ContextQMD
Back to Javascript Algorithms

Euclidean Distance

src/algorithms/math/euclidean-distance/README.md

latest1.7 KB
Original Source

Euclidean Distance

In mathematics, the Euclidean distance between two points in Euclidean space is the length of a line segment between the two points. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefore occasionally being called the Pythagorean distance.

Distance formulas

One dimension

The distance between any two points on the real line is the absolute value of the numerical difference of their coordinates

Two dimensions

Higher dimensions

In three dimensions, for points given by their Cartesian coordinates, the distance is

Example: the distance between the two points (8,2,6) and (3,5,7):

In general, for points given by Cartesian coordinates in n-dimensional Euclidean space, the distance is

References