magistrsko delo
Maša Nahtigal (Author), Matija Cencelj (Mentor)

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.

Keywords

zlato število;konstrukcija zlatega reza;zlati trikotnik;Fibonaccijevo zaporedje;

Data

Language: Slovenian
Year of publishing:
Typology: 2.09 - Master's Thesis
Organization: UL PEF - Faculty of Education
Publisher: [M. Nahtigal]
UDC: 514(043.2)
COBISS: 11689801 Link will open in a new window
Views: 679
Downloads: 105
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Other data

Secondary language: English
Secondary title: Golden section in geometry
Secondary 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.
Secondary keywords: mathematics;matematika;
File type: application/pdf
Type (COBISS): Master's thesis/paper
Thesis comment: Univ. v Ljubljani, Pedagoška fak., Predmetno poučevanje
Pages: 94 str.
ID: 10863859