SOME SIMPLE PROPERTIES OF THE LOBACHEVSKIAN GEOMETRY ON THE PLANE - Qutbaev, Aydos Bakbergen uly (SCIENCE and SOCIETY, 2026)
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.