Glossary: Mathematics - dudycooly/1235 GitHub Wiki

Euclidean distance

A point in n-dimensional Euclidean space has n coordinates:

$A=(a_1,a_2,\cdots,a_n)$

Given two points in a Euclidean space, A and B, the distance between them is:

$d(A,B)=\sqrt{\sum_{i=1}^n(a_i-b_i)^2}$

This formula can be proven by repeatedly applying the Pythagorean theorem.