Diedrska simetrija

diplomsko delo

Marko Glavan (Author), Boštjan Kuzman (Mentor), Eva Berdajs (Co-mentor)

Abstract

V diplomskem delu obravnavamo diedrsko grupo, njene lastnosti in strukturo ter diedrske simetrije različnih objektov. Diedrska grupa je ena najenostavnejših končnih grup. Ker v nasprotju s ciklično grupo ni komutativna, pa je struktura podgrup diedrske grupe bolj zanimiva. Pred samo vpeljavo pojma diedrske grupe najprej ponovimo osnovne pojme iz teorije grup in iz evklidske geometrije, ki jih potrebujemo v nadaljevanju. Nato definiramo diedrsko grupo kot grupo izometrij evklidske ravnine, ki ohranjajo pravilni n-kotnik. Poiščemo vse njene elemente in jih razvrstimo v konjugiranostne razrede. Nato opišemo tudi abstraktno karakterizacijo diedrske grupe in preučimo strukturo njenih podgrup. Za konec pa si ogledamo še nekaj konkretnih matematičnih ter ne-matematičnih objektov z diedrsko simetrijo.

Keywords

grupa;pravilni n-kotnik;zrcaljenje;izometrija;rotacija;diedrska grupa;faktor;

Data

Language:	Slovenian
Year of publishing:	2017
Typology:	2.11 - Undergraduate Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[M. Glavan]
UDC:	51(043.2)
COBISS:	11711561
Views:	1038
Downloads:	245
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Dihedral symmetry
Secondary abstract:	In this BCs thesis we describe the dihedral group, its structure and properties, and find certain objects which have dihedral symmetry. Dihedral group is one of the simplest finite groups. Since it is non-commutative, the structure of subgroups of the dihedral group is more interesting than that of the cyclic group. Before introducing the concept of the dihedral group, we make a short review of the basic notions from group theory and from the euclidean geometry that will be used in the thesis. Then we define the dihedral group as the group of isometries of the euclidean plane which preserve a regular $n$-gon. We list all its elements and classify them into conjugacy classes. We also find an abstract characterization of the dihedral group and examine the structure of its subgroups. To conclude, we list some concrete mathematical and non-mathematical objects which have dihedral symmetry.
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Bachelor thesis/paper
Thesis comment:	Univ. Ljubljana, Pedagoška fak., Dvopredmetni učitelj
Pages:	37 str.
ID:	10864985