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master's thesis
Zlatni rez i Fibonaccijevi brojevi
Zagreb: University of Zagreb, Faculty of Science, 2023. urn:nbn:hr:217:094379
Strejček, Hana
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Strejček, H. (2023). Zlatni rez i Fibonaccijevi brojevi (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:094379

Strejček, Hana. "Zlatni rez i Fibonaccijevi brojevi." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:094379

Strejček, Hana. "Zlatni rez i Fibonaccijevi brojevi." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:094379

Strejček, H. (2023). 'Zlatni rez i Fibonaccijevi brojevi', Master's thesis, University of Zagreb, Faculty of Science, accessed 30 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:094379

Strejček H. Zlatni rez i Fibonaccijevi brojevi [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2023 [cited 2024 November 30] Available at: https://urn.nsk.hr/urn:nbn:hr:217:094379

H. Strejček, "Zlatni rez i Fibonaccijevi brojevi", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:217:094379

Metadata
TitleZlatni rez i Fibonaccijevi brojevi
Title (english)Golden ratio and Fibonacci numbers
AuthorHana Strejček
MentorMarija Galić (mentor)
Committee memberMarija Galić (predsjednik povjerenstva)
Committee memberAndrej Dujella (član povjerenstva)
Committee memberAleksandra Čižmešija (član povjerenstva)
Committee memberMaja Resman (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2023-03-02, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Zlatni rez je simbol savršene skladnosti, ravnoteže te ga nalazimo već kod starih Egipćana. Zlatni rez često povezujemo s Fibonaccijevim brojevima te je ovaj diplomski rad posvećen istraživanju i opisivanju njihovih svojstava. Ovaj diplomski rad sadrži dva velika poglavlja. U prvom poglavlju nalazi se povijesni pregled zlatnog reza, opisana su njegova osnovna svojstva, što geometrijska, što numerička. Opisani su neki od geometrijskih likova koji nose epitet zlatni te gdje zlatnih rez možemo pronaći u našoj okolini. U drugom poglavlju opisano je kako su nastali Fibonaccijevi brojevi, a time i Lucasovi brojevi, dokazani su neki njihovi identiteti, opisana je kombinatorna interpretacija Fibonaccijevih brojeva i pokazano da omjer Fibonaccijevog broja i njegovog prethodnika teži zlatnom rezu.
Abstract (english)
The golden ratio is a symbol of perfect harmony and balance and has been in human history since the time of the ancient Egyptians. Fibonacci numbers are often associated with the golden ratio, and this thesis is dedicated to the golden ratio and Fibonacci numbers. This thesis contains two large chapters. In the first chapter, there is a historical overview of the golden section, its basic properties, both geometric and numerical, are described. Some of the geometric figures that bear the epithet golden are described, and where we can find the golden section in our surroundings. In the second chapter, it is described how Fibonacci numbers, and thus Lucas numbers, were created, some of their identities were proven, a combinatorial interpretation of Fibonacci numbers was described and it was shown that the ratio of the Fibonacci number and its predecessor approaches to the golden ratio.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:094379
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 on2023-08-18 11:33:58