Euclidean plane point-transformations preserving unit area or unit perimeter
type: Item
instance of: scholarly article
title: Euclidean plane point-transformations preserving unit area or unit perimeter
zbMATH Open document ID: 0563.51015
DOI: 10.1007/BF01194898
published in: Archiv der Mathematik
publication date: 1985-01-01T00:00:00Z
review text: Two results are proven: 1. (G. Martin, unpublished): Let \(x\to \bar x\) be a bijection of the Euclidean plane \(E_ 2\) onto itself such that if a,b,c are vertices of a triangle of area 1, then so are \(\bar a,\bar b\) and \(\bar c.\) Then the mapping \(x\to \bar x\) is equiaffine. 2. Let \(x\to \bar x\) be a bijection of \(E_ 2\) onto itself such that if a,b,c are vertices of a triangle of perimeter 1, then so are \(\bar a,\bar b\) and \(\bar c.\) Then \(x\to \bar x\) must be a Euclidean motion.
Mathematics Subject Classification ID: 51M05
zbMATH DE Number: 3897705
zbMATH Keywords: Euclidean plane
zbMATH Keywords: area
zbMATH Keywords: perimeter
zbMATH Keywords: Euclidean motion
author: June A. Lester
MaRDI profile type: Publication
cites work: On Isometries of Euclidean Spaces
cites work: Axiomatic relativity theory
cites work: Transformations of Robertson-Walker spacetimes preserving separation zero
cites work: Q3943557
description: scientific article; zbMATH DE number 3897705