On the Analysis of the Fibonacci Numbers: Critique to Kepler

Abstract

What has the theoretical breeding of rabbits got to do with geometry? The connection of the Fibonacci sequence to the Golden Mean was made by Johannes Kepler in the 17th century CE, which sequence was introduced by Leonardo Pissano, better known as Fibonacci, in the Liber Abaci in the 13th century CE. We judiciously ignore the historical background of the Fibonacci sequence, and proceed to analyse it mindful of the fact that the so-called Fibonacci numbers were known well before 1202. Herein the author, after presenting the ‘Kepler Paradox’ proposes and pursues a more precise analysis of the Fibonacci sequence with regard the Golden Mean using an existing geometric tool, and henceforth shows how similar sequences can be assembled, among which is the Lucas sequence