Results 1 to 4 of 4

Math Help - Interesting Word Problem

  1. #1
    Newbie
    Joined
    Jun 2010
    Posts
    4

    Interesting Word Problem

    My professor gave this word problem to us and I can't seem to navigate through all of the directions and hints to understand how to do it. I do know for sure he expects us to use the Intermediate Value Theorem.

    Prove that at any instant of time, there are two antipodal points (two
    points whose midpoint is the center of the earth) on the equator with the
    same temperature, assuming that temperature changes continuously with
    the points on earth.
    Hints
    Picture the equator as a unit circle and set up a coordinate system. Consider
    a point P on the circle. We can represent the point P by the angle theta
    between the line connecting the origin to the point P and the positive x-axis.
    This way, the points on the equator may be labeled by angles theta in [0, 2pi].
    Interesting Word Problem-circtxt.png
    Attached Thumbnails Attached Thumbnails Interesting Word Problem-circex.png  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Ruun's Avatar
    Joined
    Mar 2009
    From
    North of Spain
    Posts
    129
    Thanks
    13
    Consider T is a continuos function:

    f(0) = T(0) - T(\pi) \neq 0, thus f(0) < 0 or f(0) > 0. Now f(\pi) = T(\pi) - T(0) = -f(0) wich will be either positive or negative. In any case, 0 \in (f(0),f(\pi)) so by the Intermediate Value Theorem \exists c \in (0, \pi) : f(c) = 0
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jun 2010
    Posts
    4
    Honestly, I don't understand what is going on. It could be because of how it's presented but I am not sure between conclusions that have been made. Thanks for the help anyway. The general idea is so intuitive to me that I am having trouble understanding the necessity of the steps involved in proving it. I have always been bad with proofs haha.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member Ruun's Avatar
    Joined
    Mar 2009
    From
    North of Spain
    Posts
    129
    Thanks
    13
    I probably should considered two cases, first if f(0) < 0 and then if f(0)>0. In the first case will be f(\pi)>0 and in the second f(\pi)<0. Note that f(0) \neq 0 . In both cases we showed that the function changes it sign, so by the Intermediate value Theorem we are done.

    The point is to show that f(\theta) satifies the Intermediate Value Theorem hypothesis, and that it changes sign. thus it has, at least one root ( c \in (0, \pi) : f(c) = 0)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Interesting Problem, Please Help
    Posted in the Math Puzzles Forum
    Replies: 13
    Last Post: August 5th 2010, 03:27 AM
  2. interesting problem
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: June 3rd 2010, 05:15 AM
  3. Interesting Problem
    Posted in the Statistics Forum
    Replies: 0
    Last Post: May 15th 2009, 09:10 AM
  4. very interesting problem!!!
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: February 26th 2009, 03:00 PM
  5. an interesting word problem.
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: April 1st 2006, 08:52 PM

Search Tags


/mathhelpforum @mathhelpforum