**Dynamic Rectangles**, also called Root Rectangles, are
the series of rectangles which grow from the diagonal of a square.
They're harmoniously linked to each other and can have a powerful
effect on viewers. That's why they're specifically chosen as the
shape for many designs. You'll be surprised at the many places
these particular rectangles appear around us from diplomas, writing
paper and household objects to worldwide sacred art, crafts and
architecture from the many cultures who discovered their remarkable
properties. This highly illustrated book is its own geometry course
and will teach you about the fascinating geometry of these rectangles
through *hands-on activities* with a compass and straightedge.
After learning the simple geometry, you're invited to do constructions
on images of art and objects which use these proportions and discover
for yourself how they were intelligently designed. If you're an
artist, architect or designer, this information can be quite valuable.
Learn from the masters how they used these remarkable rectangles
to create the most beautiful and compelling works. You're probably
familiar with many of them without knowing the secrets of their
proportions.

*Dynamic Rectangles*

141 pages

**Table Of Contents**

**Introduction**
6

**The Mathematics of Root Rectangles** 8

A Square Foundation 8

Construct a Square 10

The Square’s Diagonal 11

Find The Missing Sides 12

The Scarecrow’s Misstatement 13

The Square Root 14

Spiral Of Doubling Areas 15

The Expansive Power Of The Diagonal 16

Construct a Root Two Rectangle 16

The Root Rectangle Ruler 17

Construct a Root Rectangle Ruler 17

Calculate Square Roots 18

Multiples Of Root Rectangles 19

A Sequence of Squares 20

Root Rectangle Ripples 21

Draw a Root Rectangle Platform 22

Square Roots In Three Dimensions 23

A Spiral Of Square Roots 24

Explore The Root Ruler’s Extensions 25

Root Rectangle Extension Patterns 26

Constructing Root Rectangles Within a Square 27

Construct A Root Ruler Within A Square 28

Relative Areas In A Root Rectangle 29

Divide Any Rectangle Into Equal Parts 30

Serlio’s Door 32

Divide Root Rectangles Into Equal Parts 33

Spirals Within Root Rectangles 35

Root Rectangle Rabatment 39

Rabat Squares In Root Rectangles 40

Hotspots: Points, Lines and Areas Of Visual Interest 41

Locate More Visual Points Of Interest 43

**Root Two Rectangles**
45

The International Paper Standard 46

Divide A Root Two Rectangle In Half 47

Another Way To Halve A Root Two Rectangle 48

Subdivide A Root Two Rectangle By Rabatment 49

Another Way To Subdivide The Root Two Rectangle 50

Replicate These Subdivisions of the Root Two Rectangle 51

A Bouquet Of Harmonious Rectangles 52

Another Bouquet Of Harmonious Rectangles 53

Patterns With Circles 54

Division Into Only Root Two Rectangles 55

Replicate These Patterns 56

Construct Root Two Rectangles Within A Square 57

Root Two Rectangles In The Octagon 58

Construct Overlapping Root Two Rectangles 59

**Root Two Rectangle Art**
60

Offering Tablet 61

Box Lid From Tutankhamun’s Tomb 62

Tutankhamun’s Cartouche Jewelry Box 63

Tutankhamun’s Double-Cartouche Perfume Box 64

Baboons Adoring Sunrise 65

Metternich Magical Stela 66

The Pyramid Complex Of Userkaf 68

Menorah From The Jewish Temple In Jerusalem 69

A Greek Oinochoe 70

A Greek Kylix 71

A Red Figure Kylix 72

Shakyamuni Buddha Thangka 74

Temple of Venus At Baalbeck 75

Kiva at Kawaika-A 76

Omayyad Mosque of Damascus 77

Taj Majal And Garden 78

Fatehpuri Mosque Gate 79

The Funeral Of Isfandiyar 80

Coptic Christian Funerary Stela 81

The Divine Geometer 82

Christ With Apostles 84

Page From An Ethiopian Illuminated Gospel 86

The Birth Of Adam 88

Coronation Of The Virgin 89

Laurentian Medici Library Entrance 90

Laurentian Medici Library Floor Tile 91

Silver Wine Goblet 92

West Entrance To Chartres Cathedral 93

Cathedral Of Notre-Dame of Amiens 94

Ely Cathedral 97

The Old Basilica Of Saint Peter, Rome 98

St. Patrick’s Cathedral, New York City 99

Palladio’s Villa Foscari 100

The United States Capitol Building 101

Herter Brothers Cabinet 102

Slave Market With The Disappearing Bust Of Voltaire 103

Classic Wrist Watch 104

Entrance To City Hall (San Francisco) 105

Paper Money Geometry 106

**Root Three Rectangles**
107

Construct A Root Three Rectangle 108

Rabatment In A Root Three Rectangle 109

Construct A Root Three Rectangle In A Square 111

Rotating Root Three Rectangles 112

Root Three In The Triangle 113

Construct A Double Root Three Rectangle 114

Overlapping Hexagons 114

Subdivide Hexagrams For Root Three Rectangles 115

Overlap Root Three Rectangles 155

A Different Subdivision Of Hexagrams 116

Draw Diminishing Root Three Rectangles 117

Replicate These Root Three Rectangle Constructions 118

**Root Three Rectangle Art** 120

Pectoral Of Princess Mereret 121

Another Pectoral Of Mereret 122

Stela Of Amenhotep’s Purification 123

The Sphinx Dream Stela 124

Tutankhamun’s Scarab Pectoral 125

Stela Of Ha-hat 126

Chinese Imperial Throne 127

Mourning Athena 128

Greek Cup 129

Greek Skyphos 130

Greek Hydria 131

Arch Of Constantine 132

Mayan Stela of the Maize (Foliated) Cross 133

Polyptych Of Saint Anthony 134

Gunzo’s Dream 135

Gunzo Directing The Monks 136

The Throne Of Grace 137

Strasbourg Cathedral Altar 138

A Young Woman Standing At A Virginal 139

Ivory Comb From Sri Lanka 140

**Final Word** 141

**Bibliography**
141 (= 100 x Square Root of Two)

Click on any cover to see its Table of Contents:

Overall description of the Activity Books

© 2008 Michael S. Schneider