Matematika Rubikove kocke

master's thesis

• Title (english): Rubik's Cube Mathematics
• Author: Matea Vidov
• Mentor: Matija Bašić (mentor)
• Committee member: Matija Bašić (predsjednik povjerenstva)
• Committee member: Matija Kazalicki (član povjerenstva)
• Committee member: Rudi Mrazović (član povjerenstva)
• Committee member: Sonja Štimac (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-09-30, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Cilj ovog diplomskog rada je povezati teoriju grupa sa Rubikovom kockom i upoznati se s kombinatorikom i geometrijom koja se krije u Rubikovoj kocki. Proučavanjem simetrija geometrijskih objekata uvodi se pojam grupe i prezentacije grupa. Prikazana je Burnsideova metoda prebrojavanja na bojanju kvadrata i kocke, do na simetriju. Uvode se oznake i potezi na Rubikovoj kocki te njihov prikaz pomoću ciklusa. Opisane su konfiguracije Rubikove kocke koje se mogu dobiti primjenom poteza, ali i rastavljanjem Rubikove kocke na dijelove od kojih se sastoji. Primjenom komutatora i konjugata poteza opisano je nekoliko strategija za promjenu orijentacije i pozicije nekoliko rubnih i vršnih kockica čijim je razumijevanjem moguće složiti Rubikovu kocku. U zadnjem dijelu rada je dan metodički osvrt na potencijal koji Rubikova kocka može donijeti nastavi matematike u osnovnoj i srednjoj školi i opisane su nastavne aktivnosti.

Abstract (english)

The aim of this thesis is to connect group theory with the Rubik’s cube and get to know combinatorics and geometry hidden in the Rubik’s cube. The concept of group and presentation of groups is introduced by studying the symmetries of geometric objects. Burnside’s method of counting is presented by the coloring of squares and cubes, up to symmetry. Notation and moves on the Rubik’s cube are introduced and they are represented by cycle notation. The configurations of the Rubik’s cube are described, which can be obtained by making the moves, but also by disassembling the Rubik’s cube into the parts of which it consists. By using commutators and move conjugates, several strategies for changing the orientation and position of edge and corner cubies are described, that leads to understanding of assembling the Rubik’s cube. In the last chapter, a methodical review of the potential that the Rubik’s Cube can bring to the teaching of mathematics in primary and secondary school is given, and the teaching activities are described.

• Keywords: teorija grupa; Burnsideova metoda prebrojavanja; nastava matematike
• Keywords (english): group theory; Burnside’s method of counting; teaching of mathematics
• Language: croatian
• URN:NBN: urn:nbn:hr:217:181066
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2021-03-08 10:46:18