Abstract

We introduce a new characterization of linear isometries. More precisely, we prove that if a one-to-one mapping f: ℝn→ℝn(2 ≦n ∞) maps every regular pentagon of side length a> 0 onto a pentagon with side length b> 0, then there exists a linear isometry I : ℝn→ℝnup to translation such that f(x) = (b/a) I(x).

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