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master's thesis
Plohe drugog reda i primjene
Zagreb: University of Zagreb, Faculty of Science, 2020. urn:nbn:hr:217:630852
Vukić, Barbara
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Vukić, B. (2020). Plohe drugog reda i primjene (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:630852

Vukić, Barbara. "Plohe drugog reda i primjene." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:630852

Vukić, Barbara. "Plohe drugog reda i primjene." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:630852

Vukić, B. (2020). 'Plohe drugog reda i primjene', Master's thesis, University of Zagreb, Faculty of Science, accessed 19 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:630852

Vukić B. Plohe drugog reda i primjene [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2020 [cited 2024 December 19] Available at: https://urn.nsk.hr/urn:nbn:hr:217:630852

B. Vukić, "Plohe drugog reda i primjene", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:217:630852

Metadata
TitlePlohe drugog reda i primjene
Title (english)Second order surfaces and applications
AuthorBarbara Vukić
MentorŽeljka Milin Šipuš (mentor)
Committee memberŽeljka Milin Šipuš (predsjednik povjerenstva)
Committee memberTina Bosner (član povjerenstva)
Committee memberTomislav Pejković (član povjerenstva)
Committee memberIgor Ciganović (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2020-09-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu proučavamo plohe drugog reda. Glavni cilj rada je uz pomoć linearne algebre i kvadratne forme klasificirati plohe drugog reda u realnom afinom prostoru. Iskazan je Sylvesterov zakon inericije te je pomoću njega na primjerima ilustirano kako odrediti vrstu plohe drugog reda. Takoder, opisan je geometrijski pristup određivanja vrsta ploha drugog reda. Drugi dio bavi se osnovnim definicijama i teoremima iz diferencijalne geometrije i teorije ploha. Dane su definicije ploha drugog reda i njihovi presjeci koordinatnim ravninama. Opisali smo rotacijske i translacijske plohe, a u zasebnom poglavlju definirali zakrivljenost plohe te ju pročili na pravčastim plohama. Na kraju dajemo primjere veličanstvenih gradevina moderne arhitekture u kojima vidimo primjenu ploha drugog reda.
Abstract (english)
In this thesis our main concern will be surfaces of second order. Using linear algebra and quadratic form theory our main goal is to provide classification of quadric surfaces in real affine space. In examples we illustrate how to determine the surface using the Sylvester’s law of inertia. Furthermore, we describe geometrical approach of determinating quadric surfaces. The second chapter deals with definitions and theorems in differential geometry and surface theory. We defined second-order surfaces and presented their intersections with coordinate planes. Rotational and translational surfaces are described and in a separate section we defined surface curvature which we study on ruled surfaces. Finally, we provide examples of magnificent buildings in modern architecture in which we can see the implementation of this quadric surfaces.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:630852
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 on2021-03-08 11:27:02