physical interpretation or practical meaning of a distance
$begingroup$
How can I find/understand the physical explanation or practical
meaning of a distance? For example Euclidean distance is the shortest
path between two points, how about for other distances?
geometric-interpretation
asked Oct 5 '14 at 13:27
user45297user45297
114
$endgroup$
add a comment |
$begingroup$
How can I find/understand the physical explanation or practical
meaning of a distance? For example Euclidean distance is the shortest
path between two points, how about for other distances?
geometric-interpretation
asked Oct 5 '14 at 13:27
user45297user45297
114
$endgroup$
$begingroup$
Some distance functions have physical interpretations some don't. you should specify the metric you have in mind so people can comment on that.
$endgroup$
– Buddha
Oct 5 '14 at 13:45
$begingroup$
How can we find that a distance has/has not physical/geometric interpretation, e.g. Canberra distance? What is its importance in practice?
$endgroup$
– user45297
Oct 5 '14 at 18:49
$begingroup$
you can always google it or ask here to see if a certain metric has any applications in the real world. e.g. I've found this for Canberra distance. But I don't think having an application is an intrinsic mathematical property of a function.
$endgroup$
– Buddha
Oct 5 '14 at 20:19
add a comment |
$begingroup$
How can I find/understand the physical explanation or practical
meaning of a distance? For example Euclidean distance is the shortest
path between two points, how about for other distances?
geometric-interpretation
asked Oct 5 '14 at 13:27
user45297user45297
114
$endgroup$
How can I find/understand the physical explanation or practical
meaning of a distance? For example Euclidean distance is the shortest
path between two points, how about for other distances?
geometric-interpretation
geometric-interpretation
asked Oct 5 '14 at 13:27
user45297user45297
114
asked Oct 5 '14 at 13:27
user45297user45297
114
asked Oct 5 '14 at 13:27
user45297user45297
114
asked Oct 5 '14 at 13:27
user45297user45297
114
asked Oct 5 '14 at 13:27
user45297user45297
114
114
$begingroup$
Some distance functions have physical interpretations some don't. you should specify the metric you have in mind so people can comment on that.
$endgroup$
– Buddha
Oct 5 '14 at 13:45
$begingroup$
How can we find that a distance has/has not physical/geometric interpretation, e.g. Canberra distance? What is its importance in practice?
$endgroup$
– user45297
Oct 5 '14 at 18:49
$begingroup$
you can always google it or ask here to see if a certain metric has any applications in the real world. e.g. I've found this for Canberra distance. But I don't think having an application is an intrinsic mathematical property of a function.
$endgroup$
– Buddha
Oct 5 '14 at 20:19
add a comment |
$begingroup$
Some distance functions have physical interpretations some don't. you should specify the metric you have in mind so people can comment on that.
$endgroup$
– Buddha
Oct 5 '14 at 13:45
$begingroup$
How can we find that a distance has/has not physical/geometric interpretation, e.g. Canberra distance? What is its importance in practice?
$endgroup$
– user45297
Oct 5 '14 at 18:49
$begingroup$
you can always google it or ask here to see if a certain metric has any applications in the real world. e.g. I've found this for Canberra distance. But I don't think having an application is an intrinsic mathematical property of a function.
$endgroup$
– Buddha
Oct 5 '14 at 20:19
$begingroup$
Some distance functions have physical interpretations some don't. you should specify the metric you have in mind so people can comment on that.
$endgroup$
– Buddha
Oct 5 '14 at 13:45
$begingroup$
Some distance functions have physical interpretations some don't. you should specify the metric you have in mind so people can comment on that.
$endgroup$
– Buddha
Oct 5 '14 at 13:45
$begingroup$
How can we find that a distance has/has not physical/geometric interpretation, e.g. Canberra distance? What is its importance in practice?
$endgroup$
– user45297
Oct 5 '14 at 18:49
$begingroup$
How can we find that a distance has/has not physical/geometric interpretation, e.g. Canberra distance? What is its importance in practice?
$endgroup$
– user45297
Oct 5 '14 at 18:49
$begingroup$
you can always google it or ask here to see if a certain metric has any applications in the real world. e.g. I've found this for Canberra distance. But I don't think having an application is an intrinsic mathematical property of a function.
$endgroup$
– Buddha
Oct 5 '14 at 20:19
$begingroup$
you can always google it or ask here to see if a certain metric has any applications in the real world. e.g. I've found this for Canberra distance. But I don't think having an application is an intrinsic mathematical property of a function.
$endgroup$
– Buddha
Oct 5 '14 at 20:19
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Imagine a plane of Cartesian coordinates. Now consider two different points on it.
Now tell me in how many ways you can join them??
So Euclidean distance is defined as the shortest distance between two points which is a straight line.
answered Oct 5 '14 at 13:40
JasserJasser
1,678823
$endgroup$
add a comment |
$begingroup$
A distance (between two points, say) does not have to be a straight line or a shortest path -- a distance function is what you define it to be, but it has to be well-defined and unambiguous. For example, in the Cartesian plane, the Euclidean distance between two points is defined as the shortest path joining them, but the Taxicab distance between them is the shortest path if you 'move' from one to the other only along the 'roads' or lines parallel to the axes.
answered Oct 5 '14 at 13:53
shardulcshardulc
3,6861027
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Imagine a plane of Cartesian coordinates. Now consider two different points on it.
Now tell me in how many ways you can join them??
So Euclidean distance is defined as the shortest distance between two points which is a straight line.
answered Oct 5 '14 at 13:40
JasserJasser
1,678823
$endgroup$
add a comment |
$begingroup$
Imagine a plane of Cartesian coordinates. Now consider two different points on it.
Now tell me in how many ways you can join them??
So Euclidean distance is defined as the shortest distance between two points which is a straight line.
answered Oct 5 '14 at 13:40
JasserJasser
1,678823
$endgroup$
add a comment |
$begingroup$
Imagine a plane of Cartesian coordinates. Now consider two different points on it.
Now tell me in how many ways you can join them??
So Euclidean distance is defined as the shortest distance between two points which is a straight line.
answered Oct 5 '14 at 13:40
JasserJasser
1,678823
$endgroup$
Imagine a plane of Cartesian coordinates. Now consider two different points on it.
Now tell me in how many ways you can join them??
So Euclidean distance is defined as the shortest distance between two points which is a straight line.
answered Oct 5 '14 at 13:40
JasserJasser
1,678823
answered Oct 5 '14 at 13:40
JasserJasser
1,678823
answered Oct 5 '14 at 13:40
JasserJasser
1,678823
answered Oct 5 '14 at 13:40
JasserJasser
1,678823
1,678823
add a comment |
add a comment |
$begingroup$
A distance (between two points, say) does not have to be a straight line or a shortest path -- a distance function is what you define it to be, but it has to be well-defined and unambiguous. For example, in the Cartesian plane, the Euclidean distance between two points is defined as the shortest path joining them, but the Taxicab distance between them is the shortest path if you 'move' from one to the other only along the 'roads' or lines parallel to the axes.
answered Oct 5 '14 at 13:53
shardulcshardulc
3,6861027
$endgroup$
add a comment |
$begingroup$
A distance (between two points, say) does not have to be a straight line or a shortest path -- a distance function is what you define it to be, but it has to be well-defined and unambiguous. For example, in the Cartesian plane, the Euclidean distance between two points is defined as the shortest path joining them, but the Taxicab distance between them is the shortest path if you 'move' from one to the other only along the 'roads' or lines parallel to the axes.
answered Oct 5 '14 at 13:53
shardulcshardulc
3,6861027
$endgroup$
add a comment |
$begingroup$
A distance (between two points, say) does not have to be a straight line or a shortest path -- a distance function is what you define it to be, but it has to be well-defined and unambiguous. For example, in the Cartesian plane, the Euclidean distance between two points is defined as the shortest path joining them, but the Taxicab distance between them is the shortest path if you 'move' from one to the other only along the 'roads' or lines parallel to the axes.
answered Oct 5 '14 at 13:53
shardulcshardulc
3,6861027
$endgroup$
A distance (between two points, say) does not have to be a straight line or a shortest path -- a distance function is what you define it to be, but it has to be well-defined and unambiguous. For example, in the Cartesian plane, the Euclidean distance between two points is defined as the shortest path joining them, but the Taxicab distance between them is the shortest path if you 'move' from one to the other only along the 'roads' or lines parallel to the axes.
answered Oct 5 '14 at 13:53
shardulcshardulc
3,6861027
answered Oct 5 '14 at 13:53
shardulcshardulc
3,6861027
answered Oct 5 '14 at 13:53
shardulcshardulc
3,6861027
answered Oct 5 '14 at 13:53
shardulcshardulc
3,6861027
3,6861027
add a comment |
add a comment |
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$begingroup$
Some distance functions have physical interpretations some don't. you should specify the metric you have in mind so people can comment on that.
$endgroup$
– Buddha
Oct 5 '14 at 13:45
$begingroup$
How can we find that a distance has/has not physical/geometric interpretation, e.g. Canberra distance? What is its importance in practice?
$endgroup$
– user45297
Oct 5 '14 at 18:49
$begingroup$
you can always google it or ask here to see if a certain metric has any applications in the real world. e.g. I've found this for Canberra distance. But I don't think having an application is an intrinsic mathematical property of a function.
$endgroup$
– Buddha
Oct 5 '14 at 20:19