KO‘P O‘LCHOVLI YEVKLID FAZOSIDA METRIK STRUKTURALARNI ANALITIK O‘RGANISH VA ULARNING GEOMETRIK XOSSALARI
Keywords:
Yevklid fazosi, metrik struktura, norma, masofa, ichki ko‘paytma, ortogonallik, ochiq shar, yaqinlashuv,Abstract
: Ushbu maqolada ko‘p o‘lchovli Yevklid fazosida metrik strukturalar va ularning geometrik xossalari o‘rganiladi. Natijalarda Evklid metrikasi orqali aniqlangan ochiq sharlar, yaqinlashuv, ortogonallik va burchak tushunchalari formal tarzda ifodalandi. Shuningdek, norma va ichki ko‘paytma orasidagi bog‘lanish hamda ular orqali geometrik xossalar tavsiflandi. Muhokama qismida olingan natijalar yuqori o‘lchovli fazolarda modellashtirish va optimallashtirish masalalari bilan bog‘liq holda tahlil qilindi. Xulosa sifatida metrik struktura fazoning asosiy geometrik modelini tashkil etishi ko‘rsatildi.
References
1. David Gilbert. Grundlagen der Geometrie (Geometriya asoslari). - Leipzig: Teubner, 1899.
2. Euclid. Elements. - Translated by T. L. Heath. - Cambridge: Cambridge University Press, 1908.
3. Greenberg, M. J. Euclidean and Non-Euclidean Geometries: Development and History. – 4th ed. – New York: W. H. Freeman, 2008.
4. Dilnoza, M. Use of the Acmelological Approach to Teaching Mathematics. International Journal of Innovative Analyses and Emerging Technology. c-ISSN, 2792-4025.
5. 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
6. 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).
7. Karimberdiyeva , D. ., & Mahmudova , D. . (2025). Tekislikdagi perspektiv-affin moslikning o’ziga xos xususiyatlari. Развитие педагогических технологий в современных науках, 4(3), 114–117.
8. Maxmudova, D. X. (2023). Kognitiv kompetentlikni rivojlantirishning akmeologik texnologiyasini joriy etish shart-sharoitlari. GOLDEN BRAIN, 1(34), 19-24.
9. 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).
10. 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
11. Abdiqayumov, A., & Maxmudova, D. (2025). Central and parallel projections and their properties. Теоретические аспекты становления педагогических наук, 4(8), 177-184.
12. 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
O‘zbekiston Respublikasi, Andijon viloyati, Shahrixon tumani
(+998) 945668868