Algoritmi za računanje egipčanskih ulomkov

magistrsko delo

Monia Žuran (Author), Matej Mencinger (Mentor), Simon Špacapan (Mentor)

Abstract

Egipčani so ulomke izražali kot vsote med seboj različnih, pozitivnih enotskih ulomkov. Takšne ulomke danes imenujemo egipčanski ulomki. V magistrskem delu obravnavamo algoritme za računanje egipčanskih ulomkov, ki temeljijo na aproksimacijah, na dvojiškem sistemu, na verižnih ulomkih, na metodi majhnih števcev in na obratni požrešni metodi. V prvem delu spoznamo številske sisteme, ki so jih poznali v starodavnem Egiptu, definiramo egipčanski ulomek in spoznamo osnove algoritmov. V drugem delu posamezne algoritme opišemo in predstavimo na primerih. Izbran algoritem udejanjimo v programskem jeziku C++.

Keywords

magistrska dela;enotski ulomek;egipčanski ulomek;algoritem;požrešna metoda;dvojiška metoda;verižni ulomek;obratna požrešna metoda;

Data

Language:	Slovenian
Year of publishing:	2022
Typology:	2.09 - Master's Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[M. Žuran]
UDC:	511.41(043.2)
COBISS:	111921667
Views:	71
Downloads:	8
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Algorithms for computing egyptian fractions
Secondary abstract:	The Egyptians expressed fractions as sums of different positive unit fractions. Today, such fractions are named Egyptian fractions. In this master’s thesis we discuss the algorithms for calculating Egyptian fractions based on approximations, the binary system, the chain fractions, the method of small counters and on the reverse greedy method. In the first part, we get to know the number systems that were known in ancient Egypt, define the Egyptian fraction, and learn the basics of algorithms. In the second part of the thesis, we describe and present each algorithm with the chosen examples. Then the selected algorithm is implemented in the C ++ programming language.
Secondary keywords:	master theses;unit fraction;Egyptian fraction;algorithm;greedy method;binary method;continued fraction;reverse greedy method;Verižni ulomki;Algoritmi;Univerzitetna in visokošolska dela;
Type (COBISS):	Master's thesis/paper
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	VIII, 37 f.
ID:	15081098