Simetrije ravninskih likov

diplomsko delo

Boštjan Strelec (Author), Dominik Benkovič (Mentor)

Abstract

V diplomskem delu predstavimo osnovne definicije teorije grup, ki jih potrebujemo skozi celotno diplomsko delo. Nato nekaj povemo o rotacijah v R^2 in R^3 okrog izhodišča in ortogonalnih matrikah. V naslednjih štirih poglavjih študiramo simetrijo ravninskih likov s pomočjo grupe togih gibanj v ravnini. Opišemo grupo M vseh togih gibanj v ravnini ter končne in diskretne grupe gibanj, temu sledita dva izreka, in sicer izrek o fiksni točki in izrek, da je vsako togo gibanje, translacija, rotacija, zrcaljenje, drsno zrcaljenje. V poglavju Abstraktna simetrija se srečamo s pojmi avtomorfizem, stabilizator in orbita. V nadaljevanju vpeljemo kvocientno grupo in obravnavamo operacijo na odsekih in zapišemo formulo preštevanja. V zadnjih dveh poglavjih predstavimo permutacijsko upodobitev grupe in formulo preštevanja za klasifikacijo končnih podgrup rotacijske grupe SO3.

Keywords

matematika;ravninski liki;simetrije;grupe;togo gibanje;grupe gibanj;diskretne grupe;delovanje;podgrupe;rotacijske grupe;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2010
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[B. Strelec]
UDC:	51(043.2)
COBISS:	17431304
Views:	3091
Downloads:	291
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	SYMMETRIES OF PLANE FIGURES
Secondary abstract:	In the beginning of the diploma work the basic definitions of group theory, which are important for the whole diploma work, are represented. Then we mention rotations R^2 and R^3 around the origin and orthogonal matrixes. In the next four chapters we are studying the symmetry of plane figures with the help of the group of rigid motions in a plane. We are describing the group M of all rigid motions in a plane and the finite and discrete group of motions. This is followed by two theorems, the fixed point theorem and the theorem, that every rigid motion is a translation, rotation, reflection, glide reflection or identity. In the chapter Abstract symmetry we met the therms automorphism, stabilizer and orbit. In the continuation we introduce the quotient group and are dealing with operation on cosets and write down the Counting formula. The last two chapters are including the permutation representation of the group and the Counting formula for the classification of the finite subgroups of the rotation group SO3.
Secondary keywords:	group;rigid motion;groups of motions;discrete group of motions;operation;finite subgroups of the rotation group.;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	62 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	18317