PROYEKTIV TEKISLIKDAGI IKKINCHI TARTIBLI CHIZIQLARNI KLASSIFIKATSIYALASH, ULARNING INVARIANTLARI VA KANONIK KO‘RINISHLARI TAHLILI
Keywords:
proyektiv tekislik, konika, ikkinchi tartibli chiziq, invariant, determinant, rang, kanonik ko‘rinish, kvadratik forma, gomogen koordinatalar.Abstract
Ushbu maqolada proyektiv tekislikdagi ikkinchi tartibli chiziqlar (konikalar)ning klassifikatsiyasi, ularning invariantlari va kanonik ko‘rinishlari o‘rganiladi. Natijalarda konikalar degeneratsiyalangan va degeneratsiyalanmagan holatlarga ajratildi, diskriminant va determinantlar asosiy invariantlar sifatida qaraldi. Shuningdek, konikalar kanonik ko‘rinishlarga keltirildi. Muhokama qismida ushbu natijalar chizma geometriya, optika va kompyuter grafikada qo‘llanishi bilan bog‘liq holda tahlil qilindi. Xulosa sifatida proyektiv invariantlar konikalarni to‘liq tavsiflash imkonini berishi ko‘rsatildi.
References
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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