We show that if any one-to-one mapping preserves regular n-polygons, then it is actually an isometry. More precisely, we prove that if a one-to-one mapping from R^(m) to R^(m) (m≥3) maps every regular n-polygon onto regular n-polygon, then it is an ...
We show that if any one-to-one mapping preserves regular n-polygons, then it is actually an isometry. More precisely, we prove that if a one-to-one mapping from R^(m) to R^(m) (m≥3) maps every regular n-polygon onto regular n-polygon, then it is an isometry.