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A Fuller Explanation
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Contents
Foreword
Foreword to the 1992 edition
Foreword (1992)
Preface
Preface to the 1992 edition
Preface (1992)
Acknowledgements
Note to Readers
Introduction
1 Return to Modelability
2 The Irrationality of Pi
"Nature Isn't Using Pi"
Finite accounting system
Which Way Is "Up"?
Visual Literacy
Peaceful Coexistence
3 Systems and Synergy
Conceptual and Real Systems
Limits of Resolution as Part of the Whole-Systems Approach
4 Tools of the Trade
4.1 Plato Presents
4.1.1 Triangles
Squares
Pentagons
A Limited Family
4.1.2 Euler's Law
4.1.3 Duality
4.1.4 Truncation and Stellation
4.1.5 "Intertransformability"
4.1.6 Symmetry
5 Structure and "Pattern integrity"
5.0.1 Pattern integrity
5.0.2 Structure
6 Angular Topology
6.0.1 Frequency and Size
Units of Measurement
Time and Repetition: Frequency versus Continuum
6.0.2 Topology and Vectors
Vector Polyhedra
6.0.3 Dimension
Size
Planes of Symmetry
Other Applications of Dimension
6.0.4 Angular topology
Angular Takeout: An Example
Angle Types
7 Vector Equilibrium
"Nature's Own Geometry"
Spatial Considerations
Planar Equilibrium
Cuboctahedron as _________________________Vector Equilibrium
VE: Results
7.0.1 Degrees of freedom
8 Tales Told by the Spheres: Closest Packing
Equilibrium: Equalization of Distances
Symmetry versus Specificity of Form
Organization of Identical Units
New Level of Focus
8.0.1 Background: Closepacking
Planes of Symmetry
8.0.2 Fuller Observations
Tetrahedra
A Final Philosophical Note
9 Isotropic Vector Matrix
A Quick Comparison: "Synergetics Accounting"
Cells: "Inherent Complementarity"
9.0.1 A Complete Picture
Angles
Locating New Polyhedral Systems
9.0.2 Duality and the IVM
Angles
Polyhedra
Domain
9.0.3 Framework of Possibility
Invention: Octet Truss
10 Multiplication by Division: In Search of Cosmic Hierarchy
10.0.1 Volume
Shape Comparisons: Qualities of Space
10.0.2 Multiplication by Division
Tetrahedron as Starting Point
Rhombic Dodecahedron
Multiplication by Division
10.0.3 Cosmic Hierarchy (of Nuclear Event Patternings)
11 Jitterbug
11.0.1 Folding a Polyhedron
Volume and Phase Changes
11.0.2 Other Dynamic Models
12 "All-Space" Filling: New Types of Packing Crates
12.0.1 Plane Tessellations
Two to One: A Review
13 The Heart of the Matter: A- and B-Quanta Modules
Energy Characteristics
Mirrors
Cubes into _______Mites
Rhombic Dodecahedra
Volume and Energy
13.0.1 Review: All-Space Fillers
14 Cosmic Railroad Tracks: Great Circles
Why Are We Talking About Spheres?
New Classification System
14.0.1 Great-Circle Patterns
Least Common Denominator
LCD: "Intertransformability"
LCD of 31 Great Circles
VE's 25 Great Circles
14.0.2 Operational Mathematics
Conservation of Angle
Foldable Systems
14.0.3 Energy Paths
Gas Molecules
Great-Circle Railroad Tracks of Energy
Icosahedron as Local Shunting Circuit
14.0.4 Inventory: Seven Unique Cosmic Axes of Symmetry
Excess of One
15 From Geodesic to Tensegrity: The Invisible Made Visible
Theory Behind Geodesic Structures: Summary
Geodesic Design in Nature
Geodesic Domes: Design Variables
15.0.1 Tensegrity
Nature's Example
Modeling the Invisible
Tensegrity Polyhedra
Pneumatics
Case in Point: Donald Ingber
16 "Design Science"
"Comprehensive Anticipatory Design Science"
"Comprehensive…"
"…Anticipatory…"
Dymaxion Map 52
Appendixes
16.1 Appendix A: Trigonometric Calculations
16.2 Appendix B: Volume Calculations for Three Prime Structural Systems
16.3 Appendix C: Special Properties of the Tetrahedron
16.4 Appendix D: Lists of Illustrations, Photos, Tables
Glossary
Bibliography of works cited
Other resources
Index of Synergetics-1 and -2 sections cited
Index
About the author
List of Figures
List of Tables
Bibliography
List of Figures
1
List of Figures
2
Document
3
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