Određivanje optimalnog rješenja problema premještanja kauča

master's thesis

• Title (english): Determining the optimal solution to the problem of moving the couch
• Author: Lea Glasnović
• Mentor: Marko Erceg (mentor)
• Committee member: Marko Erceg (predsjednik povjerenstva)
• Committee member: Filip Najman (član povjerenstva)
• Committee member: Goran Radunović (član povjerenstva)
• Committee member: Dijana Ilišević (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2023-09-26, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu dublje istražujemo problem pomicanja kauča, matematičku enigmu koju je prvi put postavio austrijsko-kanadski matematičar Leo Moser 1966. godine. Počevši od ranih pokušaja rješavanja, kao što je Hammersleyev model, prelazimo na revolucionarni Gerverov pristup koji je znatno utjecao na daljnje istraživanje u ovom području. Suvremene perspektive, predstavljene kroz rad Dana Romika, uvode nove koncepte i metode, uključujući rotacijske putanje i kontaktne točke, koji dodatno kompliciraju problem, ali istovremeno nude nove pravce za rješenje. Osim toga, rad se bavi i ambideksternom varijantom problema, koja predstavlja dodatni sloj izazova i komplikacija. Kroz detaljnu analizu geometrijskih i algebarskih svojstava, rad pruža sveobuhvatan pregled ovog fascinantnog i još uvijek nerješenog problema, s fokusom na otvorena pitanja i mogućnosti za buduća istraživanja.

Abstract (english)

In this thesis, we delve deeply into the Moving Sofa Problem, a mathematical enigma first posed by Austrian-Canadian mathematician Leo Moser in 1966. Starting with early attempts at solving the problem, such as Hammersley’s model, we transition to the groundbreaking approach by Gerver, which has significantly influenced further research in this field. Contemporary perspectives, represented through the work of Dan Romik, introduce new concepts and methods, including rotational paths and contact points, that both complicate the issue and offer fresh avenues for resolution. Additionally, the paper explores the ambidextrous variant of the problem, adding an extra layer of challenges and complexities. Through a detailed analysis of geometric and algebraic properties, this paper provides a comprehensive overview of this fascinating yet unsolved problem, with a focus on open questions and avenues for future research.

• Keywords: Leo Moser; Hammersleyev model; Gerverov pristup; Dan Romik
• Keywords (english): Leo Moser; Hammersley’s model; Gerver; Dan Romik
• Language: croatian
• URN:NBN: urn:nbn:hr:217:532009
• Study programme: Title: Applied Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-02-01 10:38:55