UCH O‘LCHOVLI FAZODA TO‘G‘RI CHIZIQ VA TEKISLIKNING O‘ZARO VAZIYATINI ANALITIK TADQIQ ETISH VA UNING GEOMETRIK TALQINI

Авторы

  • Sadriddinova Madina Xusanboy qizi Matematika yoʻnalishi 1-kurs talabasi Автор
  • Maxmudova Dilnoza Xaytmirzaevna Ilmiy maslahatchi: Namangan davlat universiteti O’zbekiston Автор

Ключевые слова:

fazoviy geometriya, to‘g‘ri chiziq, tekislik, parametrik tenglama, normal vektor, skalyar ko‘paytma, kesishish, parallel holat, masofa.

Аннотация

Ushbu maqolada uch o‘lchovli fazoda to‘g‘ri chiziq va tekislikning o‘zaro vaziyati analitik va geometrik jihatdan o‘rganiladi. Natijalarda yo‘nalish vektori va normal vektor orasidagi munosabatlar orqali chiziq–tekislik holatlari klassifikatsiya qilindi. Shuningdek, kesishish nuqtasini topish va masofani aniqlash formulalari keltirildi. Muhokama qismida ushbu natijalarning fazoviy tasvirlash, muhandislik va kompyuter grafikadagi qo‘llanishi tahlil qilindi. Xulosa sifatida analitik usullar orqali fazoviy geometrik munosabatlarni to‘liq tavsiflash mumkinligi ko‘rsatildi.

Библиографические ссылки

Saparboyev J.Y. (2024). O‘quvchilarning amaliy faoliyatida fazoviy tasavvurini rivojlantirish mexanizmlari. Eurasian Journal of Academic Research, 7 (Special Issue), 631-633.

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

Загрузки

Опубликован

2026-04-29

Выпуск

Раздел

Статьи

Как цитировать

UCH O‘LCHOVLI FAZODA TO‘G‘RI CHIZIQ VA TEKISLIKNING O‘ZARO VAZIYATINI ANALITIK TADQIQ ETISH VA UNING GEOMETRIK TALQINI. (2026). Молодые ученые, 4(33), 124-130. https://www.in-academy.uz/index.php/YO/article/view/38855
Innovative Academy RSC
Article metrics Views and PDF downloads
0 Views
0 Downloads