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undergraduate thesis
Geodetske krivulje
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. urn:nbn:hr:126:479069
Pavlečić, Marina
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

Institutional repository: Repository of School of Applied Mathematics and Informatics

Cite this document

Pavlečić, M. (2021). Geodetske krivulje (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:479069

Pavlečić, Marina. "Geodetske krivulje." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:479069

Pavlečić, Marina. "Geodetske krivulje." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:479069

Pavlečić, M. (2021). 'Geodetske krivulje', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 24 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:479069

Pavlečić M. Geodetske krivulje [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2021 [cited 2024 November 24] Available at: https://urn.nsk.hr/urn:nbn:hr:126:479069

M. Pavlečić, "Geodetske krivulje", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:126:479069

Metadata
TitleGeodetske krivulje
Title (english)Geodetic Curves
AuthorMarina Pavlečić
MentorLjiljana Primorac Gajčić (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2021-09-29, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Geometry and Topology
Abstract
U ovom radu upoznat ćemo se sa specijalnim krivuljama na plohi-geodetskim krivuljama. Takve krivulje promatramo pomoću specijalnog trobrida krivulja na plohi, a karakterizirane su s iščezavajućom geodetskom zakrivljenošću. Geodetske krivulje geometrijski predstavljaju najkraću spojnicu između dviju točaka na plohi i iz tog razloga se smatraju i poopćenjem pravca na plohi. U radu su analizirana njihova geometrijska svojstva i dane su diferencijalne jednadžbe koje ih određuju. Predstavljena je i specijalna parametrizacija plohe, parametrizacija geodetskim koordinatama. U radu su, primjenom navedene teorije, određene geodetske krivulje na sferi, odnosno cilindru.
Abstract (english)
In this final paper we analyze special curves on a surface-geodesic curves. Such curves are analyzed by usage of a special frame for a curve on a surface and they are characterized by a vanishing geodesic curvature. Geodesic curves geometrically represent the shortest path between two points on a surface and therefore, they are considered as generalization of a straight line on surface. In this work we analyze their geometric properties and give differential equations that determine geodesic curve. We also present a special parametrization of a surface, the parametrization with geodesic coordinates. Finally, by usage of presented theory, we determine geodesic curves on a sphere, respectively cylinder.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:479069
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
Created on2021-10-25 08:18:13