Ilim ha’m ja’miyet № 5-1 (2026) · с. 17-18

SOME SIMPLE PROPERTIES OF THE LOBACHEVSKIAN GEOMETRY ON THE PLANE

Qutbaev, Aydos Bakbergen uly, Qutbaev, Aydos Bakbergen ulı, Кутбаев, Айдос Бакберген улы

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Аннотация

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.

Yevklid geometriyasito‘g‘ri chiziqparallellik aksiomasimetrikaburchak defektiевклидова геометрияпрямаяаксиома параллельностиметрикаугловой дефект

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APA 7 
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.
GOST R 7.0.5 
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. С. 17-18.
BibTeX 
@article{uly2026,
  author  = {Qutbaev, Aydos Bakbergen uly and Qutbaev, Aydos Bakbergen ulı and Кутбаев, Айдос Бакберген улы},
  title   = {SOME SIMPLE PROPERTIES OF THE LOBACHEVSKIAN GEOMETRY ON THE PLANE},
  journal = {Ilim ha’m ja’miyet},
  year    = {2026},
  number  = {5-1},
  pages   = {17-18}
}
RIS 
TY  - JOUR
AU  - Qutbaev, Aydos Bakbergen uly
AU  - Qutbaev, Aydos Bakbergen ulı
AU  - Кутбаев, Айдос Бакберген улы
TI  - SOME SIMPLE PROPERTIES OF THE LOBACHEVSKIAN GEOMETRY ON THE PLANE
JO  - Ilim ha’m ja’miyet
PY  - 2026
IS  - 5-1
SP  - 17
EP  - 18
ER  -