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.
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
Copyright (c) 2020 O. Demirel et al.
This work is licensed under a Creative Commons Attribution 4.0 International License.
License and Copyright Policy
Chitkara University Publications for the journal (Math. J. Interdiscip. Sci.) protects author rights e.g., the results, analysis, methodology of Theoretical calculations or experiment. The copyright transfer form with open access policy under the creative common licenses of journal provides all rights specifically to the author (s); except to sell, distribution of the material in any form to any third party. Also, the authors are encouraged to submit the author’s copy of the accepted paper to an appropriate archive e.g. arxive.org and/or in their institution’s repositories, or on their personal website also.
Author(s) should mention reference of the Journal of Chitkara University Publications and DOI number of the publication carefully on the required page of the depository, in all above-mentioned cases. The copyright and license policy of Chitkara University Publications not only protect the author's rights but also protect the integrity and authenticity of the scientific records and takes very seriously about the plagiarism, fraud or ethics disputes.
Articles in Mathematical Journal of Interdisciplinary Sciences (Math. J. Interdiscip. Sci.) by Chitkara University Publications are Open Access articles that are published with licensed under a Creative Commons Attribution- CC-BY 4.0 International License. Based on a work at https://mjis.chitkara.edu.in. This license permits one to use, remix, tweak and reproduction in any medium, even commercially provided one give credit for the original creation.
View Legal Code of the above mentioned license, https://creativecommons.org/licenses/by/4.0/legalcode
View Licence Deed here https://creativecommons.org/licenses/by/4.0/
|Mathematical Journal of Interdisciplinary Sciences by Chitkara University Publications is licensed under a Creative Commons Attribution 4.0 International License. Based on a work at https://mjis.chitkara.edu.in|