The Fibonacci Sequence Through a Different Lens

Abstract

While Fibonacci numbers have been the subject of numerous works over hundreds of years, the sequence presents still more opportunities for discovery. This paper introduces a new way of perceiving this well established sequence by looking at Fibonacci relationships in terms of a specific geometric construction based on Fibonacci numbers. We first find that the properties of these shapes imply several Fibonacci relationships by themselves. Moreover, we begin to explore a general form of this construction based on Fibonacci numbers which yields additional Fibonacci relationships, confirms previous observations, and offers more conclusions about Fibonacci numbers for further research. As we work through conclusions previously reached by others, we find that there is yet another path to our known destination, which suggests other related trails for further expansion of our understanding of this enduring sequence.