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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 [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.

Author(s):

  • Oğuzhan Demirel, Afyon Kocatepe University
  • Leyla Aslan
  • Damla TOPAL

Keywords:

Euclidean geometry, Euclidean motion, The Beckman-Quarles theorem

URL:

https://mjis.chitkara.edu.in/index.php/mjis/article/view/205

References:

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

 

 

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