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master's thesis
Konike u ravninskoj diferencijalnoj geometriji
Zagreb: University of Zagreb, Faculty of Science, 2024. urn:nbn:hr:217:222727
Petrinić, Hrvoje
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Petrinić, H. (2024). Konike u ravninskoj diferencijalnoj geometriji (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:222727

Petrinić, Hrvoje. "Konike u ravninskoj diferencijalnoj geometriji." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:222727

Petrinić, Hrvoje. "Konike u ravninskoj diferencijalnoj geometriji." Master's thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:222727

Petrinić, H. (2024). 'Konike u ravninskoj diferencijalnoj geometriji', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:222727

Petrinić H. Konike u ravninskoj diferencijalnoj geometriji [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2024 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:222727

H. Petrinić, "Konike u ravninskoj diferencijalnoj geometriji", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:217:222727

Metadata
TitleKonike u ravninskoj diferencijalnoj geometriji
Title (english)Conics in plane differential geometry
AuthorHrvoje Petrinić
MentorŽeljka Milin Šipuš (mentor)
Committee memberŽeljka Milin Šipuš (predsjednik povjerenstva)
Committee memberMea Bombardelli (član povjerenstva)
Committee memberFilip Najman (član povjerenstva)
Committee memberVanja Wagner (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2024-07-16, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Cilj ovog diplomskog rada bio je opisati sve tri konike u diferencijalnoj geometriji koristeći definicije i teoreme obrađene na kolegiju Uvod u diferencijalnu geometriju. U prvom poglavlju rada detaljno su obrađena osnovna svojstva konika koja se obrađuju u srednjoj školi. U drugom poglavlju susrećemo se s fakultetskim pojmovima kao što je zakrivljenost krivulje koju opisujemo raznim formulama iz diferencijalne geometrije. Konstrukcije su obrađene u matematičkog programu GeoGebra. Od konstrukcija najvažnije su bile konstrukcije oskulacijskih kružnica konika i njihovih evoluta. Koristeći se parametrizacijom krivulje, izveli smo i parametrizaciju njihovih evoluta. Konike imaju široku primjenu u građevini i arhitekturi, ali i u svakodnevnim aktivnostima stoga ih je poželjno proučavati.
Abstract (english)
The aim of this thesis was to describe all three conics in differential geometry using the definitions and theorems processed in the course Introduction to Differential Geometry. In the first chapter, the basic properties of conics, which are studied in high school, are covered in detail. In the second chapter we meet terms from college such as the curvature of a curve, which we describe with various formulas from differential geometry. The constructions were processed in the mathematical program GeoGebra. Of the constructions, the most important were the constructions of the osculation circles of conics and their evolutes. Using the parametrization of the curve, we also derived the parametrization of their evolutes. Conics are widely used in construction and architecture, but also in everyday activities, so it is desirable to study them.
Keywords
Languagecroatian
URN:NBNurn:nbn:hr:217:222727
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: sveučilišni magistar edukacije matematike (sveučilišni magistar edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-07-24 12:50:54