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2026-05-08
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THE FIRST QUADRATIC FORM OF A SURFACE AND ITS APPLICATIONS
Temirov Azizbek
“International school of finance technology and science” instituti o‘qituvchisi
Allayarov Shoxnurbek
“International school of finance technology and science” instituti Axborot xavfsizligi yo’nalishi 24-AX-01 guruhi 2-kurs talabasi
Allayarova Mahliyoxon
Chirchiq Davlat Pedagogika Universiteti Aniq va tabiiy fanlarni oʻqitish metodikasi (matematika) 1-kurs magistranti
##semicolon## Birinchi kvadratik forma, chiziqli element, parametrik sirt, yoy uzunligi, differensial geometriya, EFG koeffitsientlar, urinma tekislik, ortogonal koordinatalar, aylanma sirt, katenoid, gelikoid
सार
This article discusses in detail the concept of the first quadratic form of a surface, its analytical expression and geometric content. The issue of determining the length of curves when the surface is given by parametric equations is considered, and the importance of the first quadratic form in this process is justified. The physical and geometric interpretation of the coefficients E, F, G, and the condition of orthogonality of coordinate lines are also analyzed. The first quadratic form is calculated for various surfaces (plane, sphere, surface of revolution, catenoid, helicoid, etc.) and their properties are shown through examples.
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