# Euclidean metric

## English

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### Noun

Euclidean metric ‎(plural Euclidean metrics)

1. (analysis) In the space ${\displaystyle \mathbb {R} ^{n}}$, the metric ${\displaystyle d({\vec {x}},{\vec {y}})={\sqrt {(x_{1}-y_{1})^{2}+(x_{2}-y_{2})^{2}+...+(x_{n}-y_{n})^{2}}}}$ where ${\displaystyle {\vec {x}}=(x_{1},...,x_{n})}$ and ${\displaystyle {\vec {y}}=(y_{1},...,y_{n})}$.