English: This picture shows a collineation (i.e. an incidence-preserving bijection) of the affine plane over the field ${\displaystyle K=\mathbb {Q} ({\sqrt {2}})}$. This collineation is not affine, since it fixes three a triangle ${\displaystyle (OE_{1}E_{2})}$ of the plane but is not the identity though: The red points are reflected at the point O. This semilinear mapping of the plane is induced by the nontrivial automorphism of the field K.