Compasses

From: TTrotsky@aol.com
Date: Mon 05 May 1997 - 13:03:40 EEST


<< Phillip Hibbs:
> 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.
 
Owen Jones:
 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. >>

     Er... I know you're a mathematician, and I know that I have't exactly
had a high record for accuracy on these pages, but I just don't see how this
can be right. Not the bit about the axiom, that's evidently true... I just
don't see how it applies in this case. Remember the lines may be of different
length, and you have no way of measuring this. I tried drawing it on paper
and it looks like Phillip is right. Can't send diagrams over e-mail, but I've
convinced meself. Two lines may meet only once, but there are an infinity of
lines that meet at the same angle, aren't there? And the angle is what you're
measuring with compasses...

     PS: sorry about including somebody else's address in the middle of my
last post. It confused the hell out of me when I read the last digest, and I
knew what I'd written...

All hail the Reaching Moon
    Trotsky

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