TerDU xabarlari Volume 1 Issue 3 (2026) · pp. 76-82

LOBACHEVSKIY TEKISLIGI KELI-KLEYN TALQININING SUN’IY INTELEKTGA ASOSLANGAN VIZUAL KOGNITIV METODLARI

Safarov, To‘lqin, Kurudirek, Abdullah, Abdujabborova, Sevinch, Safarov, To‘lqin, Kurudirek, Abdullah, Abdujabborova, Sevinch, Safarov, To‘lqin, Kurudirek, Abdullah, Abdujabborova, Sevinch

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Abstract

This article examines the integration of artificial intelligence (AI) technologies in the teaching of non-Euclidean geometry, specifically Lobachevskian geometry. It analyzes the cognitive challenges students face during the transition from Euclidean geometry to non-Euclidean spaces, focusing on complexities in conceptualizing parallelism and metrics. Based on the Cayley-Klein model, a visual-cognitive methodology titled "AI-Enhanced Projective Visualization (AEPV)" is proposed. The educational process is analyzed through the framework of Bloom’s Taxonomy, highlighting the role of AI tools at each instructional stage.

Lobachevskian geometryCayley-Klein modelartificial Intelligence (AI)visual-cognitive methodnon-Euclidean geometryhyperbolic spaceinteractive teachingmathematical visualizationBloom’s Taxonomyeducational technologies

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Cite

APA 7 
Safarov, To‘lqin, Kurudirek, Abdullah, Abdujabborova, Sevinch, Safarov, To‘lqin, Kurudirek, Abdullah, Abdujabborova, Sevinch, Safarov, To‘lqin, Kurudirek, Abdullah & Abdujabborova, Sevinch (2026). LOBACHEVSKIY TEKISLIGI KELI-KLEYN TALQININING SUN’IY INTELEKTGA ASOSLANGAN VIZUAL KOGNITIV METODLARI. TerDU xabarlari, 1(3), 76-82.
GOST R 7.0.5 
Safarov, To‘lqin, Kurudirek, Abdullah, Abdujabborova, Sevinch, Safarov, To‘lqin, Kurudirek, Abdullah, Abdujabborova, Sevinch, Safarov, To‘lqin, Kurudirek, Abdullah, Abdujabborova, Sevinch LOBACHEVSKIY TEKISLIGI KELI-KLEYN TALQININING SUN’IY INTELEKTGA ASOSLANGAN VIZUAL KOGNITIV METODLARI // TerDU xabarlari. 2026. Т. 1. № 3. С. 76-82.
BibTeX 
@article{to‘lqin2026,
  author  = {Safarov, To‘lqin and Kurudirek, Abdullah and Abdujabborova, Sevinch and Safarov, To‘lqin and Kurudirek, Abdullah and Abdujabborova, Sevinch and Safarov, To‘lqin and Kurudirek, Abdullah and Abdujabborova, Sevinch},
  title   = {LOBACHEVSKIY TEKISLIGI KELI-KLEYN TALQININING SUN’IY INTELEKTGA ASOSLANGAN VIZUAL KOGNITIV METODLARI},
  journal = {TerDU xabarlari},
  year    = {2026},
  volume  = {1},
  number  = {3},
  pages   = {76-82}
}
RIS 
TY  - JOUR
AU  - Safarov, To‘lqin
AU  - Kurudirek, Abdullah
AU  - Abdujabborova, Sevinch
AU  - Safarov, To‘lqin
AU  - Kurudirek, Abdullah
AU  - Abdujabborova, Sevinch
AU  - Safarov, To‘lqin
AU  - Kurudirek, Abdullah
AU  - Abdujabborova, Sevinch
TI  - LOBACHEVSKIY TEKISLIGI KELI-KLEYN TALQININING SUN’IY INTELEKTGA ASOSLANGAN VIZUAL KOGNITIV METODLARI
JO  - TerDU xabarlari
PY  - 2026
VL  - 1
IS  - 3
SP  - 76
EP  - 82
ER  -