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I'm a bit puzzled by Peter Hakel's "illustration" in the two pages attached 
to [10414], although the more-recent mathematical talk is quite beyond my 
grasp.

The discussion seems to be about whether various mathematical techniques 
produce a "fix". I would not describe the position circles in that example, 
which are osculating rather than intersecting, as producing a "fix". Both 
are tangential to a North-South line passing through 20� West. Although the 
point on the equator at 20� West may be the only point that actually 
satisfies the two altitudes, other positions, to its North and South, come 
so infinitesimally close to meeting that requirement that the result is 
really a "line-fix". It's an example of the degenerate situation, of two 
bodies with the same azimuth, that navigators know to avoid. In reality, 
they would choose another body, or wait a bit, in time.

In those circumstances, it's no surprise to me that difficulties arise in a 
mathematical solution. A real navigator, working from a simple plot, would 
realise what was going wrong immediately.

===================

On another matter altogether, Peter has experienced some problems in 
quadratic fitting with Excel. So have I, using Excel 2000, and in doing the 
same job, fitting a quadratic for longitude-around-noon. Excel will 
cheerfully plot a quadratic fit to such a set of points, and apparently a 
good fit too, and if asked to, will display the resulting coefficients, as 
numbers printed on top of the fitted graph. And the only way I've found to 
extract those coefficients, to use for further Excel calculation, is to read 
them off that graph, and then type them back in again. Frustrating, but 
acceptable. But, having done just that, and then used those numbers to 
regenerate the quadratic curve once again, for checking, the resuting plot 
can differ significantly from the quadratic that Excel had plotted before. 
The reason is that in  displaying those parameters, they are truncated by 
rounding-off in such a way as that significant digits have been lost. I've 
got round it by renumbering the divisions along the x-axis, so its numerical 
values increase by 10, or perhaps 100, accordingly.

If Peter can offer any insight into how to get at those coefficients 
directly, or how to alter their rounding-off, it would be helpful.

George.

contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. 


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