Fibonacci Quarterly | Books & Tables
Fibonacci Association

A Primer for the Fibonacci Numbers

Edited by Marjorie Bicknell and Verner E. Hoggatt, Jr.

Published 1973 by the Fibonacci Association

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CONTENTS

Title Page

Preface
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Table of Contents
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Brother Alfred Brousseau
Exploring Fibonacci Numbers
1
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S. L. Basin
The Fibonacci Sequence as It Appears in Nature
6
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Sister Mary de Sales McNabb
Phyllotaxis
9
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S. L. Basin and Verner E. Hoggatt, Jr.
Simple Properties of the Fibonacci Sequence and Mathematical Induction
13
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S. L. Basin and Verner E. Hoggatt, Jr.
A Matrix Which Generates Fibonacci Identities
18
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Marjorie Bicknell and Verner E. Hoggatt, Jr.
Fibonacci Matrices and Lambda Functions
23
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Verner E. Hoggatt, Jr. and I. D. Ruggles
More Fibonacci Identities From Matrices and Vectors
27
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Verner E. Hoggatt, Jr. and Marjorie Bicknell
Some New Fibonacci Identities
31
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Verner E. Hoggatt, Jr.
Fibonacci Numbers and Generalized Binomial Coefficients
34
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Verner E. Hoggatt, Jr. and I. D. Ruggles
Fibonacci and Lucas Vectors
39
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Verner E. Hoggatt, Jr. and I. D. Ruggles
Infinite Series and Fibonacci Arctangents
46
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Verner E. Hoggatt, Jr.
Generating Functions for the Fibonacci Sequences
52
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Allan Scott
Scott's Fibonacci Scrapbook
65
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A. P. Hillman and G. L. Alexanderson
A Motivation for Continued Fractions
66
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Dmitri Thoro
The Golden Ratio: Computational Considerations
70
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Marjorie Bicknell and Verner E. Hoggatt, Jr.
Golden Triangles, Rectangles, and Cuboids
74
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Marjorie Bicknell
Introduction to Fibonacci Polynomials and Their Divisibility Properties
86
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Marjorie Bicknell
Sequences of Sums from Pascal's Triangle
98
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Marjorie Bicknell
The Fibonacci Convolution Triangle, Pascal's Triangle, and Some Interesting Determinants
104
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Marjorie Bicknell and Verner E. Hoggatt, Jr.
To Prove: Fn Divides Fnk
111
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Brother Alfred Brousseau
On the Representation of Integers
118
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V. E. Hoggatt, Jr., Nannette Cox, and Marjorei Bicknell
On Representations of Integers Using Fibonacci Numbers
127
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Brother Alfred Brousseau
Fibonacci Numbers and Geometry
146
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V. E. Hoggatt, Jr. adn Janet Crump Anaya
Multisection Generating Functions for the Columns of Pascal's Triangle
159
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Solutions to Problems 166
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