On Jul 7, 3:59=A0pm, Irving Drinkwine <Idrinkw...@[EMAIL PROTECTED]
> wrote:
> What is the minimum number of points ( a point being BOTH a location
> and distance from ME) must I know to be able to plot where I am on a 2
> dimensional grid? Is it 2?
> And I'd need to know 3 , to know my location in 3 dimensions?
>
> What if I know 1 point, and the distance I am for a 2nd point, but not
> the 2nd points location. =A0That would be of no help, right?
>
> Where could I look up more information on this, any suggestions?
>
> Thanks
> Irving
> Drinkwine
In two dimensions knowing your distance to 2 locations
constrains your location to a pair of points that are
symmetric about the line through those 2 locations,
except for the special case that your location is on
that line through those 2 locations.
Think about the intersecting circles of known radii
about those two points; there are two points of
intersection which are your possible locations.
So in two dimensions distances to 2 known locations
leaves just that ambiguity of two possible solutions
(in the general case).
In this sense it is more accurate to say that to
determine your location in two dimensions, you may
need distances to 3 noncollinear known locations.
[Noncollinear means not in a straight line.]
Likewise in three dimensions, knowing your distance
to 3 known locations (necessarily lying in some
common plane) leaves an ambiguity in your location
(by virtue of symmetry with respect to the plane
through the 3 known locations), so unless you are
actually located in the plane (reducing the problem
to the two dimensional case), 4 distances to known
locations not all lying in a common plane are
needed.
regards, chip
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