Previous Page Next Page

Notice:

This online book is not the current edition.
It was digitized from the 1987 hardcover edition and placed online in 1998.
There are two subsequent editions, in 1992 (paperback), and in 2007 (paperback and ebook).
The current edition is available from online booksellers (ISBN 978-0-6151-8314-5 published by EmergentWorld).

Amy C. Edmondson A Fuller Explanation



Contents

Chapters 1 through 8 [ Chapters 9 through 16 ]





Series Editor Foreward ........................................................ xv
Preface ....................................................................... xix
Acknowledgments ............................................................... xxi
Note to Readers ............................................................... xxiii
Introduction .................................................................. xxv
1.Return to Modelability ................................................... 1
From Geometry to Geodesics: A Personal Perspective ....... 3
Operational Mathematics ...................................................... 6
Experimental Evidence ........................................................ 7
Nature's Coordinate System ................................................... 9
Universe ..................................................................... 11
Generalized Principles ....................................................... 12
Return to Modelability ....................................................... 14
2.The Irrationality of Pi ................................................ 15
"Nature Isn't Using Pi" .......................................................... 16
Finite Acounting System .......................................................... 18
Which way is "Up"? ............................................................... 19
Visual Literacy .................................................................. 22
Peaceful Coexistence ............................................................. 23
3.Systems and Synergy ...................................................... 25
Conceptual and Real Systems ......................................................... 28
Limits of Resolution as Part of the Whole-System Approach ........ 30
Synergy ............................................................................. 33
4.Tools of the Trade ....................................................... 36
Plato's Discovery ................................................................... 37
Triangles ........................................................................... 38
Squares ............................................................................. 40
Pentagons ........................................................................... 41
A limited Family .................................................................... 41
Euler's Law ......................................................................... 43
Duality ............................................................................. 45
Truncation and Stellation ........................................................... 46
An Experiment ..................................................................... . 48
"Intertransformability" ............................................................. 51
Symmetry ............................................................................ 52
5.Structure and "Pattern Integrity" ......................................... 54
Pattern Integrity ................................................................ 56
Structure ........................................................................ 60
6.Angular Topology ................................................................. 65
Frequency and Size ...................................................................... 66
Units of Measurement ................................................................. 66
Time and Repetition: Frequency versus Continuum ............ 67
Topology and Vectors .................................................................... 68
Vector Polyhedra ..................................................................... 68
Dimension ............................................................................... 70
Size ................................................................................. 72
Planes of Symmetry ................................................................... 73
Other Applications of Dimension ................................. 74
Angular Topology ........................................................................ 75
Angular Takeout: An Example ................................... 78
Angle Types .......................................................................... 79
7.Vector Equilibrium ............................................................ 82
"Nature's Own Geometry" ............................................................ 84
Spatial Considerations ............................................................. 85
Planar Equilibrium ................................................................. 87
Cuboctahedron as Vector Equilibrium ................................ 90
VE: Results ........................................................................ 91
Degrees of Freedom ................................................................. 93
8.Tales Told by the Spheres: Closest Packing ............... 100
Equilibrium: Equalization of Distances ............................................. 100
Symmetry versus Specificity of Form ............................................. 101
Organization of Identical Units ................................................. 101
New Level of Focus .............................................................. 102
Background: Closepacking ........................................................ 102
Planes of Symmetry .............................................................. 106
Fuller Observations ............................................................. 109
Tetrahedra ...................................................................... 110
Vector Equilibrium .............................................................. 114
Frequency ....................................................................... 114
Icosahedron ..................................................................... 117
Further Discoveries: Nests ...................................................... 120
"Interprecessing .................................................................. 121
A Final Philosophical Note ........................................................ 125
Appendices .......................................... 271
A. Trigonometric Calculations .......................... 271
B. Volume Calculations for three Prime Sructural Systems 273
C. Sources of Additional Information ......... 277
D. Special Properties of the Tetrahedron ........................ 279
E. Glossary .............................................. 281

Bibliography ..................................... 287
Notes ....................................... 289
Index ....................................... A-H
Index ....................................... I-R
Index ....................................... S-T
Index ....................................... U-Z
Previous Page Next Page