Fibonacci Numbers

Authors: Vorobiev, Nicolai N.

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About this book

Since their discovery hundreds of years ago, people have been fascinated by the wondrous properties of Fibonacci numbers. Being of mathematical significance in their own right, Fibonacci numbers have had an impact on areas like art and architecture, and their traces can be found in nature and even the behavior of the stock market. Starting with the basic properties of Fibonacci numbers, the present book explores their relevance in number theory, the theory of continued fractions, geometry and approximation theory. Rather than giving a complete account of the subject, a few chosen examples are treated exhaustively. They not only reveal the bearing of Fibonacci numbers on mathematics, but also provide very readable marvels of mathematical reasoning. This book is the translation of the 6th Russian edition (the first edition appeared in the early fifties and became a standard source of information on the subject).

Reviews

"Quite the special topic, the Fibonacci numbers nevertheless enjoy enormous popularity, perhaps due to their connection with the golden mean. Vorobiev's book, now translated, presents a solid overview, perfectly pitched to undergraduates. . . . Recommended; upper-division undergraduates and up."

—CHOICE

"This is a wonderful book with a huge amount of information on Fibonacci numbers. First published in the 1950s for high school students enrolled in a mathematical circle at the Leningrad State University, the book only assumes knowledge of high school mathematics, but the reader will need the sophistication of a good upper-level mathematics major. The warmth and enthusiasm of the late author comes through Mircea Martin's English translation.... This book would be useful to any mathematician with a desire to know more about the Fibonacci numbers. A student could use it for a reading project on the Fibonacci numbers.... Overall, I enjoyed the book and highly recommend it."

—MAA Online


Table of contents (6 chapters)

  • Introduction

    Vorobiew, Nicolai N.

    Pages 1-3

  • The Simplest Properties of Fibonacci Numbers

    Vorobiew, Nicolai N.

    Pages 5-50

  • Number-Theoretic Properties of Fibonacci Numbers

    Vorobiew, Nicolai N.

    Pages 51-87

  • Fibonacci Numbers and Continued Fractions

    Vorobiew, Nicolai N.

    Pages 89-123

  • Fibonacci Numbers and Geometry

    Vorobiew, Nicolai N.

    Pages 125-147

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-0348-8107-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA
  • ISBN 978-3-7643-6135-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Fibonacci Numbers
Authors
Translated by
Martin, M.
Copyright
2002
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-8107-4
DOI
10.1007/978-3-0348-8107-4
Softcover ISBN
978-3-7643-6135-8
Edition Number
1
Number of Pages
X, 178
Number of Illustrations and Tables
2 b/w illustrations
Additional Information
Originally published under the title "Chisla Fibonacci" by Nauka, Moscow, 1992.
Topics