A study of the Fibonacci sequence

As the title suggests, the purpose of this thesis is to present a study of the Fibonacci sequence of numbers. A historical development of the sequence is given, followed by the proof of the sequence's various intriguing identities and properties. Lastly, an interesting application of a property of the Fibonacci numbers is illustrated, developed, and then proved. Methods of proof in the thesis are either direct or with the first or second principle of mathematical induction. Sources are periodicals and books on number theory and history of mathematics.