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master's thesis
Svojstva Fibonaccijevih i Lucasovih brojeva
Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. urn:nbn:hr:126:443587
Turšćak, Mirna
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

Institutional repository: Repository of School of Applied Mathematics and Informatics

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Turšćak, M. (2024). Svojstva Fibonaccijevih i Lucasovih brojeva (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:443587

Turšćak, Mirna. "Svojstva Fibonaccijevih i Lucasovih brojeva." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:443587

Turšćak, Mirna. "Svojstva Fibonaccijevih i Lucasovih brojeva." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:443587

Turšćak, M. (2024). 'Svojstva Fibonaccijevih i Lucasovih brojeva', Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 17 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:443587

Turšćak M. Svojstva Fibonaccijevih i Lucasovih brojeva [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2024 [cited 2024 November 17] Available at: https://urn.nsk.hr/urn:nbn:hr:126:443587

M. Turšćak, "Svojstva Fibonaccijevih i Lucasovih brojeva", Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:126:443587

Metadata
TitleSvojstva Fibonaccijevih i Lucasovih brojeva
Title (english)Properties Of Fibonacci And Lucas Numbers
AuthorMirna Turšćak
MentorIvan Soldo (mentor)
Committee memberLjerka Jukić Matić (predsjednik povjerenstva)
Committee memberIvan Soldo (član povjerenstva)
Committee memberDragana Jankov Maširević (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2024-04-22, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
U ovom radu definirali smo Fibonaccijeve brojeve i njihova svojstva, a također smo se upoznali i s rezultatima vezanim uz djeljivost Fibonaccijevih brojeva. Proučili smo i niz brojeva usko vezan za Fibonaccijeve brojeve, a to je Lucasov niz. Osvrnuli smo se i na neka njegova svojstva, a potom i na identitete koji povezuju Lucasove i Fibonaccijeve brojeve. Uveli smo i bitne formule za Fibonaccijeve i Lucasove brojeve, a to su Cassinijeva i Binetova formula. Pomoću Binetove formule povezali smo ova dva niza brojeva sa zlatnim rezom, a potom i brojnim pojavama u arhitekturi, umjetnosti i prirodi.
Abstract (english)
In this paper, we defined the Fibonacci numbers and their properties. Also we familiarized ourselves with results related to the divisibility of Fibonacci numbers. We studied a sequence closely related to Fibonacci numbers, known as the Lucas sequence. We also discussed some of its properties, followed by identities connecting Lucas and Fibonacci numbers. We introduced formulas for Fibonacci and Lucas numbers were introduced, known as Cassini’s and Binet’s formulas. Through the Binet formula, we connected these two sequences of numbers with the golden ratio, and subsequently with numerous phenomena in architecture, art, and nature.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:443587
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-04-24 06:12:52