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Frank,

I didn't mean to be poking any sticks at you in my post, and considered
putting in a disclaimer to that effect, and I recognize that
approximate methods can be as accurate as "exact" methods, but I see no
need to change well-established terminology in this field.  As I
recall, the phrase "approximation" is used almost invariably when
series expansions, etc, are used to simplify equations; if nothing
more, they remind us that the approximate methods might not work in all
situations.  I also recognize that an understanding of the terms in an
approximate method can give one a better understanding of the physics.
I was merely trying to point out the distinction between the two
methods and to point out one advantage of the exact method for those of
us who are not as mathematically proficient as you.

I remember acquiring a TI-35 or TI-48 (can't remember the number)
programmable calculator in 1978 or so and programming in Taylor Series
expressions for sine, etc, just to see them in action and to try to
infer how many terms were in the calculator's series for sine.  So I
know about Taylor Series and what they're used for.  But it would not
be a simple matter for me to derive an approximate method for solving a
spherical trig problem, whereas it is for you.  I suppose I could do
it, but it would take me several days.  I expect it also would take me
quite some time to even do that Taylor Series for sine in the TI-35.
Thus, for me to understand the basic spherical trig problem, the
approximate method gives me little guidance, while the exact method
gives quite a bit more.

I also think it is wholly true that the approximate methods were
developed to ease the computational burdens imposed by the exact
methods.  Can you offer any other reason why the approximate methods
were developed and published?

I might add that I don't regret that my post stimulated you to educate
us more thoroughly.  But my apologies if it offended you.

Fred

   

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