Matematične uganke v teoriji grafov

na dvopredmetnem študijskem programu 2. stopnje Izobraževalna matematika

Maja Javornik (Author), Tanja Gologranc (Mentor)

Abstract

V magistrskem delu je predstavljenih več učencem zanimivih matematičnih ugank. Najprej obravnavamo različne matematične uganke skozi zgodovino vse od magičnih kvadratov do ugank novejšega časa, kot je Rubikova kocka. Nato se osredotočimo na teorijo grafov in predstavimo ikozaedersko igro, problem Köningsberških mostov, problem prečkanja reke brez mostov in problem štirih konjev. Kot uvod v obravnavo kitajskih prstanov predstavimo legendo o stolpu iz Brahme in vpeljemo Hanojske stolpe. Dokažemo optimalno rešitev Hanojskega stolpa z ▫$n \in{\mathbb{N}}_0$▫ diski. Med drugimi predstavimo variacijo Hanojskega stolpa, ki se imenuje zamenjevalni Hanojski stolp in predstavimo zgodovino kitajskih prstanov. Nazadnje problem kitajskih prstanov podrobneje raziščemo in dokažemo formulo za najhitrejšo rešitev problema.

Keywords

magistrska dela;Kitajski prstani;Hanojski stolpi;Hamiltonovi grafi;Eulerjevi grafi;ravninski grafi;

Data

Language:	Slovenian
Year of publishing:	2019
Typology:	2.09 - Master's Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[M. Javornik]
UDC:	519.17(043.2)
COBISS:	25074440
Views:	738
Downloads:	71
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Mathematical puzzles in graph theory
Secondary abstract:	The master's thesis presents several interesting mathematical puzzles for students. First of all, we deal with various mathematical puzzles throughout the history - such as magic squares and puzzles of the recent times i.e. Rubik's Cube. In the second part, emphasis is laid on graph theory, where we introduce, the icosian game, the Köningsberg Bridge problem, the problem of crossing the river without bridges, and the problem of four knights. As an introduction to the problem of Chinese rings, we present the legend of the Brahma tower and introduce the Hanoi towers. The optimal solution of the Tower of Hanoi problem with ▫$n \in{\mathbb{N}}_0$▫ disks is proven. We also present a variation of Hanoi tower, called switching Tower of Hanoi, and the history of Chinese rings. Finally, we comprehensively investigate the problem of Chinese rings in detail and prove the formula for the fastest solution of the investigated problem.
Secondary keywords:	master theses;Chinese rings;Tower of Hanoi;Hamiltonian graph;Euler graph;planar graph;
Type (COBISS):	Master's thesis/paper
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	VIII, 56 f.
ID:	11334783