# Euclidean

Euclidean space is a vector space ${\displaystyle \mathbb {R} ^{d}}$ equipped with the standard Euclidean metric

${\displaystyle ds^{2}=dx_{1}^{2}+\ldots +dx_{d}^{2}.}$

The isometries (rigid motions) of Euclidean space are generated by the translations, rotations, and reflections.