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landmark Inner circle within a triangle 5194 Posts 
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Hence the penguins.
Jack
Click here to get Gerald Deutsch's Perverse Magic: The First Sixteen Years
All proceeds to Open Heart Magic charity. |
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idris New user St. Louis, MO 38 Posts
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Steve,
True as far as you go, however there are an infinite set of other nexii (nexuses?) than the set you defined. Care to try again. (Grin) Jerry
Jerry
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drkptrs1975 Elite user North Eastern PA 452 Posts
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There is only one place where you can go south, East(or West) and back North Same distance as you went South, and end up the same place, that would be the north pole.
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Jonathan Townsend Eternal Order Ossining, NY 27300 Posts
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To start with, who said they wind up at the same place?
...to all the coins I've dropped here
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magiczim New user Philly 67 Posts
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Agreed, I thought they just found a bear and shot it...there was nothing about starting and ending in the same place
"We live within the recreation of others" - René Lavand
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Shane Wiker Inner circle Las Vegas 1199 Posts
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How could it be white? No bear I know of is white. Polar bears have black skin and transparent fur...
Shane Wiker |
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LobowolfXXX Inner circle La Famiglia 1196 Posts
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Quote:
On 2006-03-07 20:11, drkptrs1975 wrote: Not true, as posted above. There is an infinite number of places that meet that criterion.
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley. "...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us." |
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Shane Wiker Inner circle Las Vegas 1199 Posts
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Lobowolf,
Drkptrs is correct about the North Pole being the only place you can go south 1 mile, east 1 mile, then north 1 mile, ending up at the same place. However, it doesn't say anywhere in the poem that he ends up in the same place he started. Also, even if it was the North Pole, who's to say there isn't some grizzly bear that was brought to the North pole recently and is wandering around. That means it's not necessarily a polar bear (He said the answer was white). Even if it did have to be a polar bear, as I said, they aren’t white anyway. Shane Wiker |
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TomasB Inner circle Sweden 1144 Posts
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Shane, close to the South Pole you can "go south 1 mile, east 1 mile, then north 1 mile, ending up at the same place." When you go east you are on a disc with a circumference that is 1/N miles where N is a positive integer. Infinitely many places in other words.
/Tomas |
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magicjohn2278 Special user Isle of Man UK 544 Posts
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If you are standing near the South Pole (within a mile of it) can you go South 1 mile? At some point on your journey you must be AT the South Pole and therefore can't travel any further South at all?
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LobowolfXXX Inner circle La Famiglia 1196 Posts
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Quote:
On 2006-03-08 12:19, Shane Wiker wrote: No, he's not. As you approach the South Pole from the equator, the circumference of the earth gets smaller and smaller. At some point, it is exactly one mile. Start at a point one mile north of any spot along this circle. That's your starting point, A. You walk south one mile; now you're at point B, which lies on that circle. You walk one mile east, which brings you all the way around the world (because the circumference is so small there) and back to point B. Now you walk one mile north, and you're back at A. However, even if the initial post HAD said that you end up in the same spot, the answer would still be white, because there are no bears of ANY color that close to the south pole.
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley. "...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us." |
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Shane Wiker Inner circle Las Vegas 1199 Posts
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Quote:
On 2006-03-08 12:32, TomasB wrote: Yes, but you can't go south if you're exactly at the south pole. If you're near the south pole and go south 1 mile, east 1 mile, and north 1 mile, you would be very close to the same position, but it wouldn't be exact. The closer you get to the north pole, the closer to the same position you would end up, but unless you were at the north pole, it wouldn't be exact. Of course, the earth isn't exactly spherical, so you wouldn't end up at the exact same point anyway. Shane Wiker |
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LobowolfXXX Inner circle La Famiglia 1196 Posts
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Quote:
On 2006-03-08 13:55, Shane Wiker wrote: He's not saying you're AT the south pole. See my post. You never hit the south pole, but the one mile south walk brings you to a place where walking one mile east (or west, for that matter) brings you back to where you started.
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley. "...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us." |
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idris New user St. Louis, MO 38 Posts
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Shane,
You are missing the point. First let's simplify things slightly. For now we are going to assume pi is 3.0000 to simplify the arithmetic. Set your starting point 1 and 1/6 miles north of the south pole. If you go south 1 mile you will be 1/6th of a mile from the south pole. Walking east on the latitudinal line at this point will cause you to walk 1 mile to get back to the point you started the walk. (Circumference = 2 times pi times the radius; i.e. 2 times 3 * 1/6 or 1 mile). Walking one mile north at this point will put you back where you started the whole trip. Therefore any point 1 and 1/6 miles north of the south pole will give a valid solution to the problem. By definition there are an infinite set of points in any given circle so this gives you one set of infinite solutions. Now, start 1 and 1/12 miles north of the south pole. This time when you start your circle you will end up walking around the pole twice since the circumference is 1/2 of a mile (1/12 * 3 * 2), and then you can walk north 1 mile to get back to start, giving a second set of infinite solutions. You can continue to generate more solutions by starting the appropriate distance from the pole as long as you are over a mile away and the circumference is a numeric fraction 1/N as Tomas stated in his post. Enjoy,
Jerry
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Shane Wiker Inner circle Las Vegas 1199 Posts
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Wow, after reading that a second time, I think I understand. Of course, none of this has to do with the riddle.
Shane Wiker |
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Steve Martin Inner circle 1119 Posts
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Tomas + Idris,
Nice one. I knew what you were on about, but just missed the fact that when you go east you can go more than once around the circle! So as well as there being an infinity of points around each starting circle, there are in fact an infinity of starting circles. Coolio.
Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
Albert Einstein |
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LobowolfXXX Inner circle La Famiglia 1196 Posts
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Now if only there were, say, black bears near the South Pole.
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley. "...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us." |
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Posted: Mar 3, 2006 11:51 pm 
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