Research Article
Year 2023,
Volume: 44 Issue: 4, 733 - 740, 28.12.2023
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
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.
There are 9 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | December 28, 2023 |
| Submission Date | June 21, 2022 |
| Acceptance Date | September 28, 2023 |
| Published in Issue | Year 2023Volume: 44 Issue: 4 |
