PROYEKTIV GEOMETRIYANING PREDMETI, NAZARIY ASOSLARI, INVARIANTLARI VA ANALITIK TADQIQ USULLARI

Authors

  • Abdumalikova Anora Axmadjon qizi Matematika yoʻnalishi 1-kurs talabasi Author
  • Maxmudova Dilnoza Xaytmirzaevna Ilmiy maslahatchi: Namangan davlat universiteti O’zbekiston Author

Keywords:

proyektiv geometriya, invariant, gomogen koordinatalar, ikki nisbat, dualizm, proyektiv fazo, transformatsiya, analitik usul.

Abstract

Ushbu maqolada proyektiv geometriyaning predmeti, nazariy asoslari, invariantlari va analitik tadqiq usullari o‘rganiladi. Natijalarda proyektiv fazoning tuzilishi, dualizm prinsipi, invariantlarning asosiy xossalari va analitik ifodalari aniqlashtirildi. Shuningdek, bu tushunchalarning chizma geometriya, kompyuter grafika va optik modellashtirishdagi qo‘llanishi tahlil qilindi. Xulosa sifatida proyektiv geometriya invariantlar orqali geometrik strukturalarni umumlashtiruvchi fundamental nazariya ekanligi 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

Downloads

Published

2026-04-28

How to Cite

PROYEKTIV GEOMETRIYANING PREDMETI, NAZARIY ASOSLARI, INVARIANTLARI VA ANALITIK TADQIQ USULLARI. (2026). Science and Innovation, 4(30), 19-24. https://www.in-academy.uz/index.php/SI/article/view/38659
Innovative Academy RSC
Article metrics Views and PDF downloads
0 Views
0 Downloads