Older literature refers to this metric as Pythagorean metric. The technique has been rediscovered numerous times throughout history, as it is a logical extension of the Pythagorean theorem.
The Euclidean distance between points and , in Euclidean n-space, is defined as:
For two 1D points, and , the distance is computed as:
The absolute value signs are used since distance is normally considered to be an unsigned scalar value.
In one dimension, there is a single homogeneous, translation-invariant metric (in other words, a distance that is induced by a norm), up to a scale factor of length, which is the Euclidean distance. In higher dimensions there are other possible norms.
For two 2D points, and , the distance is computed as:
Alternatively, expressed in circular coordinates (also known as polar coordinates), using and , the distance can be computed as:
For two 3D points, and , the distance is computed as
For two N-D points, and , the distance is computed as
Spatial implications associated with using Euclidean distance measurements and geographic centroid imputation in health care research.(METHODS BRIEF)(Report)
Feb 01, 2010; Geographically based health care research commonly utilizes methodologies and measurements attainable using a geographic...