Euclidean metric

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 ${\displaystyle {\vec {y}}=(y_{1},...,y_{n})}$.