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HOW DID IT HAPPEN???
I think this answer
doesn't work: when you get to the South pole, how do you run West?
Yep. I presume you mean 1 mile north of south pole?
But this answer:
does: for example, any point on the circle (1 + 1/2pi) miles from the South Pole.
There's an infinite number of circles around the South Pole where he could have started.
After going South 1 mile, you're (1/2pi) miles from the Pole,
which allows you to run West 1 mile [1 lap of a 1-mile circumference circle]
and be able to go a mile North to the starting point.
As Martini noted, there is an infinite number of starting distances:
1 + 1/2Npi miles North of the South pole where N is any positive integer.
N is then the number of circular laps in your westerly mile.
e.g. N=5280 - you'd run 5280 laps around a 1-foot circumference circle.
Here's a counter question - why can't N be negative?
i.e. start closer than a mile - you could still do N laps Go to the full post
Posted 09 February 2009 - 04:58 AM
Because the earth id a sphere it wouldn't really matter how far west or east he ran. as long as he ran the exact same distance south and north than he would end up back at his starting point, the north pole.
Posted 15 February 2009 - 02:42 AM
Posted 15 March 2009 - 03:44 PM
For the south pole solution:
Let's say there's a latitude (a circle around the earth running east-west) that's exactly 1 mile in circumference. In other words, a point shortly north of the south pole that is 1 mile around the earth. If you start on any of the infinite points that are 1 mile north of that special latitude, then you can go 1 mile south and then 1 mile west to go all the way around the earth, then 1 mile north to be back where you started ;D
That works. And there are an infinite number of points exactly one mile north of that circle from which one could start.
Then if you take another circle which is one half mile in circumference, you would walk west one mile and make two trips around the circumference and then make your return trip north to your starting point. Again, there are infinite starting point for this solution.
And you could go on with a one third mile circle, one quarter mile circle, one fifth mile circle, and keep going for another infinite number of solutions.
This is all in addition to the obvious solution where you start at the North Pole.
Edited by Larry A, 15 March 2009 - 03:47 PM.
Posted 14 May 2009 - 02:33 PM
Posted 15 May 2009 - 03:34 AM
Posted 06 June 2009 - 08:55 PM
Posted 07 June 2009 - 09:44 PM
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