Euclidean Metric
The Euclidean metric is the function 
that assigns to any two vectors in Euclidean 
-space 
and 
the number
 |
(1)
|
and so gives the "standard" distance between any two vectors in 
.
The Euclidean metric in Euclidean three-space 
is given by
![(g)_(alphabeta)=[1 0 0; 0 1 0; 0 0 1],](/images/equations/EuclideanMetric/NumberedEquation2.gif) |
(2)
|
giving the line element
 |  |  |
(3)
|
 |  |  |
(4)
|
where Einstein summation has been used.
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10 - 9 + 8 - 7 + 6 - 5 + 4 - 3 + 2 - 1