## Table of Contents

**Table of Contents**

Preface

Chapter 1. Theoretical Background: Fibonacci Numbers as a Framework for Information vs. Explanaition Cognitive Paradigm

Chapter 2. From Fibonacci Numbers to Fibonacci-Like Polynomials

Chapter 3. Different Approaches to the Development of Binetâ€™s Formulas

Chapter 4. Fibonacci Sieves and Their Representation through Difference Equations

Chapter 5. Tite Explorations of Generalized Golden Ratios

Chapter 6. Exploring Cycles Using a Combination of Digital Tools

Chapter 7. Method of Iterations and Fibonacci-Like Polynomials

Chapter 8. Identities for Fibonacci-Like Polynomials

Chapter 9. Uncovering Hidden Patterns in the Oscillations of Generalized Golden Ratios

References

**Reviews**

“One of the most fascinating aspects of this book is the discovery of cycles formed by the orbits of a very simple non-linear recursive equation. An experimental nature of some results formulated by Abramovich and Leonov can serve as a motivation for rigorous mathematics research.”Â **– Nikolay Kuznetsov, Saint-Petersburg State University, Russia**

“While there is an abundance of popular and scholarly literature on Fibonacci numbers, the book offers a markedly new perspective on this classic concept made possible by the use of modern computational tools. The authors did their best in demonstrating an educational side of experimental mathematics.”Â **– Pekka NeittaanmÃ¤ki, University of JyvÃ¤skylÃ¤, Finland**

“Abramovich and Leonov have written a uniquely valuable book for secondary teachers and students. They begin with the simple sequence 1, 1, 2, 3, â€¦ and expand it into a universe of ever more sophisticated and fascinating mathematical ideas. A remarkable feat.”Â **– Pat Thompson, Arizona State University, USA**

“As a mathematics educator, I really appreciate the creative work of Gennady Leonov and Sergei Abramovich. It stimulates the design of mathematically substantial learning environments about Fibonacci numbers across the whole curriculum.”Â **– Erich Ch. Wittmann, Technical University of Dortmund, Germany**

“Abramovich & Leonovâ€™s book aims to explore Fibonacci numbers through the tools of the digital age. These range from graphing calculators to computer algebra packages enabling students from secondary mathematics to undergraduate level over a range of science and engineering disciplines to appreciate some of their properties and possibly discover some â€˜newâ€™ concepts.”Â **Martin C. Harrison, Loughborough University, United Kingdom**

**Keywords**: Fibonacci numbers, experimental mathematics, computational experiment, cycles, generalized golden ratios, spreadsheets, Maple, Wolfram Alpha

The material presented in this book can be used in secondary mathematics teacher education programs, undergraduate mathematics courses for students majoring in mathematics, computer science, electrical and mechanical engineering, as well as in other undergraduate mathematics programs that study difference equations in the broad context of discrete mathematics.