VARIOUS MODELS OF THE LOBACHEVSKY PLANE AND THEIR GEOMETRIC INTERPRETATIONS
Keywords:
Lobachevsky geometry, hyperbolic plane, Poincaré disk, Beltrami-Klein model, hyperbolic lines, non-Euclidean geometryAbstract
This article explores the fundamental models of the Lobachevsky plane, a cornerstone of hyperbolic geometry. It focuses on three major representations: the Poincaré disk model, the Beltrami-Klein model, and the upper half-plane model. The models are compared in terms of their geometric features, such as distance, angles, and parallel lines. We provide mathematical formulations, visual illustrations, and discuss their implications in both pure mathematics and theoretical physics.
Downloads
References
1. Anvarova, M., & Mahmudova, D. (2025). THE APPLICATION OF ECOND-ORDER CURVES. В THEORETICAL ASPECTS IN THE FORMATION OF PEDAGOGICAL SCIENCES (Т. 4, Выпуск 5, сс. 188–191). Zenodo. https://doi.org/10.5281/zenodo.15104205
2. Abdulhayeva, G., & Mahmudova, D. (2025). TEKISLIKDA TO'G'RI CHIZIQ TENGLAMALARI VA ULARNI AMALIYOTGA TADBIQI. В THEORETICAL ASPECTS IN THE FORMATION OF PEDAGOGICAL SCIENCES (Т. 4, Выпуск 7, сс. 35–40). Zenodo. https://doi.org/10.5281/zenodo.15167776
3. Karimberdiyeva, D., & Mahmudova, D. (2025). TEKISLIKDAGI PERSPEKTIV-AFFIN MOSLIKNING O'ZIGA XOS XUSUSIYATLARI. В DEVELOPMENT OF PEDAGOGICAL TECHNOLOGIES IN MODERN SCIENCES (Т. 4, Выпуск 3, сс. 114–117). Zenodo. https://doi.org/10.5281/zenodo.15123521
4. Abduraxmonova, R., & Mahmudova, D. (2025). NUQTADAN TO'G'RI CHIZIQQACHA BO'LGAN MASOFA. IKKI TO'G'RI CHIZIQ ORASIDAGI BURCHAK. В THEORETICAL ASPECTS IN THE FORMATION OF PEDAGOGICAL SCIENCES (Т. 4, Выпуск 7, сс. 74–78). Zenodo. https://doi.org/10.5281/zenodo.15186643
5. Ismoilova D., & Mahmudova, D. (2025). KO‘P O‘LCHOVLI YEVKLID FAZOSI: O‘QITISH TEXNOLOGIYASI ASOSIDA YONDASHUV. Innov. Conf. Published online April 17, 2025:1-7. Accessed April 18, 2025.
6. Mamatkadirova Zebo Tohirjon qizi, & Dilnoza Xaytmirzayevna Maxmudova. (2025). CONSTRUCTING AN ELLIPSE USING CONJUGATE DIAMETERS AND ITS APPLICATIONS. International Scientific and Current Research Conferences, 1(01), 48–55. Retrieved from https://orientalpublication.com/index.php/iscrc/article/view/1840
