Compasses

From: TTrotsky_at_aol.com
Date: Mon, 5 May 1997 06:03:40 -0400 (EDT)

<< 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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