Index
2- emended for this edition by J. Hausman
3 Bold –definition or section header.
Italic –illustration, photo, or table.
Bold + Italic –term in Glossary (p. 302).
4 6
6 A
7 A-module 2, 178, 203, 213, 221, 227, 228, 302
8 A-module
9 defining new framework 205, 216
10 energy characteristics 205, 211
11 net 207, 208
12 volume 215
13 Alloys 5, 36, 261, 284
14 Alloys
15 chrome-nickel-steel 37
16 Angle types, definition of
17 axial, central, dihedral, surface 87
18 Angular topology 71, 302
19 Angular topology
20 720° excess 84
21 principle of 82
22 takeout 82, 280, 293
23 Architecture 20, 88, 149, 253, 258, 259
24 housing 277
25 Avogadro, Amadeo 134, 135, 152
26 B
27 B-module 2, 178, 204, 302
28 B-module
29 energy characteristics 205, 215
30 Bamboo 256
31 Bicycle wheel 102, 103, 264, 283
32 Black Mountain College 266
33 Bohr, Niels
34 complementarity principle (1928) 191
35 Boltzmann, Ludwig 92
36 Bookshelf 2
37 Bowties 2
38 Brain-Mind distinction 14, 275, 284
39 Brooklyn Bridge (1883) 261
40 Buckminster Fuller Institute (BFI) xxii, 270, 281, 309
41 C
42 C60 carbon molecule xx
43 Carbon atoms
44 carbon fiber 261
45 diamond vs graphite 31, 150
46 general bonding of 185
47 Cell
48 as topological element 48, 135, 144, 148, 150, 160, 164, 182, 192, 196, 198, 199
49 Chinese physicists, Tsung-Dao Lee and Ning Yang 191
50 Chord 19
51 chord factors 85
52 chordal and radial equivalence in VE 180
53 chordal forces 96
54 chordal rates of convergence and divergence 180
55 great-circle arcs 220
56 great-circle chords 256, 257, 271
57 Closepacked spheres, sphere packing 2, 10, 20, 108, 111, 135, 140, 141, 147, 164, 187, 189, 194, 202, 214
58 Closepacked spheres, sphere packing
59 cubic vs hexagonal 112, 113, 114
60 formula for total numbers of spheres 123, 125, 126
61 icosahedron and sphere packing 2, 125, 127, 170
62 mathematical challenge 110, 116
63 nests 111, 119, 128, 130
64 planes of symmetry 114
65 tetrahedral clusters 116, 118, 128
66 vector equilibrium and sphere packing 109, 122
67 Complementarity 140, 168, 190, 191, 302
68 Complementarity
69 complementary quanta
70 A- and B-modules 205, 208
71 concave-convex, tension-compression, and other pairs 32, 143, 191, 259
72 fundamental complementarity in physics 190, 205
73 inherent complementarity of Universe 141, 168, 189, 190
74 of octahedron and tetrahedron 140, 149, 191
75 Compression 2
76 Consciousness
77 defined by Fuller 12, 13
78 Constant relative abundance 2
79 2 faces, 3 edges per vertex (less poles) in triangulated polyhedra 49
80 faces=2 times number of vertices minus 2 in triangulated systems 48
81 of 'dimensions' (topological elements) 81
82 Cookies 93, 138
83 Coordinate system 71, 104, 218, 254
84 Coordinate system
85 Cartesian 77, 78, 79, 95, 139, 145, 149, 164, 168, 222, 225
86 origin 36, 71, 149
87 origins, historical 15
88 spherical 78
89 Copernicus 77
90 Cosmic hierarchy 10, 152, 167, 175, 176, 177, 229, 293
91 Cosmic Railroad Tracks 2
92 Coupler 2, 213, 214, 215, 302
93 Cube 2, 43, 44, 45, 47, 50, 224
94 Cube
95 employment as basic unit of mathematics 8, 9, 15, 22, 23, 77, 80, 168, 190, 202
96 ghost 9, 75, 153
97 inherent tetrahedron in 50, 64, 65, 145, 146, 154, 190, 197
98 instability of 64, 65, 115, 133, 143, 145, 149, 154, 155, 190
99 tetrahedral volume of 162
100 used as unit of volume 153, 154, 162, 168
101 weightless 75
102 Cuboctahedron 2, 37, 53, 54, 55, 56, 97, 99
103 Cuboctahedron
104 duality of 56
105 twist 97
106 D
107 Degrees of freedom 2, 101, 123, 241, 283, 302
108 Degrees of freedom
109 conventional treatment 103
110 freedom of motion in sphere packing 118
111 in space 102, 105
112 planar analogy 101
113 tetrahedron and 103
114 Democritus 63
115 Descartes, René 82
116 Design
117 defined 274
118 Design science 2, 14, xv, 127, 150, 151, 274, 281, 283
119 comprehensive thinking 275
120 design-science revolution 284
121 Design Science Collection xv, xvi
122 Dictionary as inventory of experiences 21
123 Dimension xvi, 44, 71, 76, 302
124 Dimension
125 as direction 81
126 definition of 76
127 four-dimensional 82, 100, 180, 181, 183
128 multi-dimensional 76, 136, 138
129 other applications of 81, 82
130 three-dimensional 81, 138
131 Dodecahedron 2
132 Dodecahedron, pentagonal 44, 45, 47, 49, 53, 180, 189, 192, 227, 230
133 Dodecahedron, pentagonal
134 symmetry of 54, 180, 229
135 Dodecahedron, rhombic 2
136 Domain 227
137 Domain
138 and closepacked spheres 147, 214
139 and duality 147, 194
140 defined 147
141 Duality 2, 53, 192, 224
142 dual operations 56, 148
143 dual polyhedra 49, 54, 180, 225
144 IVM and 144, 146, 148, 193
145 Dymaxion 37, 303
146 Dymaxion
147 Map 70, 279, 281
148 E
149 Eddington, Arthur 8, 36, 158
150 Edmondson, Amy C. 6, xvi, 267
151 Einstein 12, 72
152 Einstein
153 E= mc ² 14
154 Empire State Building 9
155 Energy-event
156 descriptive term to replace 'solid' 8, 9, 30, 207, 303
157 discrete energy events 2, 19, 20, 205, 235, 236, 242, 271
158 'energy-event Universe' 16, 55, 72, 235, 240, 242
159 Engineering 150, 183, 252, 269, 270
160 Entropy xiii, 92
161 Environment control 278
162 Equilibrium 2
163 Euler, Leonhard 46
164 Euler's Law 2, 46, 49, 74, 84, 124, 244, 245
165 Everything I Know video 9, 12, 13, 33, 34, 36, 74, 91, 150, 253, 307
166 Extinction 275
167 F
168 Finite accounting system 2, 20, 133, 178, 221, 303
169 Flat-Earth thinking 15, 21, 22, 77, 153, 169, 279
170 Food system 276, 277, 278, 311
171 Four planes of symmetry 100, 114, 138, 141, 149, 180
172 Frequency 120, 241, 303
173 Frequency
174 and size 72
175 and time 73
176 angle and 73, 78, 90, 98
177 defined 120
178 formula to relate frequency and number of spheres 134, 253
179 higher-frequency polyhedra 143, 157, 164, 196, 198, 249, 252, 254, 271
180 sphere-packing and 120, 123
181 vs continuum 73, 250
182 Fuller Institute 2
183 Fuller, R. Buckminster ('Bucky')
184 Anne Hewlett Fuller 1, xvi
185 Harvard University 10
186 Milton MA 2, xvi
187 United States Navy experience 18, 90, 275
188 'careers' as inventor, architect, engineer, philosopher 2
189 G
190 General Dynamics, titanium shell experiment 253
191 Generalized principle 2, 3, 14, 36, 38, 117, 254, 303, 304
192 design science as application of 14
193 eternal not special-case 275
194 exceptionless 14
195 God
196 as unknowable totality of 15
197 humanity's wealth 306
198 invention as novel application of 14, 254, 278
199 key to humanity's success 274
200 of 12 degrees of freedom 283
201 of 720° angular takeout 84
202 of duality 55
203 of formula of nuclear sphere packings 125
204 of icosahedron as best sphere approximation 279
205 of oct-tet space-filling ratio 192, 201
206 of synergy 15
207 of triangular-number formula 117
208 of varying rates of geometric expansion 278
209 omni-interaccommodative 15, 40, 305
210 principle of angular topology 2
211 synergetics as the search for 14
212 Universe as total web of all 15
213 Geodesics 2, 241, 245, 246, 250, 251
214 defined 246
215 Expo67 U.S. pavilion dome 1
216 four-frequency icosahedron 86, 251, 255
217 geodesic breakdowns 255
218 geodesic dome 2, 3, 6, 68, 70, 250, 252, 254, 270, 274, 278
219 geodesic dome and frequency 248
220 geodesic mathematics 4, 246
221 geodesic polyhedra 84, 242, 245, 250, 254, 271
222 great-circle chords 250, 256, 278
223 God, not 'the God' 12
224 as 'greater intellectual integrity of eternally regenerative universe' 63, 274, 304
225 as 'unknowable totality of generalized principles' 15
226 as non-anthropomorphic all-encompassing greater intelligence 274
227 Golden section 20, 178
228 Gravity
229 Fuller anecdotes 3, 263
230 mass interattraction 14, 36, 218, 259, 263, 283
231 Great circles 29, 219, 303
232 Great circles
233 bowties 232, 242, 244
234 cosmic railroad tracks 243, 245
235 definition of 219
236 Energy paths 240
237 great-circle arc 220, 235, 247
238 great-circle patterns 222
239 icosahedral 226, 238, 244, 248, 249, 271
240 minimum models 236
241 shortest path 219, 220, 240, 242, 246
242 icosahedron as local shunting circuit 243
243 Greece, ancient 2
244 geometry of 8, 18, 39, 40, 81, 190, 260
245 Greek, use in nomenclature 17, 28, 29, 30, 37, 42, 44
246 H
247 Hanging bookshelf 282
248 Harvard University 10, xvi, xxii, 40, 273
249 Harvard University
250 Sever Hall 4
251 Heisenberg, indeterminism 191
252 Hexahedron 2, 154, 156
253 I
254 Icosahedron 2, 29, 42, 43, 47, 53
255 and geodesics 250
256 jitterbug and 172, 174
257 net 83
258 structural system 66
259 symmetry of 81, 127, 175, 176, 226, 247, 252, 253, 278, 279
260 volume of 174, 175
261 'dimpling' 68, 69, 303
262 'out-of-phase' role 175, 176, 178, 182, 189, 192, 229, 231
263 Icosidodecahedron 53, 54
264 Impossibles (unempirical constructs) 8
265 circle, perfect continuous 19
266 continuum 133
267 equilibrium, perfect static 173
268 line, imaginary infinite straight 5, 7, 8, 9, 17, 91
269 plane, continuous infinite 9, 75
270 point, sizeless 9, 75
271 solid-things thinking 8, 66, 196, 260, 263, 265, 283
272 solid, continuous-surface 8, 12, 18, 30, 133, 183
273 sphere, continuous-surface 19, 86, 108, 250, 252
274 surface, zero-thickness 25
275 vs 'demonstrables' 8, 9, 18, 20, 25, 72, 75, 109, 188
276 'oneness' 33
277 In-Out vs Up-Down 12
278 Infinity 2, 25
279 and irrational numbers 18
280 circle as many-sided polygon 19
281 sphere as multifaceted polyhedron 19
282 vertices on sphere surface 86
283 Ingber, Donald 5, 272
284 Interprecessing 2, 130, 131, 132
285 Intertransformabilities 50, 54, 55, 149, 152, 167, 202, 205, 217, 222, 223, 228, 231, 304
286 Invention 2, 3, 15, xxi, 25, 26, 70, 149, 254, 258, 274
287 defined 14, 254
288 gestation rates 277
289 Invisibles
290 invisible reality 3, 14, 15, 37, 174, 183, 261, 263, 265, 271, 284
291 invisible Universe 173, 265
292 Isotropic vector matrix (IVM) 2, 12, 135, 170, 175, 202, 205, 208, 304
293 Isotropic vector matrix (IVM)
294 alternating octahedra and tetrahedra 135, 136, 145, 202
295 cube and IVM 145, 147, 148
296 equilibrium 138
297 frame of reference 148, 152, 153, 155, 164, 167, 175, 176, 178, 183, 187, 192, 193, 195, 197, 201, 217, 231, 243
298 IVM' 148, 152, 160, 164, 192
299 omnisymmetry 137, 138, 145, 150, 175, 176, 195, 202
300 omnitriangulation 141
301 square cross-section of IVM 141
302 VE and IVM 2
303 IVM 2
304 J
305 Jitterbug
306 complex of jitterbugs 181, 182
307 flexible VE model 170, 180
308 transformation 171, 180, 182, 183, 184, 226, 231, 304
309 K
310 Kenner, Hugh 75
311 kissing point 214
312 Klug, Aaron 253
313 L
314 Least common denominator (LCD) 208, 209, 212, 227, 239, 248, 257
315 Lesser circle 219
316 Tropic of Cancer 219
317 Leverage 14, 15, 61
318 Life 2
319 Life-support advantage 26, 284
320 Line 2
321 chord 279
322 chord as 252
323 Euclidean 220
324 vector as replacement for 9, 41, 74
325 Local holding patterns 236, 242
326 Loeb, Arthur L. 2, 4, 6, 11, xvii, xviii, xxi, xxii, 40, 48, 49, 50, 51, 52, 53, 55, 56, 65, 105, 152, 157, 164, 165, 197, 210, 302
327 M
328 MacCready, Paul
329 Gossamer Albatross 261
330 Malthus, Thomas, Malthusian thinking 5, 284
331 Massachusetts Institute of Technology (MIT) 5, 6, 64, 71
332 Mathematics
333 defined as science of structure and pattern 64, 71, 75
334 Mercator projection 279, 280
335 Metaphysical phenomena
336 mind, life, thought, equilibrium, generalized principles, pattern integrities 4, 8, 13, 26, 35, 63, 89, 106, 107, 205, 304
337 Mite 209, 210, 212, 213, 215, 304
338 Mite
339 cubes and 211, 213
340 mirror symmetry of 211, 215
341 rearrangement of 215, 216
342 rhombic dodecahedron and 212, 213
343 More with less (ephemeralization) 261, 284, 285, 303
344 Mozart 63
345 Multiplication by division 152, 158, 168, 174, 189, 205, 225
346 N
347 Natural is what nature permits 11
348 Nature's coordinate system 3, 4, 10, 11, 12, 18, 19, 26, 37, 74, 91, 110, 206, 304
349 Navy 2
350 Nests 2, 304
351 Net, polyhedral 83, 86, 206, 304
352 Neutral axis 261
353 Nuclear spheres 2, 109, 112, 119, 214, 215
354 Nuclear spheres
355 defined 119
356 removal of 170, 175
357 tetrahedron and nuclei 121, 129
358 VE and nuclei 170
359 O
360 Octahedron 2, 41, 42, 45, 47, 80, 148
361 closepacked spheres and 114, 115
362 jitterbug and 172
363 octahedral cavities 99, 137, 141, 165, 181, 190, 196
364 octahedral core 159, 176
365 structural system 145
366 symmetry of 80, 222
367 truncated 2
368 Octant 145, 160, 161, 162, 163, 204, 213
369 Octet symmetry 2
370 Octet Truss 3, 68, 70, 137, 149, 150, 190, 211
371 Operational mathematics 7, 8, 26, 32, 33, 152, 154, 155, 232, 250
372 Operational mathematics
373 operational procedure 10, 11, 20, 158, 187, 191, 206
374 P
375 Patents 2
376 Pattern integrity 59, 61, 104, 305
377 Pattern integrity
378 knot 62, 63
379 life 10, 63
380 wave 62, 63, 183
381 Pentagonal dodecahedron 2
382 Phase changes 2
383 Philosophy (of Buckminster Fuller) 2, 6, 10, 25, 34, 35, 105, 276, 277, 284
384 Philosophy (of Buckminster Fuller)
385 philosophy 274
386 philosophy and geometry 35, 133, 168, 266
387 Planes of symmetry 114
388 Platonic polyhedra 2
389 Poles of spinnability 47, 49, 124, 221
390 Polyhedra 2
391 geodesic (triangulated) 31, 266, 294
392 irregular 67, 84, 85, 131, 266
393 regular 31, 45, 46, 57, 97, 141, 220, 266, 294, 305
394 regular-Platonic 'solids' 37, 40, 49, 51, 268, 269
395 semiregular 31, 54, 56, 57, 97, 141, 195, 200, 220, 266, 294
396 Precession 2, 59, 130, 183, 305
397 Principle of angular topology 2
398 Q
399 Quantum 2, 31, 133, 305
400 Quantum
401 discrete quanta 153, 218, 252
402 edges (six) as one 31, 68, 84, 133
403 physics 190
404 units 178
405 R
406 Regular polyhedra 2
407 Rhombic dodecahedron 2, 31, 54, 55, 56, 146, 147, 154, 163, 164, 179, 231
408 duality of 193
409 icosahedron and 146, 179, 180
410 space-filling property 193, 194, 195, 197
411 space-filling property 195
412 spheric 147, 148, 195, 212, 213, 217, 305
413 volume 163
414 Rhombic triacontahedron 28, 230, 239
415 Rhombicuboctahedron 165
416 Rhombohedron 143, 191, 197
417 S
418 S-module 178, 179, 231
419 Sadao, Shoji 268, 279
420 Saint Peter's Cathedral Dome 258, 260
421 Schlaefli's formula 48
422 Science
423 definition of 8, 36, 158
424 Science of spatial complexity 2
425 Shell, or single-layer, systems 2, 65, 126, 175, 216, 241, 252, 253
426 Sixness
427 cosmic 238
428 six positive-negative linear directions 100, 123, 283
429 Slenderness ratio 260
430 Snelson, Kenneth 266
431 Sodium chloride 36
432 Solar system as tensegrity 263
433 Solids 2
434 geometric 2, 8, 19, 37, 164
435 phase changes in chemistry 174, 184, 185
436 Solway, Carl
437 Carl Solway Gallery 182
438 Southeast Asian basketry 247
439 Space
440 science of spatial complexity 4, 10, 15, 25, 283, 285
441 self-organization/order inherent in space 10, 11, 25, 30, 64, 91, 93, 101, 114, 127, 163, 168, 179, 187, 201, 244
442 shape of space (space has shape) 11, 12, 39, 74, 75, 77, 100, 109, 110, 114, 116, 123, 137, 138, 152, 154, 155, 187, 190, 253
443 spatial constraints 10, 11, 39, 44, 45, 63, 75, 77, 91, 109, 116, 127, 128, 140, 141, 189, 222, 253, 256, 271, 273
444 Space Structures 11, 51
445 Space-filling 2
446 all-space filling 187, 195, 209, 213
447 complementarity 2, 181
448 complex 185, 187, 209, 243
449 cubes 192
450 domain of sphere 147
451 filling space with closepacked spheres 116, 242
452 formula for space filling 192, 197
453 IVM and 2, 148, 149, 192, 202
454 octet symmetry 190, 212, 217
455 rhombohedron 143, 191
456 space fillers 187, 189, 197, 200, 209, 213, 215, 217
457 space fillers, other 191
458 teams 192
459 truncated octahedron 2, 195, 217
460 Spaceship Earth 6, 22, 66, 274, 276, 277, 305
461 Special case 72, 275, 305
462 Special case
463 special case system 167
464 special-case experience 14, 31
465 Sphere 2
466 defined 108
467 frame of reference for polyhedral systems 221
468 omnisymmetrical form 122, 221, 242
469 surface area of 19, 236, 250, 278
470 Spheric 2
471 Spherical polyhedra 220, 221, 222, 223, 225, 227, 228, 234, 237, 247, 279
472 Spherical triangles 32, 223, 227, 229, 238, 240, 305
473 Spherical trigonometry 86, 257, 258
474 Spin/spinnability 2
475 Star tetrahedron 223, 238
476 Stellation
477 definition of 51
478 degenerate 55
479 degenerate stellation 52, 56, 145, 148, 193, 230
480 Straight line 2
481 Structural stability 2
482 necklace 59
483 prime structural systems 125
484 stability and jitterbug 170
485 stability formula 65
486 triangulation 64, 127, 149, 202, 240, 247, 249, 250, 256, 272
487 Structure
488 definition of 66
489 Sunrise/Sunset
490 Sunsight/Sunclipse, suggested modern-era terms 22
491 persistent misnomers evidencing misperceptions 3, 5, 22
492 Symmetry 2
493 defined 57, 109, 202
494 mirror symmetry 57, 203
495 octet symmetry 216
496 omnisymmetry 2, 95, 96, 99, 122, 148, 149, 242
497 planar symmetry 92
498 polyhedra as symmetry patterns 75, 192
499 rotational symmetry 121, 176, 181, 189, 211, 221, 223
500 seven unique axes of symmetry 114, 226, 244
501 spatial symmetry 2
502 Synergetics accounting 139
503 cosmic accounting 205
504 Synergetics\
505 Explorations in the Geometry of Thinking 5, 6, xiii, xiv, xviii, xx, xxiii, 27, 32, 36, 53, 76, 79, 81, 103, 110, 119, 186, 195, 210, 220
506 Explorations in the Geometry of Thinking
507 topology combined with vectorial geometry 74
508 Loeb's 'Contribution to Synergetics' 40, 157, 168, 178, 180, 191, 192, 210
509 Synergetics2\
510 Further Explorations in the Geometry of Thinking xiii, xviii, xx, xxiii
511 Loeb's 'Addendum' 178
512 Synergy 15, 28, 36, 151, 306
513 Synergy
514 alloys 36
515 and synergetics, synergetic-energetic-geometry 37
516 defined 36
517 in tensegrity 269
518 System
519 definition of 28, 29, 46, 48, 306
520 T
521 Takeout 2
522 Technology
523 as pure principle in action 274
524 nature's self-organization as high technology 15
525 Tensegrity 4, xv, 258, 260, 263, 306
526 Tensegrity
527 interplay of tension and compression in Universe 258, 265, 271, 272
528 models 266
529 pneumatics 271, 272
530 tensile strength 37, 261, 268, 269
531 tension materials 106, 261, 263, 269, 282
532 use of tension in construction 263, 265
533 Tessellations 41, 188, 250
534 Tetrahedron 41, 42, 45, 47, 250
535 Tetrahedron
536 basic unit in Synergetics 31, 41, 156, 158, 159, 184
537 central angle of 145, 146
538 cheese 155
539 inside-out 173
540 isotropic vector matrix and 140
541 jitterbug and 173
542 minimum system of Universe 29, 30, 34, 35, 81, 104, 140, 149, 156, 168, 173, 203, 215, 236
543 perpendicular symmetry of 130, 164, 165
544 rigidity of 150
545 sphere-cluster tetrahedra 2
546 subdivision of tetrahedron 2, 159, 160, 163, 164, 202, 203
547 surface angles of 62, 84
548 tetrahedroning 23, 24, 199
549 truncation of 51, 143
550 unit of volume 153, 156, 162, 168, 174, 215
551 Tetrakaidecahedron (truncated octahedron) 52, 143, 195, 196
552 Three-way grid 2, 247, 256, 272
553 Titanium shell experiment 253
554 Triangles 2
555 equilateral triangles in vector equilibrium 98
556 similar 155, 157
557 stability of 2, 28, 61, 172, 258, 278
558 triangular numbers 117
559 'triangling' instead of squaring 22, 23, 24
560 Tropic of Cancer 2
561 Truncation 50, 196
562 Truncation
563 definition of 51
564 degenerate 55, 98, 165
565 isotropic vector matrix and 143, 148, 195
566 Truss 2
567 Tune-in-ability 33, 34, 35, 271, 306
568 Twelve degrees of freedom 2
569 U
570 Unempirical constructs 2
571 United States Patents
572 2,682,235 (1954) 258
573 4,377,114 (1983) 282
574 2,393,676 (1946) 281
575 Universe 2, 12, 306
576 Universe
577 as 'incredible technology' 274
578 defined by Fuller 13
579 differences in Universe as modulation of angle and frequency 73
580 product of interaction between principles and energy 14, 40, 66, 173, 274
581 'scenario Universe' 12, 13, 26, 36, 61, 149, 158
582 'single-frame' Universe 12, 13
583 'trans-Universe' vs 'locally operative' 175
584 V
585 Valency 51, 176, 183, 306
586 Valency
587 definition of 32
588 in duality 55, 147, 148
589 'quadrivalent' 173
590 Valving 206, 211, 306
591 Vector 2
592 and energy events 74, 91, 135, 306
593 and forces 94, 252
594 and interactions 90, 91, 93
595 as replacement for line 2
596 sphere packing and 2
597 topology and 74
598 Vector equilibrium (VE) 2, 306
599 Vector equilibrium (VE)
600 closepacked spheres and 108, 114, 175
601 conceptual vs actual equilibrium 174, 176
602 cuboctahedron as 97
603 equilibrium defined 89
604 equilibrium in nature 263
605 hexagons and equilibrium 95, 96, 97, 101, 108, 111, 112, 114, 180
606 hidden VE inside octahedron 165, 166
607 model of 94
608 space filling and 136, 139, 181, 192, 197
609 tetrahedron and 162
610 time and equilibrium 107
611 Video 2
612 Virus 10, 11, 127, 128, 175, 252, 253, 307, 308
613 Visual literacy 25
614 Volume ratios 152, 153, 158, 159, 167, 174
615 use of volume constant 156, 157
616 volume-to-surface-area ratio 67, 127, 128, 150, 278
617 W
618 Wealth 284, 306
619 Wealth
620 generalized principles as humanity's 14, 82
621 redefined 284
622 Whole numbers 166, 168, 306
623 Whole numbers
624 whole-number relationship 19, 20, 31, 153, 154, 162, 163, 174, 175, 293
625 Whole systems 32, 33, 36, 38, 39, 40, 110, 158, 159, 166, 169, 257, 263, 269, 273, 275, 276, 277, 279, 280, 282, 293, 305, 306
626 Y
627 Yale University 272
628 Yang, Chen Ning 191
629 Z
630 Zung, Thomas T.K. 268
631 -
632 -ness (conceptionings of space/systems) 2
633 90-degreeness 81
634 betweenness 29
635 fourness 55, 81
636 handedness 191
637 insideness/outsideness 29, 35, 104, 215, 293
638 oneness 33
639 somethingness of space 12
640 thingness 13
641 twelveness 241
642 '
643 'Dare to be naïve' 27, 39
644 'Fake bubbles' 17
645 'Hands-on' mathematics 3, 26, 119, 217
646 'Impossible' achievements
647 human flight 261
648 spans exceeding 150 ft. 259
649 'Unity is plural' 33, 168, 173, 191, 302, 303