A note on closed-form representation of Fibonacci numbers using Fibonacci trees

TL;DR

This paper introduces a novel closed-form method for computing Fibonacci numbers using Fibonacci trees, enabling calculation of the nth number without prior Fibonacci knowledge.

Contribution

It presents a new tree-based representation that allows direct computation of Fibonacci numbers, differing from traditional recursive or iterative methods.

Findings

Provides a closed-form expression using Fibonacci trees

Enables direct calculation of Fibonacci numbers without previous terms

Offers potential computational efficiency improvements

Abstract

In this paper, we give a new representation of the Fibonacci numbers. This is achieved using Fibonacci trees. With the help of this representation, the nth Fibonacci number can be calculated without having any knowledge about the previous Fibonacci numbers.