LOBACHEVSKIY GEOMETRIYASI: NOEVKLID GEOMETRIYANING NAZARIY ASOSLARI, GEOMETRIK XUSUSIYATLARI VA TA’LIMDAGI AHAMIYATI
DOI:
https://doi.org/10.5281/zenodo.22032749Ключевые слова:
Lobachevsky geometry, non-Euclidean geometry, hyperbolic geometry, parallel postulate, Euclidean geometry, hyperbolic plane, Poincaré model, triangle, curvature, axiomatic reasoningАннотация
This article systematically examines the emergence of Lobachevsky geometry, its axiomatic foundations,
which differ from those of Euclidean geometry, and the main geometric properties of the hyperbolic plane. Particular
attention is paid to the alternative interpretation of the parallel postulate, hyperbolic lines, triangles, angle sums, distance,
and curvature. Non-Euclidean geometry is considered not only as a historical achievement of mathematics but also as
a theoretical tool for developing axiomatic reasoning, mathematical modeling, and logical thinking. The article discusses
the use of the Poincaré disk and upper half-plane models to visualize abstract concepts of hyperbolic geometry. It also
analyzes methodological approaches to teaching Lobachevsky geometry in higher education and its role in developing
proof skills, spatial imagination, and comparative mathematical reasoning
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