SIMETRIJE RAVNINSKIH LIKOV

Strelec, Boštjan

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Title:	SIMETRIJE RAVNINSKIH LIKOV
Authors:	ID Strelec, Boštjan (Author) ID Benkovič, Dominik (Mentor) More about this mentor...
Files:	UNI_Strelec_Bostjan_2010.pdf (1,62 MB) MD5: 61A7B584076A3DCB043E73E71EF8AAB9 PID: 20.500.12556/dkum/57900ad1-c7c1-4f06-9296-dbb2999c4b83
Language:	Slovenian
Work type:	Undergraduate thesis
Organization:	FNM - Faculty of Natural Sciences and Mathematics
Abstract:	V diplomskem delu najprej 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 pa 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 ter zapišemo formulo preštevanja. V zadnjih dveh poglavjih predstavimo permutacijsko upodobitev grupe in formulo preštevanja za klasifikacijo končnih podgrup rotacijske grupe SO3.
Keywords:	grupa, togo gibanje, grupe gibanj, diskretne grupe gibanj, delovanje, končne podgrupe rotacijske grupe.
Place of publishing:	Maribor
Publisher:	[B. Strelec]
Year of publishing:	2010
PID:	20.500.12556/DKUM-13058
UDC:	51(043.2)
COBISS.SI-ID:	17431304
NUK URN:	URN:SI:UM:DK:I79MN0OQ
Publication date in DKUM:	11.02.2010
Views:	3861
Downloads:	396
Metadata:
Categories:	FNM
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Secondary language

Language:	English
Title:	SYMMETRIES OF PLANE FIGURES
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.
Keywords:	group, rigid motion, groups of motions, discrete group of motions, operation, finite subgroups of the rotation group.

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