This article examines simple and intuitive properties of Lobachevskian (hyperbolic) geometry: the axiom of parallels, the formula for the angle of parallelism, the angular defect of a triangle and its relation to area, as well as distinctive curves such as the equidistant curve and the horocycle. The Poincaré disk model and the upper half-plane model serve as the main analytical tools, with their respective metrics presented. As a result, the fundamental differences from Euclidean geometry are illustrated through concrete numerical examples.
| Mualliflar | Qutbaev, Aydos Bakbergen uly, Qutbaev, Aydos Bakbergen ulı, Кутбаев, Айдос Бакберген улы |
|---|---|
| Jurnal | Ilim ha’m ja’miyet |
| Nashriyot | Нукус давлат педагогика институти |
| ISSN | 2010-720x, 2181-1555 |
| Nashr sanasi | 2026-08-15 |
| Son | 5-1 |
| Betlar | 17-18 |
| Til | kaa |
| Ilmiy soha | Fizika-matematika |
| Indeksga qo‘shilgan | 2026-08-26 |
Yevklid geometriyasi, to‘g‘ri chiziq, parallellik aksiomasi, metrika, burchak defekti, евклидова геометрия, прямая, аксиома параллельности, метрика, угловой дефект, Euclidean geometry, straight line, axiom of parallels, metrics, angular defect
| APA | Qutbaev, Aydos Bakbergen uly, Qutbaev, Aydos Bakbergen ulı, & Кутбаев, Айдос Бакберген улы (2026). SOME SIMPLE PROPERTIES OF THE LOBACHEVSKIAN GEOMETRY ON THE PLANE. Ilim ha’m ja’miyet, (5-1), 17-18. https://journal.ndpi.uz/index/article/view/2026-5-1-005 |
|---|---|
| GOST (OAK) | Qutbaev, Aydos Bakbergen uly, Qutbaev, Aydos Bakbergen ulı, Кутбаев, Айдос Бакберген улы SOME SIMPLE PROPERTIES OF THE LOBACHEVSKIAN GEOMETRY ON THE PLANE // Ilim ha’m ja’miyet. – 2026. – № 5-1. – B. 17-18. |
| MLA | Qutbaev, Aydos Bakbergen uly, Qutbaev, Aydos Bakbergen ulı, and Кутбаев, Айдос Бакберген улы. “SOME SIMPLE PROPERTIES OF THE LOBACHEVSKIAN GEOMETRY ON THE PLANE.” Ilim ha’m ja’miyet, (5-1), 17-18, 2026. https://journal.ndpi.uz/index/article/view/2026-5-1-005 |
| Chicago | Qutbaev, Aydos Bakbergen uly, Qutbaev, Aydos Bakbergen ulı, and Кутбаев, Айдос Бакберген улы. “SOME SIMPLE PROPERTIES OF THE LOBACHEVSKIAN GEOMETRY ON THE PLANE.” Ilim ha’m ja’miyet, (5-1), 17-18 (2026). https://journal.ndpi.uz/index/article/view/2026-5-1-005 |
| Harvard | Qutbaev, Aydos Bakbergen uly, Qutbaev, Aydos Bakbergen ulı, and Кутбаев, Айдос Бакберген улы (2026) ‘SOME SIMPLE PROPERTIES OF THE LOBACHEVSKIAN GEOMETRY ON THE PLANE’, Ilim ha’m ja’miyet, (5-1), 17-18. https://journal.ndpi.uz/index/article/view/2026-5-1-005 |
| BibTeX | @article{qutbaevaydosbakbergenuly2026,
title = {SOME SIMPLE PROPERTIES OF THE LOBACHEVSKIAN GEOMETRY ON THE PLANE},
author = {Qutbaev, Aydos Bakbergen uly and Qutbaev, Aydos Bakbergen ulı and Кутбаев, Айдос Бакберген улы},
journal = {Ilim ha’m ja’miyet},
year = {2026},
number = {5-1},
pages = {17-18},
url = {https://journal.ndpi.uz/index/article/view/2026-5-1-005}
} |
Boshqa maqola uchun iqtibos tayyorlash
The paper proves the theorem of the existence and uniqueness of the solution of the problem in Sobolev classes. The solution of the problem under consideration is constructed as the sum of a series according to the…
This paper proposes an integrated MATLAB/Simulink-based simulation architecture that enables the study of radionavigation equipment reliability within air traffic management systems, GNSS/INS integration, and…
Optics is a branch of physics that studies the properties of light, processes such as rectilinear propagation, scattering, reflection, refraction, and interference, and has been of scientific and practical importance…
This article considers the conformal mapping of the exterior of the unit disk (the domain |z|>1) onto the exterior (unbounded) domain of a regular triangle. The mapping function is derived using the exterior form of the…
To resolve the discrepancy between theory, which predicts a monotonic increase of the third-order nonlinear optical susceptibility (χ⁽³⁾) of CdSe quantum dots as the radius R decreases, and experiment, which shows sharp…
This paper investigates the preservation of data privacy generated by Internet of Things (IoT) devices during processing within artificial intelligence (AI) environments. To ensure the security of IoT data, homomorphic…
"Kungrad Soda Plant" LLC has developed a comprehensive technology for processing distillation fluid using secondary energy resources from this production, which eliminates or minimizes the amount of waste-distillation…
The article presents CardioAI-DSS for cardiovascular disease risk assessment. The system applies machine learning and CNN models to clinical data, Cardiovascular Disease datasets, and ECG signals. The models were…
This study investigates the biological, ecological and economic characteristics of Tribulus terrestris L., a medicinal plant naturally distributed in the Republic of Karakalpakstan. Morphological and anatomical…
This article analyzes wild relatives of cultivated plants from the Fabaceae Lindl. family in the Ustyurt flora and their forage value. Analysis of the abstract revealed that the wild relatives of cultivated plants in…
Ilim ha’m ja’miyet — barcha maqolalar · 2026-yil arxivi
This article presents the results of 2018-2023, such as biological diversity, inter-landscape distribution characteristics, density,and number of straggly insects identified from natural and anthropogenic areas of…
This article observational data on the species composition, distribution, population, density, and seasonal damage caused causedby herbivorus bugs. Observationes were carried out in April and September 2021. When…
In the article, the research fields of some species belonging to Paeonia, their significance in human life, adaptation features tovarious ecological conditions are highlighted, and the ecologist groups and other…
This article studies the number of species, population density of terrestrial mollusks of the Topalangdarya basin, located in theSurkhandarya region of Uzbekistan, in various altitudinal regions and biotopes and…
This article sheds light on changes in biomass formation and antimicrobial activity against test pathogenic strains under theinfluence of epigenetic modifiers and elicitors of the endophytic fungus Penicillium…
Shahimardonsoy covered issues such as the soil in the river basin and measures to increase its condition, salinity and fertility, theflora and fauna present in the basin landscape and their conservation.