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master's thesis
Zlatni rez i primjene
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. urn:nbn:hr:126:069052
Stojaković, Helena
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

Institutional repository: Repository of School of Applied Mathematics and Informatics

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Stojaković, H. (2022). Zlatni rez i primjene (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:069052

Stojaković, Helena. "Zlatni rez i primjene." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. https://urn.nsk.hr/urn:nbn:hr:126:069052

Stojaković, Helena. "Zlatni rez i primjene." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. https://urn.nsk.hr/urn:nbn:hr:126:069052

Stojaković, H. (2022). 'Zlatni rez i primjene', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 17 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:069052

Stojaković H. Zlatni rez i primjene [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2022 [cited 2024 November 17] Available at: https://urn.nsk.hr/urn:nbn:hr:126:069052

H. Stojaković, "Zlatni rez i primjene", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:126:069052

Metadata
TitleZlatni rez i primjene
Title (english)Golden Ratio and it's Applications
AuthorHelena Stojaković
MentorIvan Soldo (mentor)
Committee memberLjiljana Primorac Gajčić (predsjednik povjerenstva)
Committee memberIvan Soldo (član povjerenstva)
Committee memberLjerka Jukić Matić (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2022-12-14, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
Omjer dva različita broja jednak je zlatnom rezu ako je omjer većeg broja prema manjem jednak omjeru njihove sume i većeg broja. Zlatni rez je iracionalan broj koji iznosi \(\varphi =\frac{1+\sqrt{5}}{2}\) te je usko vezan uz Fibonaccijeve brojeve. U geometriji su poznati brojni geometrijski likovi koji su određeni ovim omjerom od kojih su neki navedeni u ovom radu. Metoda zlatnoga reza jedna je od učinkovitih optimizacijskih metodi za pronalazak točke ekstrema strogo kvazikonveksnih funkcija definiranih na intervalu. Broj ϕ jedan je od najpoznatijih brojeva u povijesti koji se može pronaći u prirodi, čovjeku, svemiru, umjetnosti, itd.
Abstract (english)
The ratio of two different numbers is equal to the golden ratio if the ratio of the larger number to the smaller number is equal to the ratio of their sum to the larger number. The golden ratio is an irrational number that is equal to \(\varphi =\frac{1+\sqrt{5}}{2}\) and is closely related to Fibonacci numbers. In geometry, there are many geometric figures that are determined by this ratio some of which are specified in this thesis. The golden section search method is one of the effective optimization methods for finding the extreme point of strictly quasiconvex functions defined on an interval. The number ϕ is one of the most famous numbers in history that can be found in nature, people, space, art, etc
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:069052
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 on2022-12-14 13:14:03