College of Arts and Sciences
This thesis offers a brief background on the life of Fibonacci as well as his discovery of the famous Fibonacci sequence. Next, the limit of the ratio of consecutive Fibonacci terms is established and discussed. The Fibonacci sequence is then defined as a recursive function, a linear homogeneous recurrence relation with constant coefficients, and a generating function. Proofs for those particular properties are introduced and proven. Several theorems and identities from the field of number theory concerning the properties of the Fibonacci numbers are also introduced and proven. Finally, the famous Fibonacci puzzle is introduced and critiqued. These fascinating characteristics and applications demonstrate not only the universal nature of the Fibonacci sequence but also the aesthetic nature of God.