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Math Help - weird topology question...

  1. #1
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    weird topology question...

    hmm... it seems like we are supposed to use the intermediate value theorem... but we run into some errors... here's the question:

    a monk takes from 6 am to 6 pm to climb to the peak of a mountain of height M. climb sarts at the base of the montain. the next day, monk spends from 6 am to 6 pm to come down and reach the base. is there a time of day on which the monk is at the same height n day 1 and day 2? prove ur findings.
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by squarerootof2 View Post
    hmm... it seems like we are supposed to use the intermediate value theorem... but we run into some errors... here's the question:

    a monk takes from 6 am to 6 pm to climb to the peak of a mountain of height M. climb sarts at the base of the montain. the next day, monk spends from 6 am to 6 pm to come down and reach the base. is there a time of day on which the monk is at the same height n day 1 and day 2? prove ur findings.
    let d_1(t) be the monks distance from the bottom to the peak as a function of time on the first day.

    let d_2(t) be the distance from the bottom on day 2

    let D be the distance from the peak to the bottom then

    d_1(0)=0 \mbox{ and } d_1(12)=D


    d_2(0)=D \mbox{ and } d_1(12)=0

    define f(t)=d_1(t)-d_2(t)

    f(0)=0-D and f(12)=D-0

    by the intermediate value theorem there exits a c such that
     <br />
f(c)=0 \iff d_1(c)-d_2(c)=0 \iff d_1(c)=d_2(c)<br />

    QED
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by squarerootof2 View Post
    prove ur findings.
    [Pet Peeve]I know this is a kind of non-sequitur but how the heck can you be in a Topology class and type the word "ur?" It just boggles my mind.[/Pet Peeve] (Maybe I'm just exceptionally sensitive tonight.)

    -Dan
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  4. #4
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    Quote Originally Posted by topsquark View Post
    [Pet Peeve]I know this is a kind of non-sequitur but how the heck can you be in a Topology class and type the word "ur?" It just boggles my mind.[/Pet Peeve] (Maybe I'm just exceptionally sensitive tonight.)

    -Dan
    sorry haha, i usually type out the whole "your"... i'll try to next time =)

    oh and thanks for the input TheEmptySet, that's genius....
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