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undergraduate thesis
Gaussov veličanstveni teorem
Osijek: Josip Juraj Strossmayer University of Osijek, Faculty of Applied Mathematics and Informatics, 2023. urn:nbn:hr:126:050681
Filipović, Janja
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

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Filipović, J. (2023). Gaussov veličanstveni teorem (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:050681

Filipović, Janja. "Gaussov veličanstveni teorem." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:050681

Filipović, Janja. "Gaussov veličanstveni teorem." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:050681

Filipović, J. (2023). 'Gaussov veličanstveni teorem', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 19 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:050681

Filipović J. Gaussov veličanstveni teorem [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2023 [cited 2024 November 19] Available at: https://urn.nsk.hr/urn:nbn:hr:126:050681

J. Filipović, "Gaussov veličanstveni teorem", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:126:050681

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Metadata
TitleGaussov veličanstveni teorem
Title (english)Gauss's Remarkable Theorem
AuthorJanja Filipović
MentorLjiljana Primorac Gajčić (mentor)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2023-09-22, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Geometry and Topology
Abstract
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
Abstract (english)
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.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:050681
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
RepositoryRepository of School of Applied Mathematics and Informatics
Created on2023-10-09 08:24:44