NOEVKLID GEOMETRIYADA LOBACHEVSKIY AKSIOMALAR SISTEMASINING NAZARIY ASOSLARI VA XOSSALARI
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noevklid geometriya, Lobachevskiy geometriyasi, giperbolik geometriya, parallellik aksiomasi, uchburchak, aksiomatik tizim, model.Abstrak
Ushbu maqolada noevklid geometriyada Lobachevskiy aksiomalar sistemasining nazariy asoslari va asosiy xossalari o‘rganiladi. Natijalarda bir nuqtadan berilgan to‘g‘ri chiziqqa cheksiz ko‘p parallel chiziqlar o‘tishi asoslandi hamda uchburchak burchaklari yig‘indisining dan kichik bo‘lishi kabi xossalar keltirildi. Muhokama qismida giperbolik geometriyaning matematik va fizik modellardagi roli tahlil qilindi. Xulosa sifatida Lobachevskiy geometriyasi mustaqil va izchil matematik tizim ekanligi ko‘rsatildi.
Iqtiboslar
David Gilbert. Grundlagen der Geometrie (Geometriya asoslari). - Leipzig: Teubner, 1899.
Euclid. Elements. - Translated by T. L. Heath. - Cambridge: Cambridge University Press, 1908.
Greenberg, M. J. Euclidean and Non-Euclidean Geometries: Development and History. – 4th ed. – New York: W. H. Freeman, 2008.
Dilnoza, M. Use of the Acmelological Approach to Teaching Mathematics. International Journal of Innovative Analyses and Emerging Technology. c-ISSN, 2792-4025.
Abduraxmonova, R., & Mahmudova, D. (2025). Nuqtadan to'g'ri chiziqqacha bo'lgan masofa. Ikki to'g'ri chiziq orasidagi burchak. В theoretical aspects in the formation of pedagogical sciences (Т. 4, Выпуск 7, сс. 74–78). Zenodo. https://doi.org/10.5281/zenodo.15186643
Abdulhayeva, G., & Mahmudova, D. (2025). Tekislikda to'g'ri chiziq tenglamalari va ularni amaliyotga tadbiqi. В theoretical aspects in the formation of pedagogical sciences (Т. 4, Выпуск 7, сс. 35–40).
Karimberdiyeva , D. ., & Mahmudova , D. . (2025). Tekislikdagi perspektiv-affin moslikning o’ziga xos xususiyatlari. Развитие педагогических технологий в современных науках, 4(3), 114–117.
Maxmudova, D. X. (2023). Kognitiv kompetentlikni rivojlantirishning akmeologik texnologiyasini joriy etish shart-sharoitlari. GOLDEN BRAIN, 1(34), 19-24.
Ismoilova, D., & Mahmudova, D. (2025). Ko ‘po ‘lchovli yevklid fazosi: o ‘qitish texnologiyasi asosida yondashuv. In Innov. Conf. Published online April (Vol. 17, No. 2025, pp. 1-7).
Khaitmirzayevna, Makhmudova D. "Pedagogical Ways of Cognitive Competences in Future Teachers Based on Acmeological Approach." World Economics and Finance Bulletin, vol. 32, 23 Mar. 2024, pp. 146-148
Abdiqayumov, A., & Maxmudova, D. (2025). Central and parallel projections and their properties. Теоретические аспекты становления педагогических наук, 4(8), 177-184.
Abdulhamidova, M., Maxmudova, D. Proyektiv geometriyaning asosiy faktlari. (2026). Zamonaviy taraqqiyot va fan: 21-asr yondashuvlari, 6(1), 282-293. https://journalss.org/index.php/zam/article/view/25424
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