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Zlati rez v geometriji
ID Nahtigal, Maša (Author), ID Cencelj, Matija (Mentor) More about this mentor... This link opens in a new window

URLURL - Presentation file, Visit http://pefprints.pef.uni-lj.si/4642/ This link opens in a new window

Abstract
Magistrska naloga se ukvarja z zlatim rezom v geometriji, ki ga lahko konstruiramo na različne načine. Po pregledu klasičnih konstrukcij in nekaj sodobnejših različic sledi obravnava nekaterih primerov zlatega reza v geometriji, predvsem na podlagi najnovejših matematičnih člankov na to temo. Izbrani članki se nanašajo na zlati rez in kvazi-dvanajstkraki zvezdasti mnogokotnik, znamenite točke v zlatih trikotnikih, pravilne mnogokotnike, parabolo, Fibonaccijevo zaporedje v verigi krožnic in iteracijo harmonične četverke v projektivni geometriji. Trditve bomo dokazovali predvsem z definicijami in izreki elementarne in delno projektivne geometrije, po potrebi pa bomo pri posameznih temah vpeljali še dodatne definicije in izreke.

Language:Slovenian
Keywords:zlati rez
Work type:Master's thesis/paper
Typology:2.09 - Master's Thesis
Organization:PEF - Faculty of Education
Year:2017
PID:20.500.12556/RUL-95039 This link opens in a new window
COBISS.SI-ID:11689801 This link opens in a new window
Publication date in RUL:19.09.2017
Views:1600
Downloads:226
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Secondary language

Language:English
Title:Golden section in geometry
Abstract:
The present thesis deals with golden section in geometry, which can be constructed in many different ways. After an overview of classical constructions and some modern cases follows a deeper examination of examples of the golden section in geometry, largely based on research articles related to this matter. Those articles refer to the golden section and quasi twelve-point star, triangle centers in the golden triangles, regular polygons, parabola, Fibonacci circle chains and iterated harmonic divisions. Propositions will mostly be proved by definitions and theorems from elementary and partly from projective geometry, with some additional ones introduced in individual cases.

Keywords:golden section

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