Direct Proofs Using Fibonacci Numbers

About the lecture

In this mini-lecture, we use the Fibonacci numbers to motivate examples of direct proofs. As we move though this mini-lecture, we consider: (i) the definition of Fibonacci numbers, F_n = F_n-1 + F_n-2, which can be used to create a sequence of numbers; (ii) mathematical patterns in the Fibonacci sequence, such as every third number being even while all others are odd; (iii) a direct proof of a property of Fibonacci numbers, which states that F_n+1 = 2F_n-1 + F_n-2; and (iv) how this property, F_n+1 = 2F_n-1 + F_n-2, can also help us deduce which terms are even and which are odd in the Fibonacci sequence.

About the lecturer

Shabnam Akhtari is an Associate Professor of Mathematics at the University of Oregon. Her research interests are in Number Theory, in particular Diophantine Analysis and the Geometry of Numbers.