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Discussion Starter #1
or does anyone else feel like they're driving UP HILL when going North?
 

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Discussion Starter #3
Fair enough if you live in the southern hemisphere I suppose.
 

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Everything in Moderation
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I always felt that I got better gas mileage driving south.

I realize now, I was going downhill. :rolleyes:


++++++++++++++

With all the emissions cheating news lately, I remembered that before EPA mileage tests, carmakers used to tout MPG achieved on downhill runs, like Reno to LA. Anybody else remember that?
 

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A riddle...

At what point on the Earth can you walk 1 mile North, 1 mile East or West, and 1 mile South and be exactly where you started?
 

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Discussion Starter #7
Wait a minute guys, you're making me dizzy.:p
 

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Good thinking but no...

The South Pole.

Now answer me this: where else on the Earth can you walk 1 mile north, then 1 mile east (or west), and 1 mile south to get exactly where you started?
The South Pole does not work. The Great Circle length one mile North of the South pole is less than a mile.
 

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The South Pole does not work. The Great Circle length one mile North of the South pole is less than a mile.
If you travel from the South Pole one mile north along the Great Circle that goes through both poles on whichever line of latitude you've chosen, travel one mile east (or west) along the 89°59'7.90'' line of latitude, you remain exactly one mile north of the South Pole (if you aren't, then you didn't walk one mile north to begin with). After the third leg of the journey you describe, you're back to where you began.
 

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I sit corrected, mostly...

If you travel from the South Pole one mile north along the Great Circle that goes through both poles on whichever line of latitude you've chosen, travel one mile east (or west) along the 89°59'7.90'' line of latitude, you remain exactly one mile north of the South Pole (if you aren't, then you didn't walk one mile north to begin with). After the third leg of the journey you describe, you're back to where you began.
Good analysis. In the phrase, "...whichever line of latitude you've chosen..." did you mean Longitude?

The concept I missed is that no matter where one is on a Latitudinal Great Circle, South still points to the South pole. You may not retrace the same path but you do wind up at the same starting point. Thanks for the correction.

The concept at the North Pole is to find a Latitudinal circle near the North Pole that is exactly one mile long, then go exactly one mile South of it and begin. This will cause you to retrace the same one-mile segment along the line of Longitude Southbound that you did Northbound.

Nicely done toast21!

Are you Navy?
 

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D'oh, you're right, I meant longitude not latitude.

Nope, not Navy, just grew up with a big book of interesting problems.

There is another solution not yet mentioned: in fact, an infinite number of them.
 

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Wait a minute guys, you're making me dizzy.:p
Well HEY, you started it. Right?


:rolleyes:

+++++++++++++++++++

The concept at the North Pole is to find a Latitudinal circle near the North Pole that is exactly one mile long, then go exactly one mile South of it and begin.
If you were at the North Pole, why wouldn't you just ask Mrs Santa Claus?

(Santa, being male, would be useless at directions...so don't ask HIM.) :)
 

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As for the infinite number, yes, but another concept?

D'oh, you're right, I meant longitude not latitude.

Nope, not Navy, just grew up with a big book of interesting problems.

There is another solution not yet mentioned: in fact, an infinite number of them.
For concept at the North Pole, find a Latitudinal Great Circle near the North Pole that is exactly one mile long, then go exactly one mile South of it and begin. This will cause you to retrace the same one-mile segment along the line of Longitude Southbound that you did Northbound - the starting point in this concept defines another Longitudinal Great Circle which is an infinite number of starting points.

Another?

BTW, What is the Title of that wonderful book of problems?
 

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(n.b. the only latitudinal Great Circle is the equator).

The infinite number of solutions I had in mind were, to take your original problem, find a line of latitude close to the South Pole that is exactly 1/2 a mile in length, then start 1 mile north of it so your journey takes you around the pole twice. Then find a line of latitude that is exactly 1/3 a mile in length, one that's 1/4 mile, etc etc. It all gets to be a bit of a blur when you're starting off just a little bit more than 1 mile from the pole.

The book was a very old one, and it's been so long that I couldn't tell you the title off the top of my head. I'll get a chance to look for it at my parents' place in a month or two, but in the meantime Martin Gardner books are worth mining.
 

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DRAT! Yet another Senior moment...

(n.b. the only latitudinal Great Circle is the equator).

The infinite number of solutions I had in mind were, to take your original problem, find a line of latitude close to the South Pole that is exactly 1/2 a mile in length, then start 1 mile north of it so your journey takes you around the pole twice. Then find a line of latitude that is exactly 1/3 a mile in length, one that's 1/4 mile, etc etc. It all gets to be a bit of a blur when you're starting off just a little bit more than 1 mile from the pole.

The book was a very old one, and it's been so long that I couldn't tell you the title off the top of my head. I'll get a chance to look for it at my parents' place in a month or two, but in the meantime Martin Gardner books are worth mining.
Of course! I have misused the term Great Circle repeatedly. Thanks for the subtle correction. I wanted to use the term Circle to emphasize the notion of a finite line length, or diameter of the circle, of one mile.

Your solution above does work but the proof is left to the student.
 

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Discussion Starter #16 (Edited)
Oh man, my head hurts so bad right now....why is the room spinning?

and yeah, I did start it, but all I was talking about was going uphill vs downhill.:p
 
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