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Title: MEDIUM: GLOBE TRAVERSAL Post by bl@ke on Jul 25th, 2002, 7:08pm Easy if you think about it. 1 place only - The North Pole. ;D You cannot do the South Pole as you cannot travel any further south that you already are. |
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Title: Re: MEDIUM: GLOBE TRAVERSAL Post by ScottP on Jul 25th, 2002, 10:14pm Regarding the hint - more than two solutions, I guess it depends which 'North' you start at. True, Grid or Magnetic! |
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Title: Re: MEDIUM: GLOBE TRAVERSAL Post by dedsman on Jul 26th, 2002, 3:11am 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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Title: Re: MEDIUM: GLOBE TRAVERSAL Post by tot on Jul 26th, 2002, 4:05am 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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Title: Re: MEDIUM: GLOBE TRAVERSAL Post by Zak Dolan on Jul 26th, 2002, 1:06pm 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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Title: Re: MEDIUM: GLOBE TRAVERSAL Post by Rhaokarr on Jul 26th, 2002, 9:12pm 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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Title: Re: MEDIUM: GLOBE TRAVERSAL Post by tot on Jul 27th, 2002, 6:10am on 07/26/02 at 21:12:34, Rhaokarr wrote:
In real terms, there is limited number of starting circles, but each circle has already infinite number of starting points. |
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Title: Re: MEDIUM: GLOBE TRAVERSAL Post by Franklinstein on Jul 31st, 2002, 5:37pm on 07/25/02 at 22:14:36, ScottP 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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Title: Re: MEDIUM: GLOBE TRAVERSAL Post by ScottP on Jul 31st, 2002, 11:33pm 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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Title: Re: MEDIUM: GLOBE TRAVERSAL Post by william wu on Aug 1st, 2002, 1:53am on 07/31/02 at 17:37:27, Franklinstein wrote:
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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Title: Re: MEDIUM: GLOBE TRAVERSAL Post by bartleby on Aug 1st, 2002, 7:08am 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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Title: Re: MEDIUM: GLOBE TRAVERSAL Post by bartleby on Aug 1st, 2002, 7:09am Oops, somebody else already pointed that out. |
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