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 2003-10-15, 15:26 #12 xilman Bamboozled!     "πΊππ·π·π­" May 2003 Down not across 11·919 Posts 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
2003-10-16, 06:39   #13
roy1942

Aug 2002

1011112 Posts

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.

 2003-10-16, 16:06 #14 graeme     Jul 2003 41 Posts larry niven and bears 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. Graeme
 2003-10-27, 09:11 #15 gtschech   3×3,251 Posts 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"
 2003-10-27, 11:01 #16 TauCeti     Mar 2003 Braunschweig, Germany 3428 Posts 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
 2003-12-09, 21:22 #17 FeLiNe     Dec 2003 23 Posts 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".
 2004-01-30, 21:42 #18 rogue     "Mark" Apr 2003 Between here and the 24·7·53 Posts 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.
 2004-01-30, 22:06 #19 garo     Aug 2002 Termonfeckin, IE 2·5·251 Posts Umm, if the skin absorbed UV and reflected everything else back, it would have appeared white!
 2004-01-31, 04:47 #20 cheesehead     "Richard B. Woods" Aug 2002 Wisconsin USA 22×3×599 Posts 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.
 2004-01-31, 06:34 #21 garo     Aug 2002 Termonfeckin, IE 2·5·251 Posts 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.....
 2004-01-31, 06:41 #22 garo     Aug 2002 Termonfeckin, IE 9CE16 Posts 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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