Research Article
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A characterization of general linear transformations by use of symmedian points of triangles

Year 2024, Volume: 9 Issue: 3, 157 - 165, 31.12.2024
https://doi.org/10.30931/jetas.1464356

Abstract

In this study, based on a geometric approach, we obtained a new characteristic of general linear transformations, also known as similarities, by use of symmedian points of triangles in complex z-plane.

References

  • [1] Li, B., Wang, Y., “A new characterization for isometries by triangles”, New York J. Math. 15 (2009) : 423-429.
  • [2] Lester, J., “Euclidean plane point-transformations preserving unit area or unit perimeter”, Arch. Math 45 (1985) : 561-564.
  • [3] Lester, J., “Martin’s theorem for Euclidean n-space and a generalization to the perimeter case”, J.Geom. 27 (1986) : 29-35.
  • [4] Benz, W., “Mappings preserving area 1 of triangles”, J.Geom. 79 (2004) : 27-30.
  • [5] Demirel, O., On mappings that preserve Fermat-Torricelli points”, Math. Commun. 26 (2021) : 21-27.
  • [6] Demirel, O., Aslan, L., Topal, D., “A characteristic of similarities by use of Steinhaus’ problem on partition of triangles”, Mathematical Sciences and Applications E- Notes 8(1) (2020) : 117-122.
  • [7] Aley, R.J., “Some properties of the symmedian point”, Proceedings o the Indiana Academy of Science 10 (1900) : 85-88.
  • [8] Haruki, H., Rassias, T.M., “A new characteristic of Möbius transformations by use of Apollonius points of triangles”, J. Math. Anal. Appl. 197(1) (1996) : 14-22.
  • [9] Pennisi, L.L., Gordon, L.I., Lasher, S., “Elements of Complex Variables”, Holt, Rinehart-Winston, New York, 1963.
  • [10] Nevanlinna, R., Paatero, V., “Introduction to Complex Analysis”, Addison-Wesley, New York, 1964.
  • [11] Nehari, Z. “Conformal Mapping”, McGraw-Hill Book, New York, 1952.

A Characterization of General Linear Transformations by Use of Symmedian Points of Triangles

Year 2024, Volume: 9 Issue: 3, 157 - 165, 31.12.2024
https://doi.org/10.30931/jetas.1464356

Abstract

In this study, based on a geometric approach, we obtained a new characteristic of general linear transformations, also known as similarities, by use of symmedian points of triangles in complex z-plane.

References

  • [1] Li, B., Wang, Y., “A new characterization for isometries by triangles”, New York J. Math. 15 (2009) : 423-429.
  • [2] Lester, J., “Euclidean plane point-transformations preserving unit area or unit perimeter”, Arch. Math 45 (1985) : 561-564.
  • [3] Lester, J., “Martin’s theorem for Euclidean n-space and a generalization to the perimeter case”, J.Geom. 27 (1986) : 29-35.
  • [4] Benz, W., “Mappings preserving area 1 of triangles”, J.Geom. 79 (2004) : 27-30.
  • [5] Demirel, O., On mappings that preserve Fermat-Torricelli points”, Math. Commun. 26 (2021) : 21-27.
  • [6] Demirel, O., Aslan, L., Topal, D., “A characteristic of similarities by use of Steinhaus’ problem on partition of triangles”, Mathematical Sciences and Applications E- Notes 8(1) (2020) : 117-122.
  • [7] Aley, R.J., “Some properties of the symmedian point”, Proceedings o the Indiana Academy of Science 10 (1900) : 85-88.
  • [8] Haruki, H., Rassias, T.M., “A new characteristic of Möbius transformations by use of Apollonius points of triangles”, J. Math. Anal. Appl. 197(1) (1996) : 14-22.
  • [9] Pennisi, L.L., Gordon, L.I., Lasher, S., “Elements of Complex Variables”, Holt, Rinehart-Winston, New York, 1963.
  • [10] Nevanlinna, R., Paatero, V., “Introduction to Complex Analysis”, Addison-Wesley, New York, 1964.
  • [11] Nehari, Z. “Conformal Mapping”, McGraw-Hill Book, New York, 1952.
There are 11 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Research Article
Authors

Çağla Ekiçi This is me 0009-0004-4715-3511

Oğuzhan Demirel 0000-0001-8948-1549

Publication Date December 31, 2024
Submission Date April 4, 2024
Acceptance Date October 23, 2024
Published in Issue Year 2024 Volume: 9 Issue: 3

Cite

APA Ekiçi, Ç., & Demirel, O. (2024). A Characterization of General Linear Transformations by Use of Symmedian Points of Triangles. Journal of Engineering Technology and Applied Sciences, 9(3), 157-165. https://doi.org/10.30931/jetas.1464356
AMA Ekiçi Ç, Demirel O. A Characterization of General Linear Transformations by Use of Symmedian Points of Triangles. JETAS. December 2024;9(3):157-165. doi:10.30931/jetas.1464356
Chicago Ekiçi, Çağla, and Oğuzhan Demirel. “A Characterization of General Linear Transformations by Use of Symmedian Points of Triangles”. Journal of Engineering Technology and Applied Sciences 9, no. 3 (December 2024): 157-65. https://doi.org/10.30931/jetas.1464356.
EndNote Ekiçi Ç, Demirel O (December 1, 2024) A Characterization of General Linear Transformations by Use of Symmedian Points of Triangles. Journal of Engineering Technology and Applied Sciences 9 3 157–165.
IEEE Ç. Ekiçi and O. Demirel, “A Characterization of General Linear Transformations by Use of Symmedian Points of Triangles”, JETAS, vol. 9, no. 3, pp. 157–165, 2024, doi: 10.30931/jetas.1464356.
ISNAD Ekiçi, Çağla - Demirel, Oğuzhan. “A Characterization of General Linear Transformations by Use of Symmedian Points of Triangles”. Journal of Engineering Technology and Applied Sciences 9/3 (December 2024), 157-165. https://doi.org/10.30931/jetas.1464356.
JAMA Ekiçi Ç, Demirel O. A Characterization of General Linear Transformations by Use of Symmedian Points of Triangles. JETAS. 2024;9:157–165.
MLA Ekiçi, Çağla and Oğuzhan Demirel. “A Characterization of General Linear Transformations by Use of Symmedian Points of Triangles”. Journal of Engineering Technology and Applied Sciences, vol. 9, no. 3, 2024, pp. 157-65, doi:10.30931/jetas.1464356.
Vancouver Ekiçi Ç, Demirel O. A Characterization of General Linear Transformations by Use of Symmedian Points of Triangles. JETAS. 2024;9(3):157-65.