EN
On Directed Length Ratios in the Lorentz-Minkowski Plane
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.
Keywords
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.
Details
Primary Language
English
Subjects
Mathematical Sciences
Journal Section
Research Article
Authors
Publication Date
December 28, 2023
Submission Date
June 21, 2022
Acceptance Date
September 28, 2023
Published in Issue
Year 2023 Volume: 44 Number: 4