Golden Ratio And Fibonacci Numbers, The

By: Richard A Dunlap

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Hardcover | 27 December 1997

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Hardcover
172 Pages

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22.4 x 16.3 x 1.7

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"This attractive and carefully written book addresses the general reader with interest in mathematics and its application to the physical and biological sciences ... this one will make a valuable addition to academic and personal libraries."

The Fibonacci Quarterly

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 for 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.

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Preface
Introduction	p. 1
Basic Properties of the Golden Ratio	p. 7
Geometric Problems in Two Dimensions	p. 15
Geometric Problems in Three Dimensions	p. 23
Fibonacci Numbers	p. 35
Lucas Numbers and Generalized Fibonacci Numbers	p. 51
Continued Fractions and Rational Approximants	p. 63
Generalized Fibonacci Representation Theorems	p. 71
Optimal Spacing and Search Algorithms	p. 79
Commensurate and Incommensurate Projections	p. 87
Penrose Tilings	p. 97
Quasicrystallography	p. 111
Biological Applications	p. 123
Construction of the Regular Pentagon	p. 137
The First 100 Fibonacci and Lucas Numbers	p. 139
Relationships Involving the Golden Ratio and Generalized Fibonacci Numbers	p. 143
References	p. 153
Index	p. 157
Table of Contents provided by Blackwell. All Rights Reserved.

Golden Ratio And Fibonacci Numbers, The

At a Glance

Hardcover

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How to return your order

Defective items

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