Ilim ha’m ja’miyet № 5-1 (2026) · Саҳифаҳои 17-18
SOME SIMPLE PROPERTIES OF THE LOBACHEVSKIAN GEOMETRY ON THE PLANE
Qutbaev, Aydos Bakbergen uly, Qutbaev, Aydos Bakbergen ulı, Кутбаев, Айдос Бакберген улы
Аннотатсия
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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