Leonardo of Pisa and the Birth of a Sequence: A Reexamination of Fibonacci’s Theory

Abstract

Leonardo Pisano Bogollo, widely known as Fibonacci, made a lasting impact on Western mathematics through his introduction of the Hindu-Arabic numeral system in his 1202 publication Liber Abaci. This work not only facilitated the widespread adoption of the place-value system and the use of zero but also introduced a sequence that would later bear his name. Among the first mathematical problems he presented was the now-famous "rabbit problem," a hypothetical scenario used to model population growth. This scenario led to the formulation of a recursive sequence that reveals the Fibonacci numbers. Although the mathematical reasoning behind the problem is straightforward in structure, the underlying mechanism by which this sequence arises from such conditions has long been puzzling. The article revisits Fibonacci's contributions with a modern lens, reflecting on the theoretical implications of the sequence and the delayed understanding of its generative principles. Recent studies have begun to explore the deeper mathematical reasons behind why certain recursive models yield Fibonacci numbers, contributing to a more complete theoretical framework.