An elementary proof of the theorem of Beckman and Quarles (Q914156)

An elegant proof of the theorem of Beckman and Quarles is given for the Euclidean space on \({\mathbb{R}}^ n\) \((1<n<\infty)\). The prerequisites needed to follow the proof are indeed elementary: The reader should only be familiar with the basic concepts of geometry in \({\mathbb{R}}^ n:\) the canonical inner product, the norm associated to this inner product, orthonormal bases and the triangle inequality.