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Topic: MEDIUM: GLOBE TRAVERSAL (Read 2548 times) |
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bl@ke
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Easy if you think about it.
1 place only - The North Pole. 
You cannot do the South Pole as you cannot travel any further south that you already are.
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ScottP
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Re: MEDIUM: GLOBE TRAVERSAL
« Reply #1 on: Jul 25th, 2002, 10:14pm » |
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Regarding the hint - more than two solutions, I guess it depends which 'North' you start at. True, Grid or Magnetic!
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dedsman
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Re: MEDIUM: GLOBE TRAVERSAL
« Reply #2 on: Jul 26th, 2002, 3:11am » |
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it says that you walk east one mile. suppose i'm not exactly at the north pole but somewhere below it, i can walk around the globe (east direction) and be back at the same place for half a mile, so when i walk 1 mile i'm still on the same place and I end up the same spot when I walk north again. this is also true if I can walk east and be back at the same place for a quarter of a mile, which puts me at a different starting point but i'll also end up there. so there's more than 2 but i don't know the mathematical function to represent it.
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tot
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Re: MEDIUM: GLOBE TRAVERSAL
« Reply #3 on: Jul 26th, 2002, 4:05am » |
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I'd say you have infinite + 1 number of poisitions. One is the North Pole, the others are circles a bit more than one mile from the South Pole, where the walk east is at least one full 360 degree circle around the pole.
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Zak Dolan
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Re: MEDIUM: GLOBE TRAVERSAL
« Reply #4 on: Jul 26th, 2002, 1:06pm » |
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Ah but the walk east would actually need to end up at the starting point... meaning that it would have to be 1/n miles circumference, where n is an integer.
In other words... you could walk south towards the south pole, then east in one or more complete circles, then north again to the same original spot. But the circles would each have to be either a mile in circumference, or 1/2 mile in circumference, or 1/3 mile in circumference, or 1/4th mile.. or...
Which would lead to an infinite number of starting points on paralell circles around the south pole.
-Z
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Rhaokarr
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Re: MEDIUM: GLOBE TRAVERSAL
« Reply #5 on: Jul 26th, 2002, 9:12pm » |
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Of course, some of these later treks to the east would end up merely spinning on your foot on the south pole... In mathematical terms, there is an infinite number, in real terms, I think that the solution is bound by the width of your foot.
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tot
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Re: MEDIUM: GLOBE TRAVERSAL
« Reply #6 on: Jul 27th, 2002, 6:10am » |
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on Jul 26th, 2002, 9:12pm, Rhaokarr wrote:| Of course, some of these later treks to the east would end up merely spinning on your foot on the south pole... In mathematical terms, there is an infinite number, in real terms, I think that the solution is bound by the width of your foot. |
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In real terms, there is limited number of starting circles, but each circle has already infinite number of starting points.
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Franklinstein
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Re: MEDIUM: GLOBE TRAVERSAL
« Reply #7 on: Jul 31st, 2002, 5:37pm » |
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on Jul 25th, 2002, 10:14pm, ScottP wrote:| Regarding the hint - more than two solutions, I guess it depends which 'North' you start at. True, Grid or Magnetic! |
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Perhaps WillyWutang has another solution in mind. His second hint says: Christopher Columbus. I don't think CC got any where near either of the poles, or even close to the magnetic poles. I don't know what grid means, but doesnt something happen to a compass at the magnetic equator?
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ScottP
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Re: MEDIUM: GLOBE TRAVERSAL
« Reply #8 on: Jul 31st, 2002, 11:33pm » |
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Franklinstein, by 'grid' I was referring to the fact that occasionally for some systems the 'north' used for a map grid doesn't always point to either magnetic or true north. Check out the Ordnance Survey of the UK [http://www.ordsvy.gov.uk/literatu/info/cr12.html]. Sorry the old cartographer coming out in me. 
Then we have to think about which 'mile' we are using here...
nautical mile (nmi): A unit of distance used in navigation and based on the length of one minute of arc taken along a great circle. Note 1: Because the Earth is not a perfect sphere, various values have been assigned to the nautical mile. The value 1852 meters (6076.1 ft.) has been adopted internationally. Note 2: The nautical mile is frequently confused with the geographical mile, which is equal to 1 min of arc on the Earth's equator (6087.15 ft.). [http://www.its.bldrdoc.gov/fs-1037/dir-024/_3480.htm].
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william wu
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Re: MEDIUM: GLOBE TRAVERSAL
« Reply #9 on: Aug 1st, 2002, 1:53am » |
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on Jul 31st, 2002, 5:37pm, Franklinstein wrote:
Perhaps WillyWutang has another solution in mind. His second hint says: Christopher Columbus. I don't think CC got any where near either of the poles, or even close to the magnetic poles. I don't know what grid means, but doesnt something happen to a compass at the magnetic equator? |
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My reasoning for my hint was as follows: You go south. Then you go a little bit west. Now if you ever go north, you will end up somewhere to the west of where you started (unless you started at the north pole, the trivial case). So you have a dilemma. You want to end up a little to the east of where you actually end up, but you can only travel west.
Columbus believed the world was round, so he traveled west to go east.
Valeriy E. Ushakov e-mailed me and said "Magellan" is a more appropriate hint. However, I like the Columbus hint a little better because it requires knowing these few details of history, besides the layman knowledge that he supposedly "discovered America". Magellan might make the solution too obvious.
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bartleby
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Re: MEDIUM: GLOBE TRAVERSAL
« Reply #10 on: Aug 1st, 2002, 7:08am » |
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You know, there's even MORE solutions than that!!
Yes, there's a ring something more than 1 mile north of the South Pole where you can start anywhere on the ring, go around once, and go back north.
But:
There's a ring a little further south than that, where you can go south 1 mile, go around the South Pole TWICE, go north, and end up where you started.
And then there's a ring a little further south than that where you go around THREE times..... Etc.
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bartleby
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Re: MEDIUM: GLOBE TRAVERSAL
« Reply #11 on: Aug 1st, 2002, 7:09am » |
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Oops, somebody else already pointed that out.
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