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Vive le Voltaire!

Hewitt

On 12/10/10, Tom Sult  wrote:
> Based on our discussion placing the position at the center of the
> cocked hat put you at good probability of not really being there...
> and the smaller the cocked hat the less likely you are to be there.  I
> find this most entertaining.  But despite the well reasoned arguments
> I can find no better way to place the "dot" than to put it someplace
> in the center-ish of the cocked hat by what ever method you find most
> stimulating.  Voltaire said of my profession "The Art of Medicine
> Consists of Amusing the Patient While Nature Cures the Disease".  I
> suspect methods for placing the "dot" are "Entertaining the Navigator
> While Waiting to Run Aground" ; )
>
> Thomas A. Sult, MD
> 3rd Opinion
> 1415 First First St. South #5
> Willmar, MN 56201
> 320 235 2101 Office
> www.3rdOpinion.us
> tsult@mac.com
>
>
>
>
> On Dec 10, 2010, at 4:22 PM, Gary LaPook wrote:
>
>> So we now have four geometric constructions (plus visual estimation
>> making a total of 5 ways) to plot the fix inside the cocked hat.
>> John Karl's probability diagram shows the probability of each of
>> these points to be essentially equal although the Symmedian point my
>> be ever so slightly more probable. So, what method should you use? I
>> think the decision should be based on ease of construction.
>> Obviously the easiest way is by eyeball and is the method I
>> recommend. The next easiest construction is my method of determining
>> the centroid by the "median" method. You only have to use dividers
>> to halve one of the LOPs, lay a straight edge from the opposite
>> corner to this point, and then use the dividers to mark the 2/3rds
>> point along the straight edge. The standard way to determine the
>> centroid is the text easiest, halve two of the LOPs and draw the two
>> lines from the opposite angles to those points. More difficult is
>> measuring the angles of two of the three corners, then dividing them
>> in half, and then finally plotting those lines. ( You can also find
>> the bisectors of the azimuths and plot them, you get the same point,
>> if the spread of azimuths exceed 180 degrees.) The most difficult
>> point to plot is the Symmedian point which requires that you first
>> plot both the medians and bisectors, measure the angle between each
>> of the lines in each set, and then draw in the additional lines
>> shifted by the angle between the lines in each set to the opposite
>> side of the bisector. Plotting the Symmedian point takes a lot more
>> work with no significant in probability that it represents the
>> actual position of the vessel.
>>
>> ( See my diagrams on the "three body fix" thread.)
>>
>> gl
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