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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: A simple three-body fix puzzle
From: Tom Sult
Date: 2010 Dec 10, 15:16 -0600
It seems to me the point of this is that the best probability of location is a "donut" that roughly follows the lop's around the hat. We have learned that we have perhaps a 25% +/- the details chance of being close to any "center" of the hat. And we can calculate the probability distribution of our location along any one of our LOP's. If the gausien distribution is centered on the LOP then we have a "fuzzy donut" probability and not a Position.

So the answer to "whitch point is it is correct?" is... There is no point.

Thomas A. Sult, MD
Sent from iPhone

On Dec 10, 2010, at 14:32, Greg Rudzinski <gregrudzinski@yahoo.com> wrote:

Herbert,

Could you inspect and comment on the linked diagrams.

The first linked diagram shows a 30°/60°/90° triangle plot with bisected vertex, internal circle tangents, vertex to tangent intersections (symmedian or Gergonne point), and the d/2 circle around point P.
(very busy plot)

The Gergonne point (Gp) seems to be dependent on the bisected angle point (Bp). Point Bp weighs each LOP equally and point Gp shifts away from the smallest angle and toward the largest angle. The d/2 circle intersects at three points along the bisection and tangent lines.

The question now is which point is correct ? Gp or one of the three d/2 intersections ? If I had to guess then I would select the intersection of the d/2 circle, P perpendicular, and 60° vertex to inner circle tangent (see second linked diagram)

Greg Rudzinski
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