Fibonacci Expansions

TL;DR

This paper introduces Fibonacci-based expansions as an alternative to Golden ratio expansions, demonstrating they exhibit improved properties in certain mathematical contexts.

Contribution

The paper presents a novel Fibonacci-based expansion method and compares its performance to Golden ratio expansions, showing it behaves better in some aspects.

Findings

Fibonacci expansions have advantageous properties over Golden ratio expansions.

The new expansions exhibit improved convergence or representation characteristics.

Fibonacci expansions are a promising area for further mathematical exploration.

Abstract

Expansions in the Golden ratio base have been studied since a pioneering paper of R\'enyi more than sixty years ago. We introduce closely related expansions of a new type, based on the Fibonacci sequence, and we show that in some sense they behave better.