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undergraduate thesis
Pravčaste plohe
2021. urn:nbn:hr:126:561238
Subašić, Katarina
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

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Subašić, K. (2021). Pravčaste plohe (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:561238

Subašić, Katarina. "Pravčaste plohe." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:561238

Subašić, Katarina. "Pravčaste plohe." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:561238

Subašić, K. (2021). 'Pravčaste plohe', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 12 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:561238

Subašić K. Pravčaste plohe [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2021 [cited 2024 November 12] Available at: https://urn.nsk.hr/urn:nbn:hr:126:561238

K. Subašić, "Pravčaste plohe", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:126:561238

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Metadata
TitlePravčaste plohe
Title (english)Ruled Surfaces
AuthorKatarina Subašić
MentorLjiljana Primorac Gajčić (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2021-09-15, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Geometry and Topology
Abstract
U ovom radu bavimo se pravˇcastim plohama, tj. plohama koje opisuje pravac koji se giba duž krivulje. S obzirom na geometrijska svojstva, pravčaste plohe dijelimo na razvojne i vitopere plohe. U radu analiziramo geometrijska svojstva za svaku klasu ploha zasebno i navodimo njihove primjere, pri čemu ćemo se više posvetiti vitoperim pravčastim plohama. Za vitopere pravčaste plohe definiramo jednu specijalnu krivulju duž koje ploha nije regularna - strikcijsku krivulju. Također definiramo Sannijin trobrid, ortonormirani trobrid koji, do na položaj u prostoru, jednoznačno određuje vitoperu plohu. Na kraju ćemo pokazati kako se Gaussova zakrivljenost vitopere pravčaste plohe može izračunati pomoću jedne specifične veličine koju nazivamo parametar distribucije vitopere plohe. U radu su navedeni i primjeri s odgovarajućim slikama ploha izrađenim u programu Mathematica.
Abstract (english)
In this work, we deal with ruled surfaces, i.e. surfaces that are created by the movement of a direction along a curve. Considering the geometric properties, ruled surfaces are divided into developable and noncylindrical surfaces. In this work, we analyze the geometric properties for each class of surfaces separately and give their examples, where we will pay more attention to the noncylindrical surfaces. For noncylindrical surfaces, we define one special curve along which the surface is not regular - the striction curve. We also define Sannia’s frame, an orthonormal frame that, up to its position in space, uniquely defines a noncylindrical surface. Finally, we will show how the Gaussian curvature of a noncylindrical surface can be calculated using a specific parameter called the noncylindrical surface distribution parameter. The work also provides examples of surfaces with corresponding images created in Mathematica
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:561238
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 09:24:16