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.
Euclidean geometry, Euclidean motion, The Beckman-Quarles theorem
Beckman F. S. and Quarles D. A.: On isometries of Euclidean spaces. Proc. Amer. Math. Soc. 4, 810-815 (1953). https://doi.org/10.2307/2032415
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
Lester, J. A.: Martin’s the or em for Euclidean-space and a generalization to the perimeter case. J. Geom. 27, 29-35 (1986). https://doi.org/10.1007/bf01230332