Öz
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.
Anahtar Kelimeler
Lorentz distance Directed lengths Angle bisector theorems Menelaus' theorem Ceva's theorem
Kaynakça
- [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.
Öz
Kaynakça
- [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.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Natural Sciences |
| Yazarlar | |
| Yayımlanma Tarihi | 28 Aralık 2023 |
| Gönderilme Tarihi | 21 Haziran 2022 |
| Kabul Tarihi | 28 Eylül 2023 |
| Yayımlandığı Sayı | Yıl 2023Cilt: 44 Sayı: 4 |
