Fibonacci Numbers and Identities

TL;DR

This paper explores Fibonacci and Lucas number identities through recurrence relations, providing alternative proofs and visual representations using trivalent graphs to enhance understanding of well-known identities.

Contribution

It introduces a novel approach using recurrence relations and trivalent graphs to prove and visualize Fibonacci and Lucas number identities.

Findings

Alternative proofs of Fibonacci and Lucas identities

Visualization of identities via trivalent graphs

Enhanced understanding of recurrence relations

Abstract

By investigating a recurrence relation about functions, we first give alternative proofs of various identities on Fibonacci numbers and Lucas numbers, and then, make certain well known identities visible via certain trivalent graph associated to the recurrence relation.