## Euclidean Distance

Euclidean Distance is the most common use of distance. In most cases when people said about distance , they will refer to Euclidean distance. Euclidean distance or simply 'distance' examines the root of square differences between coordinates of a pair of objects.

Formula

The interactive program below will enhance your understanding about Euclidean distance. Try usual input that you have learned in Pythagorean Theorem such as A = (0, 0) and B = (3, 4), then explore with your own input up to 6 dimensions.

Input coordinate values of Object-A and Object-B (the coordinate are numbers only), then press "Get Euclidean Distance" button. The program will directly calculate when you type the input.

Features Object A Object B

For example:

 Features cost time weight incentive Object A 0 3 4 5 Object B 7 6 3 -1

Point A has coordinate (0, 3, 4, 5) and point B has coordinate (7, 6, 3, -1).

The Euclidean Distance between point A and B is

The pattern of Euclidean distance in 2-dimension is circular. When the sink is on the center, it forms concentric circles around the center.

Euclidean distance is a special case of Minkowski distance with

Pseudo code of Euclidean Distance

Given: vector x1 and x2, each vector is a coordinate in N dimension

```function EuclideanDistance
dist=0
for d=1 to N   // d = dimension
dist=dist+(x1[d]-x2[d])^2
next
return sqrt(dist )
end function```
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