fibonacci-numbers

There are many other properties and identities related to Fibonacci numbers and people
have written books about it. Due to the nature of this paper and a limited scope, it is hard to
cover everything there is about for the Fibonacci numbers. For this reason, in this final section
of the paper, I will introduce some real world applications related to Fibonacci numbers and
their relationship with nature.
Fibonacci numbers are important to perform a run‐time analysis of Euclid’s algorithm to
find the greatest common divisor (GCD) of two integers. A pair of two consecutive Fibonacci
numbers makes a worst case input for this algorithm (Knuth, Art of Computer Programming,
Volume 1: Fundamental Algorithms, 1997). Fibonacci numbers have their application in the
polyphase version of the Merge Sort algorithm. This algorithm divides an unsorted list in two
lists such that the length of lists corresponds to two sequential Fibonacci numbers. The ratio of
the lengths of the lists is an approximately same as (Knuth, Art of Computer Programming,
Volume 1: Fundamental Algorithms, 1997). Fibonacci numbers are essential in the analysis of
the Fibonacci heap data structures. A network topology for parallel computing uses a Fibonacci
cube which is an undirected graph with Fibonacci number of nodes. The Fibonacci search
technique is a one‐dimensional optimization method and is developed on the basis of Fibonacci
numbers and their properties (Avriel & Wilde, 1966). IFF 8SVX audio file format in Amiga
computers uses Fibonacci sequence to compand the original audio wave for optional lossy
compression (Addison‐Wesley, 1991). The conversion factor from miles to kilometers
1.609344 . When Fibonacci numbers are replaced by their successors, the sum of the
decomposition of distance in miles into a sum of Fibonacci numbers is approximately same as
kilometer sum. This can be achieved by shifting a radix 2 number register in golden ratio base
Fibonacci numbers Page 7