section_path: In linear algebra/Abstract description/Affine description
section_name: Affine description
paragraph_text: Affine description
  
  A more abstract description still is to model physical space as a three-dimensional affine space E (3) {\displaystyle E(3)} over the real numbers. This is unique up to affine isomorphism. It is sometimes referred to as three-dimensional Euclidean space. Just as the vector space description came from 'forgetting the preferred basis' of R 3 {\displaystyle \mathbb {R} ^{3}}, the affine space description comes from 'forgetting the origin' of the vector space. Euclidean spaces are sometimes called Euclidean affine spaces for distinguishing them from Euclidean vector spaces.
  
  This is physically appealing as it makes the translation invariance of physical space manifest. A preferred origin breaks the translational invariance.