Der Satz von Beckman-Quarles im rationalen Raum. (The Beckman-Quarles theorem in rational space) (Q1819369)

The Beckman-Quarles theorem states that every unit distance preserving map \(f: {\mathbb{R}}^ n\to {\mathbb{R}}^ n\) is an affine isometry. In rational space with arbitrary non-degenerate quadratic form an analogous theorem holds for \(n>4\), but not for \(n\leq 4\). The proof uses the Hasse-Minkowski theory of rational quadratic forms.