FAZODA IKKI TO‘G‘RI CHIZIQNING O‘ZARO VAZIYATINI ANALITIK VA PROYEKTIV YONDASHUV ASOSIDA O‘RGANISH
Keywords:
to‘g‘ri chiziq, fazo, parametrik tenglama, yo‘nalish vektori, kesishish, parallel chiziqlar, qiyshiq chiziqlar, determinant, proyektiv geometriya, invariantlar.Abstract
Ushbu maqolada fazoda ikki to‘g‘ri chiziqning o‘zaro vaziyati analitik va proyektiv yondashuv asosida o‘rganiladi. Natijalarda ikki to‘g‘ri chiziqning o‘zaro vaziyati parametrik tenglamalar, yo‘nalish vektorlari va determinantal mezonlar orqali ifodalandi. Shuningdek, proyektiv yondashuv orqali chiziqlarning tekislikdagi tasviri va ularning invariant xossalari tahlil qilindi. Muhokama qismida olingan natijalar muhandislik grafika va fazoviy modellashtirish bilan bog‘liq holda ko‘rib chiqildi. Xulosa sifatida analitik va proyektiv metodlarning uyg‘un qo‘llanilishi chiziqlarning o‘zaro vaziyatini 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
