Re: More compasses

From: Loren Miller (loren@wharton.upenn.edu)
Date: Wed 07 May 1997 - 01:59:19 EEST


Telmori@t-online.de (Thomas Gottschall)
> Take a piece of paper and mark to points A and B. This are the points
> your two compasses are pointing at. Choose a point X. This is the point
> where you stand. Now decide to what directions both compasses point.
> Draw a line through point A with the direction your compass showed you,
> do the same with B. The meeting point is X of course.
> This is how you can say where you are if you have a map. Without a map
> you can't do it.

There is one more thing to complicate your example. Your example
presumes that you know an absolute direction. The problem is that you
have nothing to tell you any absolute direction.

In fact, you will have one compass that points at A. All you know
about that direction is that it points at A, so you can call the
direction A'. The other compass points at B, and the direction is
B'. Now is the time to determine your exact point, but your only
numerical data is the angle between A' and B', which ends up
describing an arc between A and B. (to demonstrate this have someone
hold their fingers a handswidth apart and then set the corner of a
square object such as a book inbetween the fingers. Now move the
point around while touching both fingers with the edge of the book.
The point will trace an arc.) You don't have the distance to either
A or B. However, given a precise enough compass, you could take your
readings, measure the angle, and then travel a day's travel towards
a landmark that bisects the angle, and then use that new A2' and B2'
in combination with A' and B' to accurately triangulate your
position. You would need another datum, such as the direction of
true north, in order to triangulate from a single measurement.

No?

+++++++++++++++++++++++23
Loren Miller <loren@wharton.upenn.edu>
A priest, a rabbi, a Penn student, and an elephant walk into
a bar. The bartender says, "what is this, some kinda joke?"

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