1. ## 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.

2. Originally Posted by squarerootof2
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 $\displaystyle d_1(t)$ be the monks distance from the bottom to the peak as a function of time on the first day.

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

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

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

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

define $\displaystyle f(t)=d_1(t)-d_2(t)$

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

by the intermediate value theorem there exits a c such that
$\displaystyle f(c)=0 \iff d_1(c)-d_2(c)=0 \iff d_1(c)=d_2(c)$

QED

3. Originally Posted by squarerootof2
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

4. Originally Posted by topsquark
[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....