Frizne grupe

delo diplomskega seminarja

Aleksander Janičijevič (Author), Aleš Vavpetič (Mentor)

Abstract

Diplomska naloga se ukvarja s friznimi grupami. Na Evklidski ravnini, opremljeni z Evklidsko metriko, definira množico vseh izometrij, nato pa obravnava najpreprostejše primere le-teh (to so translacija, rotacija in zrcaljenje). S pomočjo kompozitumov translacij, rotacij in zrcaljenj nato predstavi tudi vse frizne grupe. Cilj diplomske naloge je opisati (klasificirati) frizne grupe ter dokazati, da jih je, geometrijsko gledano, natanko sedem.

Keywords

matematika;metrični prostori;izometrije;grupe;podgrupe;podgrupa edinka;prezentacija grupe;translacija;rotacija;zrcaljenje;zrcalni zdrs;fiksne točke;orientacija;diskretne podgrupe;translacijske podgrupe;frizne grupe;

Data

Language:	Slovenian
Year of publishing:	2021
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[A. Janičijevič]
UDC:	512
COBISS:	94713603
Views:	654
Downloads:	48
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Frieze groups
Secondary abstract:	The diploma thesis deals with frieze groups. In the Euclidean space under the Euclidean metric, it defines the set of all isometries and then deals with the most basic cases of such isometries (them being translation, rotation and reflection). Using compositions of translations, rotations and reflections, it then presents all the frieze groups. The goal of the diploma thesis is to classify frieze groups and prove that there are exactly seven geometrically different types of them.
Secondary keywords:	mathematics;metric spaces;isometries;groups;subgroups;normal subgroup;presentation of a groups;translation;rotation;reflection;glide reflection;fixed points;orientation;discrete subgroups;translation subgroups;frieze groups;
Type (COBISS):	Final seminar paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	37 str.
ID:	14294139