old books and google it, but with no luck.

    any way here is the question:


    Given two function f(x,y) and g(x,y), where f(x,y) don't intersect g(x,y) at any point.

    What is the shortest distance between the two functions and what is the equation of this shortest vector?

    If it is simpler to show with f(x) and g(x), do so ... If I get the idea I can probably find how to do with f(x,y) and g(x,y)


    I would really appreciate if you can take a minute and refresh my memory. Otherwise, I guess that this question will bug me for the rest of my life

    Thank you
    Last edited by LChenier; September 25th 2012 at 09:16 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2012
    From
    AZ
    Posts
    616
    Thanks
    97

    Re: Shortest distance

    Given two points (x_1,y_1,f(x_1,y_1)) and (x_2, y_2, g(x_2, y_2)), the distance D is equal to

    D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (g(x,y) - f(x,y))^2}

    Also,

    D^2 = (x_2 - x_1)^2 + (y_2 - y_1)^2 + (g(x,y) - f(x,y))^2

    Basically, minimizing D^2 is the same as minimizing D.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2012
    From
    North Carolina
    Posts
    22

    Re: Shortest distance

    Got it to work

    I knew that it was simple.

    Thank you
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Shortest distance
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: January 2nd 2012, 02:48 PM
  2. shortest distance
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 3rd 2009, 05:41 PM
  3. Shortest distance
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 16th 2009, 05:21 PM
  4. Shortest distance possible...
    Posted in the Calculus Forum
    Replies: 5
    Last Post: November 24th 2008, 11:02 PM
  5. shortest distance
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 16th 2007, 10:10 AM

Search Tags


/mathhelpforum @mathhelpforum