The Golden Ratio and Fibonacci Numbers

Hardcover (Print)
Used and New from Other Sellers
Used and New from Other Sellers
from $43.95
Usually ships in 1-2 business days
(Save 24%)
Other sellers (Hardcover)
  • All (11) from $43.95   
  • New (5) from $49.63   
  • Used (6) from $43.95   

Overview

In this invaluable book, the basic mathematical properties of the golden ratio and its occurrence in the dimensions of two- and three-dimensional figures with fivefold symmetry are discussed. In addition, the generation of the Fibonacci series and generalized Fibonacci series and their relationship to the golden ratio are presented. These concepts are applied to algorithms fur searching and function minimization. The Fibonacci sequence is viewed as a one-dimensional aperiodic, lattice and these ideas are extended to two- and three-dimensional Penrose tilings and the concept of incommensurate projections. The structural properties of aperiodic crystals and the growth of certain biological organisms are described in terms of Fibonacci sequences.
Read More Show Less

Product Details

  • ISBN-13: 9789810232641
  • Publisher: World Scientific Publishing Company, Incorporated
  • Publication date: 12/28/1997
  • Pages: 172
  • Sales rank: 1,389,378
  • Product dimensions: 5.94 (w) x 9.12 (h) x 0.39 (d)

Table of Contents

Preface
Ch. 1 Introduction 1
Ch. 2 Basic Properties of the Golden Ratio 7
Ch. 3 Geometric Problems in Two Dimensions 15
Ch. 4 Geometric Problems in Three Dimensions 23
Ch. 5 Fibonacci Numbers 35
Ch. 6 Lucas Numbers and Generalized Fibonacci Numbers 51
Ch. 7 Continued Fractions and Rational Approximants 63
Ch. 8 Generalized Fibonacci Representation Theorems 71
Ch. 9 Optimal Spacing and Search Algorithms 79
Ch. 10 Commensurate and Incommensurate Projections 87
Ch. 11 Penrose Tilings 97
Ch. 12 Quasicrystallography 111
Ch. 13 Biological Applications 123
App. I Construction of the Regular Pentagon 137
App. II The First 100 Fibonacci and Lucas Numbers 139
App. III Relationships Involving the Golden Ratio and Generalized Fibonacci Numbers 143
References 153
Index 157
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)