从三角不等式看Beckman–Quarles定理

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2021-06-24 DOI:10.1515/advgeom-2020-0024

V. Totik

引用次数: 0

摘要

摘要我们给出了经典Beckman–Quarles定理的一个简短、初等和非计算的证明，该定理断言欧几里得空间到自身的映射（保持距离1）必须是等距的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The Beckman–Quarles theorem via the triangle inequality

Abstract We give a short, elementary and non-computational proof for the classical Beckman–Quarles theorem asserting that a map of a Euclidean space into itself that preserves distance 1 must be an isometry.

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来源期刊

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.