20.500.12556/DKUM-13058 SIMETRIJE RAVNINSKIH LIKOV SYMMETRIES OF PLANE FIGURES 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. 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. grupa togo gibanje grupe gibanj diskretne grupe gibanj delovanje končne podgrupe rotacijske grupe. group rigid motion groups of motions discrete group of motions operation finite subgroups of the rotation group. true true false [B. Strelec] Slovenski jezik Angleški jezik Diplomsko delo 2010-01-25 20:08:18 2010-02-11 13:22:42 2022-04-12 10:52:43 2022-04-20 03:27:51 2010 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 51(043.2) 17431304 URN:SI:UM:DK:I79MN0OQ UNI_Strelec_Bostjan_2010.pdf UNI_Strelec_Bostjan_2010.pdf 1 61A7B584076A3DCB043E73E71EF8AAB9 8b3038b2a71fed6d58f1289c91ee43a00a5d8ccf45adb0748450f2434a57e9c2 ced5d0dc-7c03-11eb-bb7a-00155d0001ca 20.500.12556/dkum/57900ad1-c7c1-4f06-9296-dbb2999c4b83 https://dk.um.si/Dokument.php?lang=slv&id=12914 Fakulteta za naravoslovje in matematiko 0 0 0