The Fibonacci Numbers form a sequence starting with 0 and 1, nothing and something. The rule is that each two numbers add to make the next, resulting in the famous Fibonacci Series:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...

Active involvement, not just reading, is the key phrase for this
highly illustrated book about the Fibonacci numbers and Golden
Mean. It's for teachers of children and adults who are looking
for hands-on activities to explore these fascinating topics. It
also has great value for artists, architects, craftspeople and
designers who wish to see how the Fibonacci numbers and Golden
Mean have been applied to art since pre-dynastic Egypt.

The main idea behind the Fibonacci numbers and Golden Mean, besides building on the recent past, is harmony. These numbers and shapes grow in patterns which also appear in the harmonious designs of nature and in the proportions of great art. The book's underlying theme is interconnected unity, wholeness, balance and stability during growth and change. The idea of harmony weaves through every page.

one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio.

The first we may compare to a measure of gold; the second we may name a precious jewel."

-- Johannes Kepler

This book will guide some people to become interested in "number theory", the wonderful connections 'behind' and among numbers. Artists, craftspeople, architects and designers will see how the Fibonacci numbers and Golden Mean have been applied by creative people across the centuries and cultures with most masterful excellence. Teachers will appreciate that the activities are clearly described and thoroughly illustrated.

This book has four parts:

* **The Fibonacci Numbers**, demonstrating the underlying principles
of this harmony through "Figurate" arithmetic, representing
numbers as piles of beans.

* **Fibonacci Numbers In Nature**, showing where, how and why
these principles are expressed in living growth, with plenty of
activities suggested.

* **Geometry of the Golden Mean**, teaching geometric skills
for exploring patterns in nature and art. Get your compass!

* **The Golden Mean In Art**, seeing how the Golden Mean was
applied to art, and with many hands-on examples to explore.

164 pages

**Table Of Contents**

**Introduction** 6

**The Fibonacci Numbers** 7

Weaving Fibonacci Number Patterns 10

Dividing Fibonacci Numbers 13

Adding Consecutive Fibonacci Numbers 14

Adding Every Other Fibonacci Number (Odd Subscripts) 15

Adding Every Other Fibonacci Number (Even Subscripts) 16

Adding Fibonacci Number Squares 17

A Fibonacci Rhythm 18

The Math Behind The Checkerboard Puzzle 18

Fibonacci Rectangles And Squares 21

Subtracting From Fibonacci Rectangles 22

Creating Fibonacci Rectangles 23

Creating Fibonacci Squares 24

Square Fibonacci Symmetry 25

Triple Fibonacci Numbers 26

Ten Fibonacci Piles Will Split Into Eleven Equal Parts 27

Adding Fibonacci Squares Makes Fibonacci Rectangles 28

Fibonacci Numbers In Three Dimensions 29

**Fibonacci Numbers In Nature** 30

The Whirlpool Structure 32

Draw The Spirals 33

Fibonacci Spiral Flower Software 35

Painting Pine Cones 36

A Spiraling Leaf 38

Painting Cauliflowers 39

Fibonacci Potatoes 40

Pineapple Patterns 41

Pineapple Stars 42

Weave a Pineapple Basket 43

Fibonacci Branching 44

A Spiraling Plant Model 46

Pentagonal Growth Pattern 48

Fibonacci Numbers In The Solar System 50

Audible Fibonacci Rhythms 51

Fibonacci Numbers In The Stock Market 52

Fibonacci Patterns In Art 53

Phi -- The Golden Mean 55

Phi Body Balance 59

**The Geometry Of The Golden Mean**
64

Divide A Line At The Golden Mean 65

Byrne's Euclid 66

Finding The Golden Mean In Double-Squares 68

Phi In The Vesica Piscis 69

Phi In A Triangle 70

Phi In The Pentagon 71

Unfurling Powers Of Phi 72

Whirling Golden Triangles 73

Flowing Vines 75

The Golden Rectangle 76

The "Most Pleasing Rectangle" Survey 77

A Three-Dimensional Golden Frame 78

Visual Points Of Interest 79

Whirling Squares 80

Another Turn At The Golden Spiral 81

Balance Of The Golden Spiral 82

Enlarging A Golden Rectangle 83

Rabatment 84

Subdivide A Square 87

The Root-Five Rectangle 92

Phi Rectangles and the Pentagram 97

Build Golden Mean Calipers 98

Golden Mean Calipers And The Human Body 99

**The Golden Mean In Art **101 (The
Golden Mean of this book)

Gebel el-Arak Knife 105

Dual Aker Lions 106

Tutankhamun's Ring With Solar Barque 106

Tutankhamun's Ushabti Box 106

Stela of Bai (Hearing Ear Stela) 107

Mortuary Temple of Neb-Hepet-Ra Mentuhotep (Mentuhotep II) 108

Lintel of Sesostris III 109

Household Stele of Akhenaton and Family 110

Eyes Painted On A Sarcophagus 111

Stela of Ahmose 112

Tutankhamen's Alabaster Boat 113

Stela of Djed-Amon-Iu-Ankh 114

Karnak Temple Floorplan 115

Stela of King Djet 116

The Great Pyramid and Squared Circle 118

“Ebony Fan” of Tutankhamen 120

Tablet of Shamash 121

Meditation And Serpent 122

Narada's Great Ancient Tale 122

Ragmala Paintings 123

The Forbidden City 124

Bonsai Trees 125

The Parthenon 126

Greek Pottery 128

European Painting 135

Jason and the Quest for the Golden Fleece 135

The Ascension 135

Très Belles Heures of the Duc the Berry 136

The Baptism Of Jesus 137

The Virgin of the Rocks 138

The Haywain (Hay Cart) 139

The Birth Of Venus 140

Saint Gregory the Great 141

The Seventh Trumpet 142

Alexander being lowered from a ship in a glass barrel to view
the wonders of the sea 142

Lindisfarne Gospels 143

The Annunciation 144

Philosophy Consoling Boethius and Fortune Turning the Wheel 145

Man: Body and Soul 145

Trinity 146

Fall of the Rebel Angels 146

Abbot Vivian and the Monks of Tours Present the Bible to Charles
the Bald 147

Philosophy Instructing Boethius On The Role of God 147

Saint Foy Abbey-Church 148

Ka'aba Door 149

Salaman and Absal on the Heavenly Isle 150

Woman 151

Harmony in Red/La desserte 151

The Comtesse d'Haussonville 152

Anne In White 152

Guernica 153

Herter Brothers Furniture 154

Everyday Household Objects 156

Modern Soup Ladle 156

Eames Chair 156

Classic Coffee Pot 156

Desktop Radio 157

Early Transistor Radio 157

Credit Cards 158

Candy Wrappers 158

**Appendix**

Hambidge's Phi-related rectangles 159

**Web Pages and Books** 163

Overall description of the Activity Books

© 2008 Michael S. Schneider