On Jan 7, 7:25 am, marcelo <[email protected]> wrote:
> On Jan 7, 3:18 pm, Markw65 <[email protected]> wrote:
>
> > If you're going to pick nits, no, its not a lune, because a lune is
> > defined by *two* great circles, and there's only one in my example
>
> There are two.
> The Prime Meridian + anti-meridian is one and the Equator is another.
> So, it's a lune.
But what you're missing, is that there are an infinite number. Why do
you pick on the Equator?
I explained in my last post why the correct choice is the one through
the pole. But again, all of this is irrelevant to my actual claim.
>
> > I'll admit that I should have put the third point at 1,180 to avoid
> > that problem. Again, it doesnt change anything as far as the original
> > problem goes.
>
> Correct. Because 1,180 is still on the anti-meridian. :-)
>
> > > > But to be honest, Im not sure your definition is particularly
> > > > authoritative - simply because it *does* exclude degenerate triangles.
>
> > > Search for other definitions until you find a site you trust and show
> > > us a link.
> > > All the definitions I can find refer to three great circles, not more
> > > not less.
>
> > I'll admit that I couldnt find one. But its doesnt affect the argument
> > at all.
>
> Of course it does. If I can prove my claim with links to definitions
> and you cannot.
The only thing its relevant to is the definition of a spherical
triangle - which has *no bearing* on the correctness of Mike's
formula, or on the validity of my proof.
So it doesnt affect the argument *at all*.
>> So where is the centre of gravity on that great circle? (29,60) may
>> well be a reasonable answer for the spherical triangle drawn on the
>> surface of the earth.
And my response was:
> Not by any definition of "reasonable". The spherical "triangle" is
> just a line (an arc, if you will). That point is nowhere near the arc.
Which was intended to point out that its not a triangle at all (or
rather, its what I would call a degenerate triangle - but we
apparently disagree on that point).
But for the 57th time, its totally irrrelevant!!!!!
> In more general terms, this is your first thread in this forum and
> you're saying that both Mike and Andrew, who have been crowned as
> 'Gurus' by Google, are wrong.
They are (but, just for the record, Im not talking about whether or
not they are right about the definition of spherical triangle, just
about whether or not mike's method for computing the center of gravity
of three points is correct or not).
> I'd suggest you use the web interface to Google Groups to check out
> the profiles. :-)
They are both smart guys. I've read a lot of their posts. And some of
Mike's tutorials.
Which is why it was important to point out the flaw in Mike's formula.
Too many people would accept it blindly.
> I still think there's nothing wrong with Mike's method. If you think
> there is, then I think you need to provide better proof of what you're
> claiming.
I proved it in my first post.
- My first example was somewhat obscured by the fact that I picked two
opposing points on the equator. I see that that was a mistake -
because it led to too many red herrings. But it *still* shows that the
formula is wrong.
- My second example (from that same post) doesnt have that problem,
but it still suffers from the "is it or is it not a triangle" problem
(which, yet again, doesnt affect anything. Who cares if its a
triangle? The center of gravity of the three points is nowhere near
the point given by Mike's formula).
And finally, the cleaned up examples from my last post avoided all the
problems *and* demonstrated the error in the formula.
I have provided counter examples. What better proof could there be?
Mark
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