A New Proof of the Lester’s Perimeter Theorem in Euclidean Space
An injection defined from Euclidean space n-space E^n to itself which preserves the triangles of perimeter 1 is an Eucldean motion. J. Lester gave two different proofs for this theorem in Euclidean plane  and Euclidean space . In this study a new technique is developed for the proof of this theorem which is valid in both Euclidean plane and Euclidean space.
Lester, J. A.: Euclidean plane point transformations preserving unit area or unit perimeter. Arch. Math. (Basel ) 45, 561-564 (1985). https://doi.org/10.1007/bf01194898 DOI: https://doi.org/10.1007/BF01194898
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