Jeremiah N. Alexander

November 28, 2007

The Fibonacci Sequence

For my research, I plan to do work on the exposition of the Fibonacci sequence of numbers. While this sequence was originally used as a method for predicting the growth of the population of rabbits, it has many other practical uses. They are important in Euclid's algorithm in determining the greatest common divisor of two numbers. Fibonacci numbers have a relation to the golden ratio, used in both mathematics and arts. Recently, Fibonacci numbers have even be used to predict trends in the world market.

Many interesting discoveries have been made in regards to the Fibonacci sequence. For my research, I wish to focus my study in the around applications of the generalized recursive rule. I also want to spend time researching two-term recurrences and the connection between Fibonacci numbers and Lucas numbers. I hope to use my research to work out a new theory regarding the sequence.

To complete this research I will take advantage of the skills I have developed as a computer information systems major. I can utilize computer and programming skills to aid me in the solving of difficult problems. Also, I can use mathematical induction as a way to help solve and prove problems I come across in my research.

My greatest motivation for researching the Fibonacci numbers is simply a curiosity for what they can do and a love of mathematics. I find this sequence of numbers very interesting and wish to spend time to be able to learn more about it. It would also be interesting to find a way to use the sequence in cryptology to new, stronger type of security.