Everything we know about geometry, mathematics, and the organization of matter has, up to now, been demonstrated by cutting into the wholeness of the sphere. By cutting the sphere we have pieces, parts, and fragments; it is no longer Whole. By compressing a sphere to a flat plane nothing is lost, all spatial information is compressed into a flat circle disc that remains Whole. Folding circles decompresses spherical information. All 2-D information is in the creases, 3-D information is replicated in the spatial reconfigurations, while mathematical functions are expressed in the movement of the circle. Generating this information is not possible by drawing circles, only by folding, reforming, and joining circles. Folding circles can generate traditional polygons, polyhedra, and many other beautiful and complex systems that not possible by using any other methods of modeling. Series Book 3 is an expansion of material introduced in both Series Books 1 & 2, bringing together the full octave of possibilities in the 8-frequency diameter grid of the circle. Published in 2006 by Wholemovement Publications. 64 pp. Spiralbound. ISBN 978-0-9766773-4-5 (0-9766773-4-2)
Table of Contents
6 PRINCIPLES
7 CIRCLE UNITY
8 Tips for folding circles
9 Start folding
10 Three diameters
11 Six diameters
12 4-Frequency diameter grid folding
13 8-Frequency diameter grid folding
14 Fractal nature of folded grid
15 Three/Six Symmetry
The tetrahedron
16 Truncated tetrahedron
17 Hexagon development
18 Square opening
22 Variations of hexagon folding
Folding inscribed hexagon
23 Tetrahedron variations
26 Benzene ring
29 Off-center hexagon
30 Five/Ten Symmetry
The pentagon
33 Folded variations
37 Four/Eight Symmetry
The square
39 Off-center square
43 Tubes, helixes, and cones
45 Parallel accordion folding
47 Rotational accordion folding
49 Hexagon Variation
50 Half circle accordion folding
51 Column development
53 Rhombicosidodecahedron
55 Bisecting Creases
Adding 9 more Creases
56 Adding 6 Creases
59 Variations on 6 Creases
63 Front Cover
64 Statement