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    Re: Cocked hats, again.
    From: Gary LaPook
    Date: 2007 Mar 21, 10:54 -0700

    GAry LaPook wrote:
    
    Well, this thought experiment did help. It is hard to dispute the 1 in
    4 arguement so I will accept that point.
    
    But the important point about this whole discussion is to demonstrate
    to all of us who were taught that our position must be inside the
    cocked hat that it ain't necessarily so and a simple statement like
    "only 1 in 4" is a good way to drive that point home.
    
    Gl
    
    On Mar 15, 11:44 pm, Paul Hirose  wrote:
    > My cocked hat "thought experiment" confirms Huxtable's Theorem.
    >
    > Imagine three perfect observations, so the LOPs all meet at a point.
    > That's the true position of the vessel.
    >
    > In the real world all observations have error. None of the LOPs will
    > pass precisely through that point. To simulate observational error, move
    > each LOP some random distance toward or away from its body.
    >
    > Moving the first LOP generates a triangle with the true position at one
    > vertex. For the remaining two LOPs (which meet at the vertex) there are
    > four possible permutations of toward and away. Only one yields a
    > triangle containing the true position: 1) move one LOP in the direction
    > that enlarges the triangle, 2) move the other LOP in the direction that
    > enlarges the triangle.
    >
    > If you move the LOP in step 1 the other way, the true position is
    > outside the triangle, and on the LOP that hasn't moved yet. Then no
    > matter which direction you move that LOP, it's impossible to form a
    > triangle containing the point.
    >
    > None of this depends on how the sights are distributed in azimuth. As
    > long as all three are equally likely to err toward or away, there's a
    > 25% probability that the true position lies within the triangle.
    >
    > Skewing the toward/away probability will change that. For example, if
    > the azimuths are about equally spaced and you forget to apply the dip
    > correction, it becomes *more* likely that the cocked hat contains the
    > true position!
    >
    > --
    > I block messages that contain attachments or HTML.
    
    
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