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Frank

I agree on average sight. Cocked hat is not very helpful - except for
comic value I suppose.

The Symmedian point makes some sense from its construction and the
isogonal conjugate of a median ("symmetric median"). However the
alternative name, especially popular in the French literature is the
Lemoine point.  Now for the case of more than three lines in the plane
it is still called the (generalized) Lemoine point.  For example see
Thas's paper (Thas, C. (2003), ‘A generalization of the Lemoine
point’, Forum Geometricorum 3, 161–167.)  It might also be called the
Grebe point.

The symmedian point makes sense for triangle and it also makes sense
for n+1 equations in n dimensions (for example n=3, GPS with four
sats) as the construction is the reflection of some kind of median.
(papers by Sadek et al) Again it does not make sense for  more than
n+1 equations.

There is an alternative. The Encyclopedia of Quadrifigures calls it
QL-P26 the "least squares point"
https://chrisvantienhoven.nl/ql-items/ql-points/ql-p26

The Encylopedia of Polyfigures, similarly lists the Least Squared
Distances Point
https://chrisvantienhoven.nl/nl-items/nl-obj/nl-pts/nl-n-p6

One nice thing is that as there is a systematic list of triangle,
quadrilateral and polyfigure points we should not have the situation
in the 1800s when several people come up with the same point and don't
know it has already been discovered.  Or at least there is no excuse!

Details of some the things I mention are in the paper I submitted with
Kimberling and Moses to the Journal of Navigation.  If anyone on the
list is interested I can send a sneak preview but it is not on
"general release" yet! (bill.lionheart@manchester.ac.uk)

Best wishes


Bill
On Sun, 2 Dec 2018 at 18:20, Frank Reed  wrote:
>
> Bill Lionheart, you asked:
> "On this subject of terminology can I check what you call the result of 
averaging a series of sights of the same body? Is it still called a sight?"
>
> I suggest that we stick with plain language whenever possible, so I call 
that "the average" or "an averaged altitude" or "an average of sights". It 
doesn't need a new name.
>
> Speaking of altitudes, one of the most common cases of jargon confusion in 
celestial navigation comes from the shorthand names used in sight reduction. 
We have Hs for the "raw sextant altitude" and Ho for the "corrected sextant 
altitude" and sometimes we even throw in Ha at an intermediate stage. These 
"names" are about as obscure as they could be. You have to learn the names 
eventually, at least Hs and Ho, to follow the literature, but training 
beginners to "talk the jargon talk" should be a low priority. Save it for 
later if possible. It's much more comprehensible if we write these out in a 
bit of "longhand": write out "raw sextant altitude" and write out "corrected 
sextant altitude" when possible.
>
> And then, of course, there's the symmedian point. This is a dreadful name, 
but if we want to discuss the concept mathematically, that's it --that's the 
standard name. There's no significant alternative. Myself, I have never once 
used the phrase "symmedian point" in a class for beginners since it covers 
only a limited case: the three-body fix with equally weighted sights and no 
systematic error. This is not worth the time, and --even though it sounds 
less technical-- I also never define the "cocked hat" since that's just a 
weird name for something simple. We need the latter name to follow the 
culture of navigation, the coded conversations of the subject (english 
language navigation culture), but not to understand the subject and 
principles of celestial navigation itself.
>
> (I originally wrote per se for "itself" but that's its own sort of jargon.. 
going Latin is a bit passé... uh-oh... per se is passé??)
>
> Frank Reed
>
> 

   

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