A relation between tudung saji weaving patterns and group theory

Tudung saji is a traditional utensil used by the Malays to cover their food to be served. Tudung saji is woven with strands of dried leaves using a specific technique called triaxial weave, where the strands are plaited in three directions. Previously, a tool known as triaxial template had been crea...

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Main Author:	Amzee Zamri, Siti Norziahidayu
Format:	Thesis
Language:	English
Published:	2015
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/54619/25/SitiNorziahidayuMFS2015.pdf
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spelling	my-utm-ep.546192020-10-21T00:48:34Z A relation between tudung saji weaving patterns and group theory 2015-02 Amzee Zamri, Siti Norziahidayu QA Mathematics Tudung saji is a traditional utensil used by the Malays to cover their food to be served. Tudung saji is woven with strands of dried leaves using a specific technique called triaxial weave, where the strands are plaited in three directions. Previously, a tool known as triaxial template had been created to represent the patterns of tudung saji weaving in a planar pattern. Based on this template, many beautiful and symmetrical patterns were successfully generated, creating some of the original patterns of tudung saji. These patterns are categorized according to the number of colours of the strands, from the basic 2-strand up to 6-strand template. The purpose of study is to find several finite groups to represent the triaxial weaving patterns on two dimensional templates, focussing only on the 2 and 3-strand templates. It is found that the symmetric group of two letters, 2 S and the cyclic group of order six, 6 C are isomorphic to the triaxial template of Flock of Pigeons and Sailboats patterns, respectively. These isomorphisms are determined by mapping the elements of the Flock of Pigeons and Sailboats onto the elements of the two groups. Using a software iMac Grapher, several graphs are generated based on the elements of the triaxial template patterns. Next, graph theory is used to analyze the properties of these graphs. The graphs are sorted by the numbers of strands, namely the graphs of block two, graphs of block three up to the graphs of block six. All such graphs are found to feature the characteristics of three types of graphs, namely a complete graph with three vertices, 3 K , a simple graph with six vertices, and an a cyclic graph. Lastly, this research reports on modifications to the template by adding extra colours to the framework strands and the insertion strands. This is done by using new colour ordering in addition to the same colour ordering for the 2-strand template. As a result, a new characteristic on the modified template has been found, namely the existence of different triaxial patterns in one template. 2015-02 Thesis http://eprints.utm.my/id/eprint/54619/ http://eprints.utm.my/id/eprint/54619/25/SitiNorziahidayuMFS2015.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:86187 masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Amzee Zamri, Siti Norziahidayu A relation between tudung saji weaving patterns and group theory
description	Tudung saji is a traditional utensil used by the Malays to cover their food to be served. Tudung saji is woven with strands of dried leaves using a specific technique called triaxial weave, where the strands are plaited in three directions. Previously, a tool known as triaxial template had been created to represent the patterns of tudung saji weaving in a planar pattern. Based on this template, many beautiful and symmetrical patterns were successfully generated, creating some of the original patterns of tudung saji. These patterns are categorized according to the number of colours of the strands, from the basic 2-strand up to 6-strand template. The purpose of study is to find several finite groups to represent the triaxial weaving patterns on two dimensional templates, focussing only on the 2 and 3-strand templates. It is found that the symmetric group of two letters, 2 S and the cyclic group of order six, 6 C are isomorphic to the triaxial template of Flock of Pigeons and Sailboats patterns, respectively. These isomorphisms are determined by mapping the elements of the Flock of Pigeons and Sailboats onto the elements of the two groups. Using a software iMac Grapher, several graphs are generated based on the elements of the triaxial template patterns. Next, graph theory is used to analyze the properties of these graphs. The graphs are sorted by the numbers of strands, namely the graphs of block two, graphs of block three up to the graphs of block six. All such graphs are found to feature the characteristics of three types of graphs, namely a complete graph with three vertices, 3 K , a simple graph with six vertices, and an a cyclic graph. Lastly, this research reports on modifications to the template by adding extra colours to the framework strands and the insertion strands. This is done by using new colour ordering in addition to the same colour ordering for the 2-strand template. As a result, a new characteristic on the modified template has been found, namely the existence of different triaxial patterns in one template.
format	Thesis
qualification_level	Master's degree
author	Amzee Zamri, Siti Norziahidayu
author_facet	Amzee Zamri, Siti Norziahidayu
author_sort	Amzee Zamri, Siti Norziahidayu
title	A relation between tudung saji weaving patterns and group theory
title_short	A relation between tudung saji weaving patterns and group theory
title_full	A relation between tudung saji weaving patterns and group theory
title_fullStr	A relation between tudung saji weaving patterns and group theory
title_full_unstemmed	A relation between tudung saji weaving patterns and group theory
title_sort	relation between tudung saji weaving patterns and group theory
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2015
url	http://eprints.utm.my/id/eprint/54619/25/SitiNorziahidayuMFS2015.pdf
_version_	1747817689958580224

A relation between tudung saji weaving patterns and group theory

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