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removed deprecated (geometry) tag - see the tag info: http://mathoverflow.net/tags/geometry/info; if there are some other geometry-related tags which are suitable, please use some of them instead
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Martin Sleziak
Martin Sleziak
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Does list of distances define points uniquely  ?

typos, formatting
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Gerry Myerson
Gerry Myerson
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Is Does list of distances definingdefine points uniquely ?  

There isare N points on a plane. Is isit feasible to reproduce theretheir relative location having only the list of distances. Assuming that translation, rotation and mirror are allowed in the result. The list contains only distances between every pair of points, but not which points these are.

For a simple triangle like A=(0,0) B=(1,0) C=(1,1) the distance are: 
|AB| = 1 
|AC| = sqrt(2) 
|BC| = 1

The list would be: 1, 1, sqrt(2).

Is list of distances defining points uniquely ?  

There is N points on a plane. Is is feasible to reproduce there relative location having only list of distances. Assuming that translation, rotation and mirror are allowed in the result. The list contains only distances between every pair of points, but not which points these are.

For simple triangle like A=(0,0) B=(1,0) C=(1,1) the distance are: |AB| = 1 |AC| = sqrt(2) |BC| = 1

The list would be: 1, 1, sqrt(2).

Does list of distances define points uniquely ?

There are N points on a plane. Is it feasible to reproduce their relative location having only the list of distances. Assuming that translation, rotation and mirror are allowed in the result. The list contains only distances between every pair of points, but not which points these are.

For a simple triangle like A=(0,0) B=(1,0) C=(1,1) the distance are: 
|AB| = 1 
|AC| = sqrt(2) 
|BC| = 1

The list would be: 1, 1, sqrt(2).

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janst
janst
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Is list of distances defining points uniquely ?

There is N points on a plane. Is is feasible to reproduce there relative location having only list of distances. Assuming that translation, rotation and mirror are allowed in the result. The list contains only distances between every pair of points, but not which points these are.

For simple triangle like A=(0,0) B=(1,0) C=(1,1) the distance are: |AB| = 1 |AC| = sqrt(2) |BC| = 1

The list would be: 1, 1, sqrt(2).