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undergraduate thesis
Normalna zakrivljenost plohe
2021. urn:nbn:hr:126:331377
Baričević, Ema
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

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Baričević, E. (2021). Normalna zakrivljenost plohe (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:331377

Baričević, Ema. "Normalna zakrivljenost plohe." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:331377

Baričević, Ema. "Normalna zakrivljenost plohe." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:331377

Baričević, E. (2021). 'Normalna zakrivljenost plohe', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 30 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:331377

Baričević E. Normalna zakrivljenost plohe [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2021 [cited 2024 November 30] Available at: https://urn.nsk.hr/urn:nbn:hr:126:331377

E. Baričević, "Normalna zakrivljenost plohe", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:126:331377

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Metadata
TitleNormalna zakrivljenost plohe
Title (english)Normal Curvature of a Surface
AuthorEma Baričević
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 završnom radu upoznat ćemo se s normalnom zakrivljenošću plohe. Najprije ćemo definirati neke osnovne pojmove lokalne teorije krivulja, kao što su parametrizirana krivulja, Frenetov trobrid i Frenetove formule krivulje. Navest ćemo definiciju plohe, odnosno regularne plohe te ćemo definirati prvu, odnosno drugu fundamentalnu formu plohe, kao i operator oblika plohe. Normalna zakrivljenost u točki plohe u smjeru tangencijalnog vektora \(v_{p}\) se računa kao kvocijent skalarnog produkta vektora \(v_{p}\) i vektora dobivenog djelovanjem operatora oblika plohe na vektor \(v_{p}\) i kvadrata norme vektora \(v_{p}\). Geometrijski, takva zakrivljenost predstavlja zakrivljenost krivulje dobivene kao presjek plohe i ravnine koju razapinju vektor (v_{p}\) i vektor plošne normale. Rad ćemo završiti iskazom i dokazom dva važna teorema vezana uz normalnu zakrivljenost plohe.
Abstract (english)
In this final paper we will analyze the normal curvature of a surface. First we will define the basic concepts of local theory of curves, i.e. a parametrized curve, Frenet frame field and Frenet formulas for parametrized curve. After that we will define what is surface, regular surface and we will say something more about the first and the second fundamental form, as well as about the shape operator of a surface. The normal curvature of a surface in a point on a surface in a direction of tangent vector \(v_{p}\) is calculated as the quotient of inner product of vectors \(v_{p}\) and vector obtained by the shape operator applied on a vector \(v_{p}\), and squared norm of vector \(v_{p}\). Geometrically, such curvature represents the curvature of a curve obtained as the intersection of a surface and plane determined by a tangent vector \(v_{p}\) and surface normal. We finish this work with two important theorems related to the normal curvature of a surface.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:331377
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 06:57:55