Aspects of Fibonacci numbers
Author
Yücel, Gülnihal
Advisor
Yıldırım, Yalçın
Date
1994Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Show full item recordAbstract
This thesis consists of two parts. The first part, which is Chapter 2, is
a survey on some aspects of Fibonacci numbers. In this part, we tried to
gather some interesting properties of these numbers and some topics related to
the Fibonacci sequence from various references, so that the reader may get an
overview of the subject. After giving the basic concepts about the Fibonacci
numbers, their arithmetical properties are studied. These include divisibility
and periodicity properties, the Zeckendorf Theorem, Fibonacci trees and their
relations to the representations of integers, polynomials used for deriving new
identities for Fibonacci numbers and Fibonacci groups. Also in Chapter 2, natural
phenomena related to the golden section, such as certain plants having Fibonacci
numbers for the number of petals, or the relations of generations of bees with the
Fibonacci numbers are recounted.
In the second part of the thesis. Chapter 3, we focused on a Fibonacci based
random number sequence. We analyzed and criticized the generator Sfc = k(j>—[k(j)]
by applying some standart tests for randomness on it.
Chapter 5, the Appendix consists of Fortran programs used for executing the
tests of Chapter 3.
Keywords
Fibonacci numbersGolden section
golden rectangle
Binet form
Fibonacci representation
Zeckendorf theorem
Fibonacci tree
tree codes
Pell polynomials
Pell Lucas polynomials
Pell diagonal functions
Fibonacci Polynomials
Lucas Polynomials
Fibonacci groups
random number
independent
uniform
QA241 .Y83 1994
Fibonacci numbers.
Golden section.
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