yet more on compasses

From: Owen Jones (oj@maths.anu.edu.au)
Date: Tue 06 May 1997 - 04:13:57 EEST


Apologies to all those with no interest in geometry. Also, apologies to
Philip Hibbs for the undeservedly uncompromising tone of my response to
his initial posting: after a bit more thinking, I think I see where Philip
is coming from, and my own understanding becomes clearer.

Philip Hibbs and Trotsky are certainly correct to say that to pinpoint
your location you need more information than that given by two needles
pointing at two different locations. A third reference is needed, such as
that given by a third compass, or (for the lunars) the position of the Red
Moon in the sky, or (for the sun domers) an estimate of North based on the
sun (put a stick in the ground, when its shadow is shortest, the shadow is
pointing South, assuming you are in the Northern hemisphere, and that this
works in Glorantha). So, doing this at night in Prax would be difficult,
as it would be anywhere along the equator. The (unjustified) assumption I
made was that a Gloranthan compass would give you an angle from North
(say), rather than just pointing in whatever direction. In trigonometric
terms, to solve a triangle you need three bits of information. With just
two compasses you only get one angle and the length of the opposite side
(calculated from a map say). A third bearing gives you enough information
to work out the other two angles.

Back to the relatively straight forward investigation of stochastic
processes!

Owen

Owen Jones
Centre for Maths and its Applications, School of Math. Sciences
Australian National University, ACT 0200
Ph +61 6 249 2897 (office) 249 4552 (direct) Fax +61 6 249 4675
Web page http://wwwmaths.anu.edu.au/~oj/

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