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From: martinl@molihp.UUCP (Martin M Lacey)
Newsgroups: net.puzzle
Subject: Re: Explorer paradox * SEMI-SPOILER *
Message-ID: <128@molihp.UUCP>
Date: Tue, 7-Jan-86 16:03:11 EST
Article-I.D.: molihp.128
Posted: Tue Jan  7 16:03:11 1986
Date-Received: Wed, 8-Jan-86 10:03:07 EST
References: <2667@sunybcs.UUCP> <1478@sphinx.UChicago.UUCP> <1011@ecsvax.UUCP>
Reply-To: martinl@HP-UX.UUCP (Martin M Lacey)
Organization: Moli Energy, Vancouver, B.C., CANADA
Lines: 49
Summary: 

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.