compasses

From: Owen Jones (oj@maths.anu.edu.au)
Date: Mon 05 May 1997 - 03:26:26 EEST


Sorry, but professionalism wouldn't let this one pass...

Philip Hibbs on compasses:

> Gloranthan compasses - You actually need three different compasses to
> pin your location exactly, two will tell you that you are somewhere on
> a circular line between the two compass points. eg. if they point at
> right-angles to each other, you are on a semicircular line from one to
> the other, if they are at an acute angle, the circlular segment is more
> than a semicircle.

Not in any geometry I'm familiar with, Euclidean or otherwise. Not even
if you were willing to abandon the concept of the line as the shortest
distance between two points. One of the fundamental axioms of any
geometry is that two (different) straight lines meet at most once. So,
assuming a compass works by pointing in a straight line to some
reference, if you are on two lines given by two compasses, your
position is uniquely determined. The only time you will have problems

is when your compasses give the same line. In theory this problem can
be solved by moving a yard to your left or right. In practice you may
have to move a lot more for a measurable difference in bearings to
manifest.

> See http://ourworld.compuserve.com/homepages/PHibbs/Compass.PNG

Tried, but not in a format my machine could translate.

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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