Brain Teasers
North Pole
How far will you travel if you start at the equator and go to the North Pole always heading north-west?
Answer
Infinity. You will never reach the North Pole. If you were at the North Pole, the only direction in which you can leave is South. Therefore you must arrive by walking North. But you are walking North-west.Hide Answer Show Answer
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Comments
No I don't agree with this, if you are at the equator facing north, turn 45 degrees to your left.Move towards the north pole with out changing the way you are facing. In this way you are moving in a northwesterly direction. Directions are relative to where you are.
Likewise if you are at the north pole, you can turn and go eastwards.
Likewise if you are at the north pole, you can turn and go eastwards.
Sorry cathalmccabe, but the given answer is correct. Directions such as North, North-West depend only on your position on the earth, not on the direction you are facing. On the north pole, every direction is south - you cannot turn to your left and go east. Furthermore, if you started on the equator, turned 45 degrees to the left and kept walking in a straight line without changing direction, you would walk a "great circle" route which would miss the north pole by several thousand miles, and eventually bring you back to your starting point.
Wow cathalmaccabe! you may have a brilliant mind when it comes to math, but remind me never to go on a hike with you! Even allowing for slight deviation between magnetic and true north (normally, but not always, about 4 degrees I think?) there is no way you would ever reach the North Pole.
While it's true that you can only go south
from the North Pole, that's irrelevant to this
question. At every other point in the Northern
Hemisphere, NorthWest is a definite direction that
will take you to a higher latitude. The actual path
would be a form of spiral that would converge to the
North Pole at its limit. I'm sure it's possible to
compute the actual length along the spiral with a bunch
of Spherical Geometry and Calculus, but it
would take a lot more work and research than I'm willing
to give it. To the degree that this is solvable,
it belongs in Math, not Logic.
from the North Pole, that's irrelevant to this
question. At every other point in the Northern
Hemisphere, NorthWest is a definite direction that
will take you to a higher latitude. The actual path
would be a form of spiral that would converge to the
North Pole at its limit. I'm sure it's possible to
compute the actual length along the spiral with a bunch
of Spherical Geometry and Calculus, but it
would take a lot more work and research than I'm willing
to give it. To the degree that this is solvable,
it belongs in Math, not Logic.
Yes, I agree with dewtell. If you keep going northwest you will eventually end up at the north pole.
The argument ensuing is that of a theoretical basis (I.e. If I were to keep travelling in half-distances, I would never reach where I was going), and an applied basis (even if there are an infinite halves left, I would just step over to my destination).
I thought you couldnt actually GET there.
You will never reach the North Pole. Imagine where you start on the equator to be right on the origin point of a Cartesian Graph dividing the Earth into four equal pieces, North being the top of the Y axis. Travel at a heading of 45° (NorthWest), and you will eventually reach the origin point again, but never the top of the Y axis. You will essentially travel the same distance as walking around the equator one lap.
Hmm... So- so.
its ok thats all
Jun 27, 2008
Radioguy, that is right id the Earth would be in 2D. In three dimensions the Earth is an (aproximate) sphere, walking NW from the Equador will get you to the North pole via a spherical trajectory. Although i think you'll only get close to the north Pole as you'd have to fly in order to keep those 45deg.
Isn't it a converging series, like Archilles and the tortoise? The maths is beyond me for a sphere though.
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