martinl@molihp.UUCP (Martin M Lacey) (01/08/86)
In article <1011@ecsvax.UUCP> hes@ecsvax.UUCP (Henry Schaffer) writes: >> >> > From: colonel@sunybcs.UUCP (Col. G. L. Sicherman) >> > Message-ID: <2667@sunybcs.UUCP> >> > Here's a new one: a practical joker tampered with the Great Explorer's >> > gyrocompass, so it points 45 degrees off. The Great Explorer thinks >> > he's going due north on his way to the North Pole, but he's really going >> > due northwest! >> > >> > Will he reach the North Pole anyway? (Geographers keep out of this one!) >> My own thoughts about this are as follows. If this explorer is following the compass at all, he should eventually arrive at the north pole after a number of spirals toward it. My thinking goes like this; if this compass points anything less that 90 degress away from north, he will eventually find north by its vector quality. That is to say, if you subtract the e-w direction component away from the vector, you are left with the north component of the vector. This northern component may be small, but it exists; so the explorer shall eventually get there. The greater the e-w component as compare to the norther component of the vector (ie. closer to 90 degrees from north) the longer the distance (number of spirals) before the explorer gets to the North Pole. It can be easily visualized if you think as the world as flat and repeating, and the north pole is a straight line on the top. This way the problem can be solved using simple geometry. Eg. Earth1 Earth2 Earth3 Earth4 ... ---------------------------------...-------NORTH POLE LINE-- | | | | * |... ^ | | | * |... | | | | * | |... | | | * | | |... X | * | | |... | | * | | | |... | _________________________________...____________+_______ <------------Y------------> where * is the explorer, and each one the earths represents one revolution of the planet. The less the angle at Y start, the more earths the explorer has to pass through, hence the distance. Anyone care to comment....It seemed logical to me; but I may be missing something fundamental - unlikely though :-). Martin the Magician.
dobro@ulowell.UUCP (Chet Dobro) (01/21/86)
> In article <1011@ecsvax.UUCP> hes@ecsvax.UUCP (Henry Schaffer) writes: > >> > >> > From: colonel@sunybcs.UUCP (Col. G. L. Sicherman) > >> > Message-ID: <2667@sunybcs.UUCP> > >> > Here's a new one: a practical joker tampered with the Great Explorer's > >> > gyrocompass, so it points 45 degrees off. The Great Explorer thinks > >> > he's going due north on his way to the North Pole, but he's really going > >> > due northwest! > >> > > >> > Will he reach the North Pole anyway? (Geographers keep out of this one!) > >> > > My own thoughts about this are as follows. If this explorer is following > the compass at all, he should eventually arrive at the north pole after > a number of spirals toward it. My thinking goes like this; if this compass > points anything less that 90 degress away from north, he will eventually > find north by its vector quality. That is to say, if you subtract the > e-w direction component away from the vector, you are left with the north > component of the vector. This northern component may be small, but it > exists; so the explorer shall eventually get there. The greater the > e-w component as compare to the norther component of the vector (ie. closer > to 90 degrees from north) the longer the distance (number of spirals) > before the explorer gets to the North Pole. It can be easily visualized > if you think as the world as flat and repeating, and the north pole is a > straight line on the top. This way the problem can be solved using simple > geometry. > > > Anyone care to comment....It seemed logical to me; but I may be > missing something fundamental - unlikely though :-). > > Martin the Magician. This is correct given that the compas poins to the north pole and not magnetic-north. Gryphon
cipher@mmm.UUCP (Andre Guirard) (01/30/86)
>> >> > From: colonel@sunybcs.UUCP (Col. G. L. Sicherman) >> >> > Message-ID: <2667@sunybcs.UUCP> >> >> > Here's a new one: a practical joker tampered with the Great Explorer's >> >> > gyrocompass, so it points 45 degrees off. The Great Explorer thinks >> >> > he's going due north on his way to the North Pole... >> >> > Will he reach the North Pole anyway? >> Henry Schaffer replies: >> My own thoughts about this are as follows. If this explorer is following >> the compass at all, he should eventually arrive at the north pole after >> a number of spirals toward it... Chet Dobro adds: >This is correct given that the compass points to the north pole and not >magnetic north. If you read carefully, you see the puzzle refers to a "gyrocompass". I am not familiar with the term, but I assume it means that the heading is maintained by a gyroscope rather than the Earth's magnetic field. Therefore, the explorer's path will not spiral in to the pole, but will instead continue in a "straight line" (i.e. a sphere geometry "line"). -- /''`\ Andre Guirard ([]-[]) De Tuss from de Tonn \ o / ihnp4!mmm!cipher `-'
king@kestrel.ARPA (02/04/86)
From: dobro@ulowell.UUCP (Chet Dobro) Newsgroups: net.puzzle Date: 21 Jan 86 08:31:52 GMT > In article <1011@ecsvax.UUCP> hes@ecsvax.UUCP (Henry Schaffer) writes: > >> > >> > From: colonel@sunybcs.UUCP (Col. G. L. Sicherman) > >> > Message-ID: <2667@sunybcs.UUCP> > >> > Here's a new one: a practical joker tampered with the Great > >> > Explorer's gyrocompass, so it points 45 degrees off. The Great > >> > Explorer thinks he's going due north on his way to the North Pole, > >> > but he's really going due northwest! > >> > > >> > Will he reach the North Pole anyway? (Geographers keep out of this > >> > one!) > >> > > My own thoughts about this are as follows. If this explorer is following > the compass at all, he should eventually arrive at the north pole after a > number of spirals toward it. My thinking goes like this; if this compass > points anything less that 90 degress away from north, he will eventually > find north by its vector quality. That is to say, if you subtract the e-w > direction component away from the vector, you are left with the north > component of the vector. This northern component may be small, but it > exists; so the explorer shall eventually get there. The greater the e-w > component as compare to the norther component of the vector (ie. closer to > 90 degrees from north) the longer the distance (number of spirals) before > the explorer gets to the North Pole. It can be easily visualized if you > think as the world as flat and repeating, and the north pole is a straight > line on the top. This way the problem can be solved using simple > geometry. > > > Anyone care to comment....It seemed logical to me; but I may be > missing something fundamental - unlikely though :-). > > Martin the Magician. This is correct given that the compas poins to the north pole and not magnetic-north. Gryphon Seems to me that with a GYROcompass this wouldn't work. Let us say that a gyrocompass points north when it is aimed at the north star (although a gimbal arrangement may let us find a northward direction). We get to the point under that star. If the compass is twisted, it points to a different star and the explorer ends up somewhere else. He may smell a rat when the compass moves during the night, which it wouldn't do if it was pointed at a pole. -dick