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From the Golden Rectangle to the Fibonacci Sequences

  • Textbook
  • © 2023

Overview

Authors:
  1. Opher Liba

    1. Jerusalem, Israel

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    You can also search for this author in PubMed   Google Scholar

  2. Bat-Sheva Ilany

    1. Hebrew University of Jerusalem, Academic Hemdat College,, Netivot, Israel

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Presents the Golden Ratio and the Fibonacci Sequences for teaching purposes
  • Introduces novel perspectives to classic mathematical concepts and problems
  • Contains over 200 challenging exercises

Part of the book series: Springer Texts in Education (SPTE)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-XX
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  2. The Golden Rectangle and the Golden Ratio

    • Opher Liba, Bat-Sheva Ilany
    Pages 1-39

  3. Introducing Golden Triangles

    • Opher Liba, Bat-Sheva Ilany
    Pages 41-53

  4. The Fibonacci Sequence

    • Opher Liba, Bat-Sheva Ilany
    Pages 55-83

  5. The Lucas Sequence

    • Opher Liba, Bat-Sheva Ilany
    Pages 85-103

  6. The General Fibonacci-Like Sequences

    • Opher Liba, Bat-Sheva Ilany
    Pages 105-129

  7. In Opher’s Footsteps—Challenges for Exploration

    • Opher Liba, Bat-Sheva Ilany
    Pages 131-139

  8. Back Matter

    Pages 141-160
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Keywords

About this book

The book takes us on a fascinating journey through one of the most beautiful and fascinating topics of mathematics. It presents a wealth of information about the golden ratio and the Fibonacci sequence.  The book introduces the reader to novel perspectives to classic mathematical concepts and problems. 


The book’s structure engages with the reader actively, leading to more profound understanding, satisfaction and deep insights in learning mathematics. 


The book strengthens and expands the readers' mathematical knowledge, allowing them a glimpse of several advanced academic concepts. It demonstrates and instils the essence of mathematical research, along the lines of George Polya: observation, conjecture, proof, implementation, generalization and raising new questions.


Reviews

“From the Golden Rectangle to the Fibonacci Sequences is both a stimulating read … . Each concept presented in this book is done so with precision, accompanied by appropriate definitions, and followed by rigorous mathematical proofs. ... This book is intended for advanced high school students, college students, and interested readers with a strong mathematics background. ... The chapter closes with over 80 exercises for the reader to accomplish. There are answers or hints provided for each of the exercises.” (Tom French, MAA Reviews, September 4, 2023)

Authors and Affiliations

  • Jerusalem, Israel

    Opher Liba

  • Hebrew University of Jerusalem, Academic Hemdat College,, Netivot, Israel

    Bat-Sheva Ilany

About the authors

Opher Liba 
The late Opher Liba was a distinguished teacher of mathematics at all levels. Opher organised and convened several mathematics conferences and wrote numerous books and papers for both teachers and students of mathematics. Opher was particularly interested in the Fibonacci sequences. He conducted original research on this topic and wrote extensively about it for students at various levels.


Dr Bat-Sheva Ilany is a distinguished mathematics educator. She has published many books, papers and teaching material for primary, secondary and tertiary levels. Bat-Sheva has been teaching at various universities and teacher training colleges, and has supervised many PhD and MSc students. 

Bat Sheva consults to the Ministry of Education and to organisations that develop books, games and teaching materials.


Isaac Nativ studied mathematics and mathematics education at Monash University as well as at Melbourne University. He has been teaching gifted students for many years



Bibliographic Information

  • Book Title: From the Golden Rectangle to the Fibonacci Sequences

  • Authors: Opher Liba, Bat-Sheva Ilany

  • Series Title: Springer Texts in Education

  • DOI: https://doi.org/10.1007/978-3-030-97600-2

  • Publisher: Springer Cham

  • eBook Packages: Education, Education (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023

  • Softcover ISBN: 978-3-030-97599-9Published: 09 May 2023

  • eBook ISBN: 978-3-030-97600-2Published: 08 May 2023

  • Series ISSN: 2366-7672

  • Series E-ISSN: 2366-7680

  • Edition Number: 1

  • Number of Pages: XX, 160

  • Number of Illustrations: 34 b/w illustrations, 18 illustrations in colour

  • Topics: Mathematics Education, Teaching and Teacher Education, Educational Psychology, Research Methods in Education

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