Title Simetrije, algoritmi i matematika Rubikove kocke
Title (english) Symmetries, Algorithms and Mathematics of Rubick's Cube
Author David Miličević
Mentor Neven Grbac (mentor)
Mentor Tihana Galinac Grbac (komentor)
Committee member Darko Brborović (predsjednik povjerenstva)
Committee member Neven Grbac (član povjerenstva)
Committee member Tihana Galinac Grbac (član povjerenstva)
Committee member Sven Maričić (član povjerenstva)
Granter University of Pula (Juraj Dobrila University of Pula, Department of Engineering) Pula
Defense date and country 2024-05-29, Croatia
Scientific / art field, discipline and subdiscipline NATURAL SCIENCES Mathematics Algebra
Abstract Završni rad "Simetrije, matematika i algoritmi Rubikove kocke" istražuje složenost i matematičke aspekte povezane s Rubikovom kockom, počevši od uvoda u osnovne koncepte simetrije. U radu se detaljno analiziraju grupe i simetrije koje karakteriziraju strukturu kocke, te se uvode osnovni pojmovi teorije grupa potrebni za razumijevanje ove analize. Povijesni kontekst nastanka Rubikove kocke i njezin mehanizam također su obrađeni kako bi se pružio sveobuhvatan pregled.
Glavni dio rada posvećen je matematici i algoritmima koji se koriste za rješavanje Rubikove kocke. Obrađene su permutacije, paritet, podgrupe, Cayleyev graf, komutator i konjugacija kao ključni matematički koncepti. Detaljno je objašnjen početnički algoritam za rješavanje kocke kroz sedam koraka, uključujući:
Postavljanje prvog sloja (bridovi i kutevi),
Rješavanje drugog sloja (F2L),
Formiranje žutog križića,
Zamjena bočnih središnjih dijelova sa žutim bridovima,
Postavljanje žutih kockica na točnu poziciju,
Orijentacija zadnjeg sloja Rubikove kocke.
Kroz ovaj rad, demonstrirano je kako matematički principi i algoritmi mogu optimizirati proces rješavanja Rubikove kocke, pružajući dublji uvid u njezinu strukturu i složenost. Ovaj rad ističe važnost matematike u razumijevanju i rješavanju problema Rubikove kocke, te nudi pregled mogućih smjerova za daljnje istraživanje i primjenu matematičkih načela u sličnim slagalicama.
Abstract (english) The thesis "Symmetries, Mathematics, and Algorithms of the Rubik's Cube" explores the complexity and mathematical aspects associated with the Rubik's Cube, starting with an introduction to basic concepts of symmetry. The thesis provides a detailed analysis of the groups and symmetries characterizing the structure of the cube and introduces fundamental concepts of group theory necessary for understanding this analysis. The historical context of the invention of the Rubik's Cube and its mechanism are also covered to provide a comprehensive overview.
The main part of the thesis is dedicated to the mathematics and algorithms used for solving the Rubik's Cube. Key mathematical concepts such as permutations, parity, subgroups, Cayley graph, commutator, and conjugation are discussed. The beginner's algorithm for solving the cube is thoroughly explained through seven steps, including:
Solving the first layer (edges and corners),
Solving the second layer (F2L - First Two Layers),
Forming the yellow cross,
Swapping the side center pieces with yellow edges,
Placing the yellow pieces in their correct positions,
Orienting the last layer of the Rubik's Cube.
This thesis demonstrates how mathematical principles and algorithms can optimize the process of solving the Rubik's Cube, providing deeper insight into its structure and complexity. The importance of mathematics in understanding and solving the Rubik's Cube is highlighted, offering an overview of possible directions for further research and the application of mathematical principles in similar puzzles.
Keywords
Rubikova kocka
simetrije
algoritmi
teorija grupa
permutacije
paritet
podgrupe
Cayleyev graf
komutator
mehanika Rubikove kocke
kombinatorika.
Keywords (english)
Rubik's Cube
symmetries
algorithms
group theory
permutations
parity
subgroups
Cayley graph
commutator
mechanics of the Rubik's Cube
combinatorics.
Language croatian
URN:NBN urn:nbn:hr:137:577293
Study programme Title: Computing - Bachelor programme Study programme type: university Study level: undergraduate Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka računarstva)
Type of resource Text
File origin Born digital
Access conditions Open access
Terms of use
Created on 2024-05-31 09:36:51