Beckman–Quarles theorem
= Beckman–Quarles theorem
{wiki=Beckman–Quarles_theorem}
The Beckman–Quarles theorem is a result in the field of metric geometry pertaining to the nature of certain distance-preserving transformations. Specifically, it states that if \\( f: \\mathbb\{R\}^n \\to \\mathbb\{R\}^n \\) is a function that preserves distances (i.e.