The Euclidean distance between points 
and 
in Euclidean
space is
 |
It is the distance induced by the Euclidean norm and satisfies positivity, symmetry, and the triangle inequality, so it is a metric.
Euclidean Distance
See also
Distance, Euclidean Norm, MetricExplore with Wolfram|Alpha
References
Burago, D.; Burago, Y.; and Ivanov, S. A Course in Metric Geometry. Providence, RI: Amer. Math. Soc., 2001.Cite this as:
Weisstein, Eric W. "Euclidean Distance." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EuclideanDistance.html