Author(s): Oğuzhan Demirel, Leyla Aslan, Damla Topal, Afyon Kocatepe University
Keywords: Euclidean isometry, Euclidean motion, Beckman-Quarles theorem
An injection defined from Euclidean n-space E^n(2<=n<∞) to itself which preserves the triangles of perimeter 1 is an Euclidean motion. J. Lester presented two different proofs for this theorem in Euclidean plane (Lester 1985) and Euclidean space (Lester 1986). In this study we present a general proof which works both in Euclidean plane (n=2) and Euclidean space (2<n< ∞).
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