Jon G. wrote:
> Suppose you have 3 timbers of odd lengths, and plant them on the ground
to
> form a pyramid. If you know the lengths of the 3 timbers, and where you
> plant them on the ground, this Excel worksheet will find the apex of the
> pyramid where the 3 timbers meet. You only need use Sheet 1 for instant
> answers.
>
> http://www.freefileserver.com/index/p_download/hash_Ihywe3KYeyzT/
>
> The math behind this is in my web site,
>
> http://mypeoplepc.com/members/jon8338/math/index.html
>
I fail to see quite why you would want to approach this problem in such
a complex way. Given your static A, B and C point, with the distances to
your unknown point D, it is fairly trivial 3D geometry to locate D (if
there exists a solution).
E.g. you could note that D lies on the circular locus implied by its
distances from A and B, plus it also lies on the appropriate sphere
about C. The circle may intersect the sphere in two points, reflections
in ABC (or coincident in that plane). A somewhat "lop-sided" route, but
it works.
I think that the conditions for a solution to exist are simply that each
of the three triangles formed above ABC must be possible individually.
However, I'm not certain about that being necessary (nine
inequalities sounds too many) and sufficient (although maybe it is).
--
Lau AS! d-(!) a++ c++++ p++ t+ f-- e++ h+ r--(+) n++(*) i++ P- m++
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