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master's thesis
Fundamentalni teorem za krivulje
Zagreb: University of Zagreb, Faculty of Science, 2015. urn:nbn:hr:217:991987
Bešenić, Ivan
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Bešenić, I. (2015). Fundamentalni teorem za krivulje (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:991987

Bešenić, Ivan. "Fundamentalni teorem za krivulje." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:991987

Bešenić, Ivan. "Fundamentalni teorem za krivulje." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:991987

Bešenić, I. (2015). 'Fundamentalni teorem za krivulje', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:991987

Bešenić I. Fundamentalni teorem za krivulje [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2015 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:991987

I. Bešenić, "Fundamentalni teorem za krivulje", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:217:991987

Metadata
TitleFundamentalni teorem za krivulje
AuthorIvan Bešenić
MentorŽeljka Milin-Šipuš (mentor)
Committee memberŽeljka Milin-Šipuš (predsjednik povjerenstva)
Committee memberMirko Polonijo (član povjerenstva)
Committee memberFranka Miriam Bruckler (član povjerenstva)
Committee memberMarko Vrdoljak (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2015-09-23, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Fundamentalni teorem za krivulje jedan je od najvažnijih rezultata diferencijabilne geometrije za krivulje. Fundamentalni teorem za krivulje u \(\mathbb{R}^3\) kaže da postoji jedinstvena, do na orijentaciju i položaj u prostoru (do na izometriju), krivulja sa zadanom pozitivnom fleksijom \(\kappa\) i torzijom \(\tau\). Jednadžbe \(\kappa=\kappa(s)\) i \(\tau=\tau(s)\), gdje je \(s\) parametar duljine luka krivulje, nazivaju se prirodnim jednadžbama i one ne ovise o izboru koordinatnog sustava. Analogan rezultat također vrijedi i u \(\mathbb{R}^2\), samo što je u \(\mathbb{R}^2\) krivulja jednoznačno određena, do na orijentaciju i položaj u ravnini, samo relacijom između orijentirane zakrivljenosti \(\kappa_s\) i parametra duljine luka \(s\).
Abstract (english)
Fundamental Theorem of Curves is one of the most important achievements of differential geometry of curves. Fundamental Theorem of Curve in \(\mathbb{R}^3\) states that there exists a unique space curve, determined up to the orientation and a position in space (up to an isometry), with prescribed positive curvature \(\kappa\) and torsion \(\tau\). Equations \(\kappa=\kappa(s)\) and \(\tau=\tau(s)\), where \(s\) is the arc length of a curve, are called naturals equations of a curve. They are called natural because do not depend on the choice of a coordinate system. The analogue result is also obtained in \(\mathbb{R}^2\), the only difference is that a curve in \(\mathbb{R}^2\) is uniquely determined, up to the orientation and a position in plane, by a relation between signed curvature \(\kappa_s\) and arc length \(s\).
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:991987
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2017-05-25 10:29:01