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

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© 2008 Michael S. Schneider