Re: The mathematics of Triangulation

From: Daniel W. Johnson (panoptes_at_iquest.net)
Date: 08/30/04 

Date: Sun, 29 Aug 2004 21:07:10 -0500

sbben <sbben@comcast.net> wrote:

> Ok, I think I get it. Will the difference in delay be due to the arc
> of the sound wave?

I suppose you could describe it as a consequence of the fact that sound
travels in straight lines rather than following taxicab geometry.

Another way relies on the triangle inequality. Using your picture:

          gunshot -]
                                  ] 3 seconds of distance
                                 -] in this span
reciver1 reciever2
                                 -]
                                  ] 6 seconds of distance
                                  ] in this span
                                  ]
                                  ]
         reciever3 -]

Call the site of the gunshot point G and the three receivers points A,
B, and C respectively. Your calculation assumed GC = GB + BC, but this
is only true if B is on the line from G to C. Otherwise, GC < GB + BC. 

-- 
Daniel W. Johnson
panoptes@iquest.net
http://members.iquest.net/~panoptes/
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