Grupe ornamenata i njihova primjena u nastavi geometrije

master's thesis

• Author: Martina Dolčić
• Mentor: Željka Milin Šipuš (mentor)
• Committee member: Željka Milin Šipuš (predsjednik povjerenstva)
• Committee member: Franka Miriam Brückler (član povjerenstva)
• Committee member: Boris Muha (član povjerenstva)
• Committee member: Tina Bosner (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-09-29, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Inspirirani očitom simetrijom i ljepotom uzoraka ornamenata koje pronalazimo na drevnim zgradama, tkaninama, nakitu, posuđu itd., u ovom diplomskom radu tražit ćemo načine kako klasificirati te uzorke s gledišta matematičara. Matematički gledano, ornamenti su geometrijski ravninski uzorci čija se struktura ponavlja beskonačno mnogo puta u jednom smjeru. Ovisno o izometrijama koje komponiramo dobivamo različite uzorke, a ovisno o tome razlikovat ćemo grupe ornamenata. Grupa simetrija ornamenata naziva se grupa ornamenata i pokaže se da postoji točno sedam grupa ornamenata. Klasifikacija ornamenata po grupama temelji se na kompoziciji nekih od sljedećih izometrija: translacije duž fiksne horizontalne osi L, rotacije za 180° oko točke na osi L, osne simetrije s obzirom na horizontalnu os, osne simetrije s obzirom na vertikalnu os te klizne simetrije. Svaka od sedam grupa ornamenata potkrijepljena je primjerima. Također, prikazan je i primjer prepoznavanja grupe ornamenata na uzorcima na vazi i tradicionalnoj narodnoj nošnji. U posljednjem poglavlju predstavljene su mogućnosti upotrebe ornamenata u modernoj nastavi matematike kroz razne aktivnosti.

Abstract (english)

Inspired by obvious symmetry and beauty of frieze patterns found on ancient buildings, fabrics, jewelry, pots etc., in this thesis we will look for possible ways for classification of those patterns from mathematical point of view. Mathematically speaking, friezes are geometrical planar patterns structured in such a way that they repeat themselves in one direction indefinitely. Depending on isometries combined we get various samples and based on that we discern frieze groups. The symmetry group of a frieze pattern is called a frieze group, and a proof that there are exactly seven types of frieze groups will be presented in the thesis. This classification is based on fact that the only possible motions for the frieze pattern are: translation along a fixed horizontal line L, 180 rotation about point on L, a horizontal mirror through L, vertical mirrors and glide symmetry. Examples will be provided for each of the seven groups. Further on, it will be shown how to recognize a type of group when one is presented with a pattern on an object such as a vase or a traditional Croatian dress. The final chapter considers the possibilities of various friezeusing activities in modern math class.

• Keywords: simetrija; geometrijski ravninski uzorci; grupa ornamenata; izometrija
• Keywords (english): symmetry; geometrical planar patterns; isometries; frieze group
• Language: croatian
• URN:NBN: urn:nbn:hr:217:781811
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-12-10 11:58:28