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From: hes@ecsvax.UUCP (Henry Schaffer)
Newsgroups: net.puzzle
Subject: Re: Polar paradox * SEMI-SPOILER *  (i.e., answer but no analysis)
Message-ID: <1011@ecsvax.UUCP>
Date: Thu, 2-Jan-86 22:27:00 EST
Article-I.D.: ecsvax.1011
Posted: Thu Jan  2 22:27:00 1986
Date-Received: Sat, 4-Jan-86 05:37:27 EST
References: <2667@sunybcs.UUCP> <1478@sphinx.UChicago.UUCP>
Organization: NC State Univ.
Lines: 35

> 
> > 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!)
> 
> Yes he will, and after travelling only a finite distance.  However, while
> spiralling in towards the Pole, he will go around it an infinite number
> of times.   (All this assumes we've shrunk him to a point, a sad fate
> for a Great Explorer.)
> -- 
>             -- Mitch Marks @ UChicago 
   The Great Explorer is just following a gyrocompas which (initially) is
pointing NW.  What it is labeled shouldn't matter to the gyrocompass at all.
If he follows the initial arc (which may not be due NW after
a while) he will traverse a circle, not necessarily a great circle, which
will not touch the North Pole. 

  My assumption is that the gyrocompass will point along the same arc on
the globe - and also that it doesn't care about the curvature in the
globe, only about not wavering in the left-right direction.  I don't see
how it would  lead to a spiral (but then again I don't understand precession,
and how the rotation of the earth as well as movement around the curvature
of the earth might affect the precession.)

  After we all flounder around, would someone not only supply the answer
but also explain it well.

--henry schaffer
(Good Grief!  I just realized that this sort of stuff is *out of place* in
this newsgroup!  It should go into net.physics!