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On Directed Length Ratios in the Lorentz-Minkowski Plane

Year 2023, Volume: 44 Issue: 4, 733 - 740, 28.12.2023
https://doi.org/10.17776/csj.1133780

Abstract

The linear structure of the Lorentz-Minkowski plane is almost the same as Euclidean plane. But, there is one different aspect. These planes have different distance functions. So, it can be interesting to study the Lorentz analogues of topics that include the distance concept in the Euclidean plane. Thus, in this study, we show that the relationship between Euclidean and Lorentz distances is given depending on the slope of the line segment. Following, we investigate Lorentz analogues of Thales’ theorem, Angle Bisector theorems, Menelaus’ theorem and Ceva’s theorem.

References

  • [1] Birman G.S., Nomizu K., Trigonometry in lorentzian geometry, The American Mathematical Monthly, 91 (9) (1984) 543–549.
  • [2] Catoni F., Boccaletti D., Cannata R., Catoni V., Nichelatti E., Zampetti P., The Mathematics of Minkowski Space-Time, With an Introduction to Commutative Hypercomplex Numbers. Berlin, (2008) 27-57.
  • [3] Duggal, K.L., Bejancu, A., Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications. Amsterdam, (1996) 1-5.
  • [4] Nešovi´c E., Petrovi´c-Torgašev M., Some trigonometric relations in the lorentzian plane, Kragujevac Journal of Mathematics, 33 (25) (2003) 219– 225.
  • [5] O’Neill B., Semi-Riemannian Geometry, with applications to relativity. London, (1983) 126-185.
  • [6] Ratchlife J.G., Foundations of hyperbolic manifolds. 2nd ed. New York, (2006) 54-98.
  • [7] Shonoda, E.N., Classification of conics and Cassini curves in Minkowski space-time plane, Journal of Egyptian Mathematical Society, 24 (2016) 270-278.
  • [8] Yaglom, I.M., A Simple Non-Euclidean Geometry and Its Physical Basis. New York, (1979) 174-201.
  • [9] Ozcan M., Kaya R., On the Ratio of Directed Lengths in the Taxicab plane and Related Properties, Missouri J. of Math. Sci., 14 (2) (2002) 107-117.
Year 2023, Volume: 44 Issue: 4, 733 - 740, 28.12.2023
https://doi.org/10.17776/csj.1133780

Abstract

References

  • [1] Birman G.S., Nomizu K., Trigonometry in lorentzian geometry, The American Mathematical Monthly, 91 (9) (1984) 543–549.
  • [2] Catoni F., Boccaletti D., Cannata R., Catoni V., Nichelatti E., Zampetti P., The Mathematics of Minkowski Space-Time, With an Introduction to Commutative Hypercomplex Numbers. Berlin, (2008) 27-57.
  • [3] Duggal, K.L., Bejancu, A., Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications. Amsterdam, (1996) 1-5.
  • [4] Nešovi´c E., Petrovi´c-Torgašev M., Some trigonometric relations in the lorentzian plane, Kragujevac Journal of Mathematics, 33 (25) (2003) 219– 225.
  • [5] O’Neill B., Semi-Riemannian Geometry, with applications to relativity. London, (1983) 126-185.
  • [6] Ratchlife J.G., Foundations of hyperbolic manifolds. 2nd ed. New York, (2006) 54-98.
  • [7] Shonoda, E.N., Classification of conics and Cassini curves in Minkowski space-time plane, Journal of Egyptian Mathematical Society, 24 (2016) 270-278.
  • [8] Yaglom, I.M., A Simple Non-Euclidean Geometry and Its Physical Basis. New York, (1979) 174-201.
  • [9] Ozcan M., Kaya R., On the Ratio of Directed Lengths in the Taxicab plane and Related Properties, Missouri J. of Math. Sci., 14 (2) (2002) 107-117.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Natural Sciences
Authors

Abdulaziz AÇIKGÖZ 0000-0002-4424-4870

Publication Date December 28, 2023
Submission Date June 21, 2022
Acceptance Date September 28, 2023
Published in Issue Year 2023Volume: 44 Issue: 4

Cite

APA AÇIKGÖZ, A. (2023). On Directed Length Ratios in the Lorentz-Minkowski Plane. Cumhuriyet Science Journal, 44(4), 733-740. https://doi.org/10.17776/csj.1133780