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# Here's One to Get Your Brain in Gear

A man walks south for 5 miles, then walks west for 5 miles, and then north for 5 miles. At the end he is at the exact place where he started.

Only at magnetic north?
Why would it be the magnetic north pole? I'd think the geographic north pole would work. It's way too early in the morning though to work through geometry problems on spheres.
Yuki,

Close, but no cigar.

KevinF,

Great, you got it. The obvious answer, well sort of obvious, is the North Pole. Now the real question. Is there (Are there) any other place(s) that this is true for?

Now the gears start to grind. Grab your coffee guys.
I am sorry, I was thinking of a different type of 'gear'. Coming from a 'gear whore', I an sure you can understand.
Quote:
 Originally Posted by T-Square Is there (Are there) any other place(s) that this is true for?
I had to churn the brain for a while, but there are a couple places in the southern hemisphere where this works. Walk five miles south to a spot where the circumference of the Earth is exactly five miles around. Once you head five miles east, you will have circumnavigated the globe. Walk five miles north, and you're right back to where you started.

Alternatively, you can walk five miles south to a spot where the Earth is one mile in circumference, walk around the world five times : : and then head back north. You get the idea.

Now, the next question is that since you just crossed the international date line five times, what time / day will it be when you get back?
Wow!! Great analysis. You nailed it on the head. Good way to see polar cordinate geometry. Actually the number of places is infinate. Your southern starting points are actually a series of circles.

The date line is interesting. Actually, you may have gone through two days, however, you always return to the same time. It is much easier to see and understand while looking at the top of a globe.

Boy do I love this type of brain twister. Sort of like the ones on Car Talk. You guys got any?
Cool!
I admit it I'm a geek and Science is Coool!
Quote:
 Originally Posted by T-Square A man walks south for 5 miles, then walks west for 5 miles, and then north for 5 miles. At the end he is at the exact place where he started. Is this possible? Explain your answer.
T2,

Thanks for giving me the panic attack:. I read your question and the next thing I knew I was back in geometry class sweating bullets trying to solve story problems. I just woke up on the floor in a fetal position with my underwear on my head... Why ya gotta do that: : :
It is a trigonometry problem, spherical trig, not euclidian (plain) trig.

And I do it just because I can.
Quote:
 Originally Posted by T-Square It is a trigonometry problem, spherical trig, not euclidian (plain) trig.
Oh, that makes me feel much better!
Now if you want to get into differential equations ...

Get Physicsman on the horn!
Quote:
 Originally Posted by T-Square Yuki, Close, but no cigar. KevinF, Great, you got it. The obvious answer, well sort of obvious, is the North Pole. Now the real question. Is there (Are there) any other place(s) that this is true for? Now the gears start to grind. Grab your coffee guys.
I think Yuki got it right. South is a compass point, so you would have to walk south based on a compass, etc., etc. which means your point of reference would be magnetic north. I know that, looking at the globe, north pole makes sense, but not when you are doing it on the ground.
Compasses don't work worth a damn at the North Magnetic Pole. The lines of flux screw them up. You have to navigate near the magnetic poles using some other form of direction finding.

### T-Square's right...

Directionally, the earth is geographic, not magnetic.

On your follow-up question T-Square, you said the answer is infinite due to the number of times you could circumnavigate the various circles. Not so. For example, if you tried it where the circumference is two miles, you could only go two and a half revolutions before you started heading north again and you would wind up on the 'opposite side of the world' from where you started. So, you have to start at the five mile circumference mark and work down from there in divisible increments.

Come to think of it, if your feet are small enough, it is infinite......

Â

Edit: Don't mind me, just trying an experiment...

Edited by GoldMember - 11/28/12 at 2:41pm
The question was caged as a "linear" one and did not involve magnetics or "navigation".

When I "walked" it through to test it though ... I was using doppler ...
Ok. Let's start easy.

"Therein lies the secret", said Scheming Suzy. "For you see, there is a seven-letter word in the English language that contains ten words without rearranging any of its letters."

What is the word?
therein
the
there
he
her
here
herein
ere
rein
in
oooooo.....english problems. I hate that. Can we stick with math? My english is a little suspect. 'Therein' lies the problem. Please stick with Math!!!

Dangit! I got beat! (edited....spent too much time looking it up...)
Ahhh, geometry class, yes right between Sharon and Lydia. The point where the erection began every morning - an infinite number of erections if I were at the South Pole, or was it North Pole or Magnetic North? Just keep your legs crossed for the rest of the class, ouch.
Quote:
 Originally Posted by bumpdad Ahhh, geometry class, yes right between Sharon and Lydia. The point where the erection began every morning - an infinite number of erections if I were at the South Pole, or was it North Pole or Magnetic North? Just keep your legs crossed for the rest of the class, ouch.
Dude, I'm not surprised you didn't get a response to that, however you are no longer that this thread's killer, BUWAHAHAHAHAHAHAHA!!!!!
Quote:
 Originally Posted by volantaddict Dude, I'm not surprised you didn't get a response to that, however you are no longer that this thread's killer, BUWAHAHAHAHAHAHAHA!!!!!
Geez dude - you couldn't let his erections alone, could you?
yeah, leave my erection alone
Kevin was almost right. He didn't mean "where the circumference of the earth is 5 miles around." Its circumference is always the same, assuming the earth is a perfect sphere. He meant "where the latitude line is five miles around".
Ok. Here's another:

Professor Bumble, who is getting on in years, is growing absent minded. On the way to a lecture one evening, he went through a red light and turned down a one way street in the wrong direction. A policeman observed the entire scene but did nothing about it. How can Professor Bumble get away with such behavior?
For the Math wizards:

There are four volumes of "Humour in Accounting" sitting on a book shelf in ascending order, left to right. Each book is exactly 8 cm thick. The pages of each book constitute 7 cm and the covers are each half a centimeter thick. A starving beetle starts easting at page one of volume one and eats straight through to the last page of volume four. How many centimeters does the beetle travel?
Quote:
 Originally Posted by Bonni For the Math wizards: There are four volumes of "Humour in Accounting" sitting on a book shelf in ascending order, left to right. Each book is exactly 8 cm thick. The pages of each book constitute 7 cm and the covers are each half a centimeter thick. A starving beetle starts easting at page one of volume one and eats straight through to the last page of volume four. How many centimeters does the beetle travel?
31 cm because he didn't eat the front cover of vol 1 or the back cover of vol 4. But I want to know how he ate everything except those covers.

This question is a lot like doing the math for figuring out the materials for building a fence. Each section is 8' long. If you want a fence of 80', how many fence posts do you need? A=11
Quote:
 Originally Posted by Bonni Ok. Here's another: Professor Bumble, who is getting on in years, is growing absent minded. On the way to a lecture one evening, he went through a red light and turned down a one way street in the wrong direction. A policeman observed the entire scene but did nothing about it. How can Professor Bumble get away with such behavior?
He was walking.
Professor Bumble is also a police officer.

(Think outside the box.)
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