A New Proof of the Lester’s Perimeter Theorem in Euclidean Space

  • Oğuzhan Demirel Afyon Kocatepe University
  • Leyla Aslan
  • Damla TOPAL
Keywords: Euclidean geometry, Euclidean motion, The Beckman-Quarles theorem


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 [1] and Euclidean space [2]. In this study a new technique is developed for the proof of this theorem which is valid in both Euclidean plane  and Euclidean space.


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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 DOI: 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 DOI: 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 DOI: https://doi.org/10.1007/BF01230332

How to Cite
Demirel, Oğuzhan, Leyla Aslan, and Damla TOPAL. 2020. “A New Proof of the Lester’s Perimeter Theorem in Euclidean Space ”. Mathematical Journal of Interdisciplinary Sciences 8 (2), 57-59. https://doi.org/10.15415/mjis.2020.82007.