Euclidean plane point-transformations preserving unit area or unit perimeter
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 (G. Martin, unpublished): Let \(x\to \bar x\) be a bijection of the Euclidean plane \(E_ 2\) onto itself such that if a,b,c are vertices of a triangle of area 1, then so are \(\bar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.
scientific article; zbMATH DE number 3897705