of Nature and Art

118 pages

**Table Of Contents**

Introduction 1

**1 The Circle** 3

Turning Circles 3

Tip For Drawing Diameters 4

Connecting Two Points Accurately 5

A Curious Truth About Circles 7

Shapes And Areas 7

**2 The Almond** 8

Construct The Almond 8

Use The Almond To Divide Any Line Segment In Half 9

Replicate These Almond Constructions 10

Create Your Own Constructions In The Almond 13

Arithmetic, Geometry And Music 14

Music As Architecture 16

Design Your Own Musical Art, Crafts And Architecture 18

**3 The Triangle** 19

Finding Triangles 20

Constructing Triangles 21

Fold A Tetrahedron 22

TetraBubble 22

What Are Dimensions? 23

Fold An Octahedron 24

Octahedron-To-Cube Flip Movie 24+

Fold An Icosahedron 25

Subdivide A Triangle 26

Triangle Design In Nature And Art 27

Design Your Own Art 30

Construct A Triangle By "Walking Six-Around-One" 31

Subdivide A Triangle 32

Another Subdivision Of The Triangle 33

Another Way To Build The Space Enclosing Forms 34

Replicate These Constructions 35

The Mean Orbits of Planets 38

Create Your Own Patterns 39

Triangular Designs In Nature 40 -- [Microscopic Radiolaria, Flowers
and Fruits, Beetle, Moth, Bee's Face]

Triangles In Arts, Crafts And Architecture 43 -- [Horus Hawk Gold
Pectoral of Tutankhamen, Classic design from Thailand, Cathedral
design by Caesarino, "Seven Gifts Of The Holy Spirit"
Church Window]

Design Your Own Art, Crafts And Architecture 45

**4 The Square** 46

English words about Squares and Fours 46

Constructing A Square Around A Circle 47

Construct A Square Upon A Line Segment 49

A Curious Truth About The Square 51

Subdivide A Square 52

Subdivide Square Designs In Nature 53 -- [Microscopic Radiolarian
Skeletons, Jellyfish, Molecule]

Design Your Own Natural Form 54

Subdivide Square Designs In Art 55 -- [Chinese Plates, Celtic
Brooch, Classic Design from Thailand, Jewish Plate, Greek painting
in a kylix bowl, Navajo Sand Painting, Byzantine Dome Ceiling,
Italian Villa Floor Plan by Palladio]

Design Your Own Square Art 58

Replicate These Constructions 59

The Orbits Of Mars, Jupiter And Saturn 62

Rearrange A Square Into A Triangle 64

Construct And Fold A Cube 65

Build A Cube With Circles 66

Make Soap Bubble Cubes 66

**5 The Pentagon** 67

Tie A Penta Knot 68

Construct A Pentagon In A Circle 69

Construct A Pentagon In A Square 71

Another Pentagon Construction In A Square 73

Construct A Pentagon On A Line Segment 75

Construct Durer's Pentagon 77

Married Pentagons 79

Expanding A Pentagon 81

How To Find The Center Of A Pentagon 83

Subdivide A Pentagram Star 83

Subdivide A Pentagon Into Smaller Pentagram Stars 84

Replicate These Pentagonal Patterns 87

Create Your Own Pentagonal Design 89

Construct A Dodecahedron With Twelve Pentagons 90

Construct A Dodecahedron With Two Pentagons 91

Construct A Dodecahedron With Twelve Circles 92

Draw A Dodecahedron 93

A Pentagram Dissection 94

A Five Piece Pentagon Puzzle 95

Pentagonal Forms Of Nature 96 -- [Ivy Leaf, Columbine Flower,
Apple Slice, Starfishes, Starfish Mouth, Sea Cucumber, Coral,
Tiger Face]

A Pentagonal Bird Pattern 100

Pentagonal Proportions Of The Human Body 102

Pentagon Design In Arts, Crafts And Architecture 104 -- [Gold
Mask of Pharaoh Tut-Ankh-Amen, *The Alba Madonna* by Raphael,
Greek Amphitheater Plan, Greek Traveler's Water Canteen, Greek
Corinthian Capital, Chartres Cathedral Sculpture, Stradivarius
Violin, State Seal of Texas]

Design Your Own Pentagonal Art 110

Click on any cover to see its Table of Contents:

Click here to see an overall description of the Activity Books series

© 2008 Michael S. Schneider