math solution, fyi
in [Physics]
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From: Jon on 11 Jun 2010 19:57 If you have Excel, here is the solution to a problem involving vectors: http://mypeoplepc.com/members/jon8338/sitebuildercontent/sitebuilderfiles/triangulation00.xls You input the lengths of three lines and their starting coordinates, and the engine calculates where they intersect ( in three dimensions). I solved the problem when I was in the mental hospital in 1988. It was all I could do to keep my sanity. This is ~some~ of the math used to determine GPS coordinates. It also calculates the two points as the result of the intersection of three spheres. Jon Giffen intrepid(a)bellaire.tv
From: Uncle Al on 12 Jun 2010 10:48 Jon wrote: > > If you have Excel, here is the solution to a problem involving vectors: > > http://mypeoplepc.com/members/jon8338/sitebuildercontent/sitebuilderfiles/triangulation00.xls > > You input the lengths of three lines and their starting coordinates, and the > engine calculates where they intersect ( in three dimensions). [snip] Why should three lines in (presumed Euclidean) 3-D intersect? There are *eight* primary geometries of 3-space, Bull. Amer. Math. Soc. 6 357-381 (1982) Bull. Lond. Math. Soc. 15(5) 401-487 (1983) WP Thurston, "Three-dimensional geometry and topology," Vol. 1. Princeton Mathematical Press, Princeton, NJ, 1997. -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz4.htm
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