Gaussov veličanstveni teorem ; Gauss's Remarkable Theorem

U ovom radu iskazat ćemo i dokazati Gaussov Veličanstveni teorem (Theorema Egregium), jedan od najznačajnijih rezultata diferencijalne geometrije koji ima veliku teorijsku vrijednost, kao i važnu praktičnu primjenu. Tim teoremom iskazana je ovisnost Gaussove zakrljivnosti plohe isključivo o fundamentalnim veličinama prvog reda. U radu su navedene definicije osnovnih pojmova lokalne teorije ploha, kao što su karta, prva i druga fundamentalna forma, Gaussova i srednja zakrivljenost te je proučavana lokalna izometrija ploha. Analiza takvog preslikavanja dovela je do Gaussovog Veličanstvenog teorema ; In this work we will consider Gauss’s Remarkable Theorem (Theorema Egregium), one of the most significant results in differential geometry that has outstanding theoretical value, as well as important practical application. The Gauss’s Theorema Egregium states the dependence of the Gaussian curvature of a surface entirely in terms of the first fundamental form. The work provides definitions of fundamental concepts in the local theory of surfaces, such as patch, first and second fundamental forms, Gaussian and mean curvature and observe the local isometry of surfaces. The analysis of that mappings led to Gauss’s Remarkable Theorem.