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undergraduate thesis
Geometrija zlatnog reza
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. urn:nbn:hr:126:660998
Katušić, Kristina
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Applied Mathematics and Computer Science
Applied Mathematics and Optimization Research Group

Institutional repository: Repository of School of Applied Mathematics and Computer Science

Cite this document

Katušić, K. (2017). Geometrija zlatnog reza (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:660998

Katušić, Kristina. "Geometrija zlatnog reza." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:660998

Katušić, Kristina. "Geometrija zlatnog reza." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2017. https://urn.nsk.hr/urn:nbn:hr:126:660998

Katušić, K. (2017). 'Geometrija zlatnog reza', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 21 June 2024, https://urn.nsk.hr/urn:nbn:hr:126:660998

Katušić K. Geometrija zlatnog reza [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2017 [cited 2024 June 21] Available at: https://urn.nsk.hr/urn:nbn:hr:126:660998

K. Katušić, "Geometrija zlatnog reza", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:126:660998

Metadata
TitleGeometrija zlatnog reza
AuthorKristina Katušić
MentorZdenka Kolar-Begović (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Applied Mathematics and Computer Science)
(Applied Mathematics and Optimization Research Group)
Osijek
Defense date and country2017-10, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Geometry and Topology
Abstract
Dužina je podijeljena u omjeru zlatnoga reza, ako je omjer duljine većega dijela dužine prema duljini manjeg dijela jednak omjeru duljine cijele dužina prema duljini većega dijela. To je iracionalan broj koji se označava slovom φ, a njegova vrijednost je \( \frac{1+\sqrt{5}}{2}\) i približno je jednaka 1.61803. Razlika konstante zlatnog reza i njegove recipročne vrijednosti je 1. Poznate su brojne konstrukcije zlatnog reza. U radu su navedene neke od konstrukcija. Razmatrana su svojstva figura kao što su zlatni pravokutnik, zlatni trokut, pravilni peterokut te analizirani omjeri dužina u tim figurama koji su jednaki φ. Navedena su i proučavana geometrijska tijela kod kojih je također na različite načine uočeno postojanje broja φ. Pojavljuje se još od davnina, kod Keopsove piramide i Partenona. Broj φ se javlja i u brojnim poznatim umjetničkim djelima te u građi živog svijeta što je također proučavano u radu. U novije vrijeme u dizajnu logo znakova, web stranica i uređaja se često susreće postojanje ovog oku ugodnog omjera
Abstract (english)
If a line segment is divided into two lengths such that the ratio of the longer length to the shorter length is equal to the ratio of the segment’s entire length to the longer length, then the segment has been divided into the Golden Ratio. This is an irrational number that is denoted with φ and its value is \( \frac{1+\sqrt{5}}{2}\) and is approximately equal 1.61803. The difference of the golden ratio constant and its reciprocal is 1. There are many construction of the golden ratio. In this thesisare mentioned some constructions. There are considered the properties of a figures such as a golden rectangle, a golden triangle, a regular pentagon and the analyzed ratios of lengths in those figures which are equal to φ. The geometrical shapes at which the existence of the φ number was noticed on diferent ways were stated and studied. It has appeared since ancient times, at the Keops Pyramid and Parthenon. It appears in famous works of art, in the structure of living world which has also been mentioned. In the resent time in the design of logos, web-pages and devices, the existence of this eye pleasing ratio is often being encountered.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:660998
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2017-10-06 07:53:33