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Old 2003-10-15, 15:26   #12
xilman
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I observe that if the hunter starts at (1 + \epsilon) miles from the south pole, he is likely to get very dizzy on the second leg of his trek and is unlikely to avoid tripping over his pack, let alone get back to his starting place.

There are a whole bunch of further solutions, in both hemispheres, if we drop the assumption of a spherical earth. If the hunter's mates have gouged a furrow with a snowplough or built a hill with a bulldozer, for instance, he can travel a mile in a particular direction in a path different from an arc of a great circle and so reach a slightly different latitude or travel through a slightly different separation in longitude. I concede this is nit-picking.

Paul
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Old 2003-10-16, 06:39   #13
roy1942
 
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Quote:
Originally posted by Wacky
In particular, there is a small circle around the South Pole whose circumference is exactly one mile. It is located 1/ (2*pi) miles from the Pole.
Now let's get really picky: We are doing our geometry on a sphere, so this circle is NOT EXACTLY 1/(2*pi) miles from the pole. If we assume the earth is a perfect sphere of radius R then the distance from the pole is R*arcsin(1/(2*pi*R)). (This is the distance walking on the surface of the earth - the straight line distance will be a different answer still.)

For our 1 mile circle on a R=4000 mile earth, the difference is very small. Using Excel to do double precision math which my pocket calculator can't do, I get:

1/(2*pi) = 0.159154943091895
4000*arcsin(1/(2*pi*4000))=0.159154943133890

The difference is less than 3 millionths of an inch, so maybe you won't notice it while you are hunting bears.
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Old 2003-10-16, 16:06   #14
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In the last of his Dream Park novels, Larry Niven has a variation on this. It start off as normal going south 1 mile, east 1 mile but then the hunter runs over a bird (instead of shooting a bear) before going north 1 mile. What colour is the bird?

I'll give the answer straight away (because much of the work has already been done). We are at the south pole so the bird is a penguin, so "black" or perhaps "black and white" is the answer.

If you don't think there are any penguins at the south pole you're in good company, but hey - it's Larry Niven's puzzle not mine.

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Old 2003-10-27, 09:11   #15
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I principally agree with the fact that the location could be on the southern half of the earth, but this concept contradicts to the fact that the hunter kills a bear, for those do not live in the antarctis.

If you want to satistfy this fact, the hunter will have to take the bear with him (or, if he is of more wealth, some adventure tours team will have put the bear at the requested location), which leaves the answer as "any", because if there is an adventure rous team, what hinders them to paint the bear flashing red to be spotted more easily in a totally white environment ?

So the answer is: "any, if enough money is provided"
 
Old 2003-10-27, 11:01   #16
TauCeti
 
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Before you also take into account the year of the hunt (to determine grayness of the fur related to pollution), one should note that a shot bear has a high probability to be white and red.

http://www.drfrederickcook.com/bradl...s/shotbear.jpg

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Old 2003-12-09, 21:22   #17
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I'm pretty sure that the Antarctic Treaty forbids hunting for sport in Antarctica, even if the bears were transported there (and I'm pretty damn sure that it forbids the import of non-native predatory species).

However I note that the original post didn't specify what planet we were talking about, so if the whole operation were located on Mars, the correct answer might conceivably be "green".
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Old 2004-01-30, 21:42   #18
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Actually, polar bears have black skin and transparent hair. They appear white because their skin absorbs unltraviolet light and reflects the rest, which appears white. So if the polar bear has no hair, it would be black.
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Old 2004-01-30, 22:06   #19
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Umm, if the skin absorbed UV and reflected everything else back, it would have appeared white!
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Old 2004-01-31, 04:47   #20
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Perhaps rogue meant that the hair absorbs ultraviolet light and reflects the rest, so that though a bare bear is black, a hairy bear appears white.
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Old 2004-01-31, 06:34   #21
garo
 
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Well then the hair wouldn't be transparent would it? It would be white. Unless of course we have that sinister total internal reflection coming into the picture.....
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Old 2004-01-31, 06:41   #22
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Okie.... This site should help:
http://www.nsf.gov/od/lpa/nstw/teach...cte/clrbr1.htm

So the hair is transparent allowing some transmission and some reflection and some TIR.

Why does fibre-optic cables appear white when they are transparent? Does their cylindrical shape have something to do with it?

[PS: The questions above are rhetorical.]
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