An elementary proof of the theorem of Beckman and Quarles
type: Item
instance of: scholarly article
title: An elementary proof of the theorem of Beckman and Quarles
zbMATH Open document ID: 0701.51013
published in: Elemente der Mathematik
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/141394
review text: 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.
reviewed by: Hans Havlicek
Mathematics Subject Classification ID: 51N20
Mathematics Subject Classification ID: 51M04
zbMATH DE Number: 4149043
zbMATH Keywords: Beckman-Quarles theorem
author: Walter Benz
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4149043