Euclidean N-D Space to Model Great-Circle Distances
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Assuming you have a graph and know the distances between the points.
You know that they can roughly be modeled as points on the 2D surface of a sphere by treating the distances as great-circle or orthodromic distances, but not quite.
How effectively could we use an euclidean N-D space to model great-circle distances?
I guess my question would be answered by a graph/chart that plots the deviation/error by distance and dimension.
linear-algebra graph-theory spherical-geometry
asked Jan 9 at 19:12
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7017
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$begingroup$
Assuming you have a graph and know the distances between the points.
You know that they can roughly be modeled as points on the 2D surface of a sphere by treating the distances as great-circle or orthodromic distances, but not quite.
How effectively could we use an euclidean N-D space to model great-circle distances?
I guess my question would be answered by a graph/chart that plots the deviation/error by distance and dimension.
linear-algebra graph-theory spherical-geometry
asked Jan 9 at 19:12
guestguest
7017
$endgroup$
1
$begingroup$
I suspect it might never work. if we set/start with the distance between north and south poles, any points on the equator will always fall on the line between north and south, i.e: all points on the equator will collapse into one point, in any dimension.
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– guest
Jan 9 at 19:41
$begingroup$
maybe if we use the largest regular polytope in the dimension as a sort of backbone?
$endgroup$
– guest
Jan 9 at 20:10
add a comment |
$begingroup$
Assuming you have a graph and know the distances between the points.
You know that they can roughly be modeled as points on the 2D surface of a sphere by treating the distances as great-circle or orthodromic distances, but not quite.
How effectively could we use an euclidean N-D space to model great-circle distances?
I guess my question would be answered by a graph/chart that plots the deviation/error by distance and dimension.
linear-algebra graph-theory spherical-geometry
asked Jan 9 at 19:12
guestguest
7017
$endgroup$
Assuming you have a graph and know the distances between the points.
You know that they can roughly be modeled as points on the 2D surface of a sphere by treating the distances as great-circle or orthodromic distances, but not quite.
How effectively could we use an euclidean N-D space to model great-circle distances?
I guess my question would be answered by a graph/chart that plots the deviation/error by distance and dimension.
linear-algebra graph-theory spherical-geometry
linear-algebra graph-theory spherical-geometry
asked Jan 9 at 19:12
guestguest
7017
asked Jan 9 at 19:12
guestguest
7017
asked Jan 9 at 19:12
guestguest
7017
asked Jan 9 at 19:12
guestguest
7017
asked Jan 9 at 19:12
guestguest
7017
7017
1
$begingroup$
I suspect it might never work. if we set/start with the distance between north and south poles, any points on the equator will always fall on the line between north and south, i.e: all points on the equator will collapse into one point, in any dimension.
$endgroup$
– guest
Jan 9 at 19:41
$begingroup$
maybe if we use the largest regular polytope in the dimension as a sort of backbone?
$endgroup$
– guest
Jan 9 at 20:10
add a comment |
1
$begingroup$
I suspect it might never work. if we set/start with the distance between north and south poles, any points on the equator will always fall on the line between north and south, i.e: all points on the equator will collapse into one point, in any dimension.
$endgroup$
– guest
Jan 9 at 19:41
$begingroup$
maybe if we use the largest regular polytope in the dimension as a sort of backbone?
$endgroup$
– guest
Jan 9 at 20:10
1
1
$begingroup$
I suspect it might never work. if we set/start with the distance between north and south poles, any points on the equator will always fall on the line between north and south, i.e: all points on the equator will collapse into one point, in any dimension.
$endgroup$
– guest
Jan 9 at 19:41
$begingroup$
I suspect it might never work. if we set/start with the distance between north and south poles, any points on the equator will always fall on the line between north and south, i.e: all points on the equator will collapse into one point, in any dimension.
$endgroup$
– guest
Jan 9 at 19:41
$begingroup$
maybe if we use the largest regular polytope in the dimension as a sort of backbone?
$endgroup$
– guest
Jan 9 at 20:10
$begingroup$
maybe if we use the largest regular polytope in the dimension as a sort of backbone?
$endgroup$
– guest
Jan 9 at 20:10
add a comment |
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$begingroup$
I suspect it might never work. if we set/start with the distance between north and south poles, any points on the equator will always fall on the line between north and south, i.e: all points on the equator will collapse into one point, in any dimension.
$endgroup$
– guest
Jan 9 at 19:41
$begingroup$
maybe if we use the largest regular polytope in the dimension as a sort of backbone?
$endgroup$
– guest
Jan 9 at 20:10