Index
1- emended for this edition by J. Hausman
23Bold definition or section header.
Italic illustration, photo, or table.
Bold + Italic term in Glossary (p. 302).
4 6
5
7 A
89A-module 2, 178, 203, 213, 221, 227, 228, 302
1011A-module
1213defining new framework 205, 216
1415energy characteristics 205, 211
1617net 207, 208
1819volume 215
2021Alloys 5, 36, 261, 284
2223Alloys
2425chrome-nickel-steel 37
2627Angle types, definition of
2829axial, central, dihedral, surface 87
3031Angular topology 71, 302
3233Angular topology
3435720ř excess 84
3637principle of 82
3839takeout 82, 280, 293
4041Architecture 20, 88, 149, 253, 258, 259
4243housing 277
4445Avogadro, Amadeo 134, 135, 152
46 B
4748B-module 2, 178, 204, 302
4950B-module
5152energy characteristics 205, 215
5354Bamboo 256
5556Bicycle wheel 102, 103, 264, 283
5758Black Mountain College 266
5960Bohr, Niels
6162complementarity principle (1928) 191
6364Boltzmann, Ludwig 92
6566Bookshelf 2
6768Bowties 2
6970Brain-Mind distinction 14, 275, 284
7172Brooklyn Bridge (1883) 261
7374Buckminster Fuller Institute (BFI) xxii, 270, 281, 309
75 C
7677C60 carbon molecule xx
7879Carbon atoms
8081carbon fiber 261
8283diamond vs graphite 31, 150
8485general bonding of 185
8687Cell
8889as topological element 48, 135, 144, 148, 150, 160, 164, 182, 192, 196, 198, 199
9091Chinese physicists, Tsung-Dao Lee and Ning Yang 191
9293Chord 19
9495chord factors 85
9697chordal and radial equivalence in VE 180
9899chordal forces 96
100101chordal rates of convergence and divergence 180
102103great-circle arcs 220
104105great-circle chords 256, 257, 271
106107Closepacked spheres, sphere packing 2, 10, 20, 108, 111, 135, 140, 141, 147, 164, 187, 189, 194, 202, 214
108109Closepacked spheres, sphere packing
110111cubic vs hexagonal 112, 113, 114
112113formula for total numbers of spheres 123, 125, 126
114115icosahedron and sphere packing 2, 125, 127, 170
116117mathematical challenge 110, 116
118119nests 111, 119, 128, 130
120121planes of symmetry 114
122123tetrahedral clusters 116, 118, 128
124125vector equilibrium and sphere packing 109, 122
126127Complementarity 140, 168, 190, 191, 302
128129Complementarity
130131complementary quanta
132133A- and B-modules 205, 208
134135concave-convex, tension-compression, and other pairs 32, 143, 191, 259
136137fundamental complementarity in physics 190, 205
138139inherent complementarity of Universe 141, 168, 189, 190
140141of octahedron and tetrahedron 140, 149, 191
142143Compression 2
144145Consciousness
146147defined by Fuller 12, 13
148149Constant relative abundance 2
1501512 faces, 3 edges per vertex (less poles) in triangulated polyhedra 49
152153faces=2 times number of vertices minus 2 in triangulated systems 48
154155of ’dimensions’ (topological elements) 81
156157Cookies 93, 138
158159Coordinate system 71, 104, 218, 254
160161Coordinate system
162163Cartesian 77, 78, 79, 95, 139, 145, 149, 164, 168, 222, 225
164165origin 36, 71, 149
166167origins, historical 15
168169spherical 78
170171Copernicus 77
172173Cosmic hierarchy 10, 152, 167, 175, 176, 177, 229, 293
174175Cosmic Railroad Tracks 2
176177Coupler 2, 213, 214, 215, 302
178179Cube 2, 43, 44, 45, 47, 50, 224
180181Cube
182183employment as basic unit of mathematics 8, 9, 15, 22, 23, 77, 80, 168, 190, 202
184185ghost 9, 75, 153
186187inherent tetrahedron in 50, 64, 65, 145, 146, 154, 190, 197
188189instability of 64, 65, 115, 133, 143, 145, 149, 154, 155, 190
190191tetrahedral volume of 162
192193used as unit of volume 153, 154, 162, 168
194195weightless 75
196197Cuboctahedron 2, 37, 53, 54, 55, 56, 97, 99
198199Cuboctahedron
200201duality of 56
202203twist 97
204 D
205206Degrees of freedom 2, 101, 123, 241, 283, 302
207208Degrees of freedom
209210conventional treatment 103
211212freedom of motion in sphere packing 118
213214in space 102, 105
215216planar analogy 101
217218tetrahedron and 103
219220Democritus 63
221222Descartes, René 82
223224Design
225226defined 274
227228Design science 2, 14, xv, 127, 150, 151, 274, 281, 283
229230comprehensive thinking 275
231232design-science revolution 284
233234Design Science Collection xv, xvi
235236Dictionary as inventory of experiences 21
237238Dimension xvi, 44, 71, 76, 302
239240Dimension
241242as direction 81
243244definition of 76
245246four-dimensional 82, 100, 180, 181, 183
247248multi-dimensional 76, 136, 138
249250other applications of 81, 82
251252three-dimensional 81, 138
253254Dodecahedron 2
255256Dodecahedron, pentagonal 44, 45, 47, 49, 53, 180, 189, 192, 227, 230
257258Dodecahedron, pentagonal
259260symmetry of 54, 180, 229
261262Dodecahedron, rhombic 2
263264Domain 227
265266Domain
267268and closepacked spheres 147, 214
269270and duality 147, 194
271272defined 147
273274Duality 2, 53, 192, 224
275276dual operations 56, 148
277278dual polyhedra 49, 54, 180, 225
279280IVM and 144, 146, 148, 193
281282Dymaxion 37, 303
283284Dymaxion
285286Map 70, 279, 281
287 E
288289Eddington, Arthur 8, 36, 158
290291Edmondson, Amy C. 6, xvi, 267
292293Einstein 12, 72
294295Einstein
296297E= mc š 14
298299Empire State Building 9
300301Energy-event
302303descriptive term to replace ’solid’ 8, 9, 30, 207, 303
304305discrete energy events 2, 19, 20, 205, 235, 236, 242, 271
306307’energy-event Universe’ 16, 55, 72, 235, 240, 242
308309Engineering 150, 183, 252, 269, 270
310311Entropy xiii, 92
312313Environment control 278
314315Equilibrium 2
316317Euler, Leonhard 46
318319Euler’s Law 2, 46, 49, 74, 84, 124, 244, 245
320321Everything I Know video 9, 12, 13, 33, 34, 36, 74, 91, 150, 253, 307
322323Extinction 275
324 F
325326Finite accounting system 2, 20, 133, 178, 221, 303
327328Flat-Earth thinking 15, 21, 22, 77, 153, 169, 279
329330Food system 276, 277, 278, 311
331332Four planes of symmetry 100, 114, 138, 141, 149, 180
333334Frequency 120, 241, 303
335336Frequency
337338and size 72
339340and time 73
341342angle and 73, 78, 90, 98
343344defined 120
345346formula to relate frequency and number of spheres 134, 253
347348higher-frequency polyhedra 143, 157, 164, 196, 198, 249, 252, 254, 271
349350sphere-packing and 120, 123
351352vs continuum 73, 250
353354Fuller Institute 2
355356Fuller, R. Buckminster (’Bucky’)
357358Anne Hewlett Fuller 1, xvi
359360Harvard University 10
361362Milton MA 2, xvi
363364United States Navy experience 18, 90, 275
365366’careers’ as inventor, architect, engineer, philosopher 2
367 G
368369General Dynamics, titanium shell experiment 253
370371Generalized principle 2, 3, 14, 36, 38, 117, 254, 303, 304
372373design science as application of 14
374375eternal not special-case 275
376377exceptionless 14
378379God
380381as unknowable totality of 15
382383humanity’s wealth 306
384385invention as novel application of 14, 254, 278
386387key to humanity’s success 274
388389of 12 degrees of freedom 283
390391of 720ř angular takeout 84
392393of duality 55
394395of formula of nuclear sphere packings 125
396397of icosahedron as best sphere approximation 279
398399of oct-tet space-filling ratio 192, 201
400401of synergy 15
402403of triangular-number formula 117
404405of varying rates of geometric expansion 278
406407omni-interaccommodative 15, 40, 305
408409principle of angular topology 2
410411synergetics as the search for 14
412413Universe as total web of all 15
414415Geodesics 2, 241, 245, 246, 250, 251
416417defined 246
418419Expo67 U.S. pavilion dome 1
420421four-frequency icosahedron 86, 251, 255
422423geodesic breakdowns 255
424425geodesic dome 2, 3, 6, 68, 70, 250, 252, 254, 270, 274, 278
426427geodesic dome and frequency 248
428429geodesic mathematics 4, 246
430431geodesic polyhedra 84, 242, 245, 250, 254, 271
432433great-circle chords 250, 256, 278
434435God, not ’the God’ 12
436437as ’greater intellectual integrity of eternally regenerative universe’ 63, 274, 304
438439as ’unknowable totality of generalized principles’ 15
440441as non-anthropomorphic all-encompassing greater intelligence 274
442443Golden section 20, 178
444445Gravity
446447Fuller anecdotes 3, 263
448449mass interattraction 14, 36, 218, 259, 263, 283
450451Great circles 29, 219, 303
452453Great circles
454455bowties 232, 242, 244
456457cosmic railroad tracks 243, 245
458459definition of 219
460461Energy paths 240
462463great-circle arc 220, 235, 247
464465great-circle patterns 222
466467icosahedral 226, 238, 244, 248, 249, 271
468469minimum models 236
470471shortest path 219, 220, 240, 242, 246
472473icosahedron as local shunting circuit 243
474475Greece, ancient 2
476477geometry of 8, 18, 39, 40, 81, 190, 260
478479Greek, use in nomenclature 17, 28, 29, 30, 37, 42, 44
480 H
481482Hanging bookshelf 282
483484Harvard University 10, xvi, xxii, 40, 273
485486Harvard University
487488Sever Hall 4
489490Heisenberg, indeterminism 191
491492Hexahedron 2, 154, 156
493 I
494495Icosahedron 2, 29, 42, 43, 47, 53
496497and geodesics 250
498499jitterbug and 172, 174
500501net 83
502503structural system 66
504505symmetry of 81, 127, 175, 176, 226, 247, 252, 253, 278, 279
506507volume of 174, 175
508509’dimpling’ 68, 69, 303
510511’out-of-phase’ role 175, 176, 178, 182, 189, 192, 229, 231
512513Icosidodecahedron 53, 54
514515Impossibles (unempirical constructs) 8
516517circle, perfect continuous 19
518519continuum 133
520521equilibrium, perfect static 173
522523line, imaginary infinite straight 5, 7, 8, 9, 17, 91
524525plane, continuous infinite 9, 75
526527point, sizeless 9, 75
528529solid-things thinking 8, 66, 196, 260, 263, 265, 283
530531solid, continuous-surface 8, 12, 18, 30, 133, 183
532533sphere, continuous-surface 19, 86, 108, 250, 252
534535surface, zero-thickness 25
536537vs ’demonstrables’ 8, 9, 18, 20, 25, 72, 75, 109, 188
538539’oneness’ 33
540541In-Out vs Up-Down 12
542543Infinity 2, 25
544545and irrational numbers 18
546547circle as many-sided polygon 19
548549sphere as multifaceted polyhedron 19
550551vertices on sphere surface 86
552553Ingber, Donald 5, 272
554555Interprecessing 2, 130, 131, 132
556557Intertransformabilities 50, 54, 55, 149, 152, 167, 202, 205, 217, 222, 223, 228, 231, 304
558559Invention 2, 3, 15, xxi, 25, 26, 70, 149, 254, 258, 274
560561defined 14, 254
562563gestation rates 277
564565Invisibles
566567invisible reality 3, 14, 15, 37, 174, 183, 261, 263, 265, 271, 284
568569invisible Universe 173, 265
570571Isotropic vector matrix (IVM) 2, 12, 135, 170, 175, 202, 205, 208, 304
572573Isotropic vector matrix (IVM)
574575alternating octahedra and tetrahedra 135, 136, 145, 202
576577cube and IVM 145, 147, 148
578579equilibrium 138
580581frame of reference 148, 152, 153, 155, 164, 167, 175, 176, 178, 183, 187, 192, 193, 195, 197, 201, 217, 231, 243
582583IVM’ 148, 152, 160, 164, 192
584585omnisymmetry 137, 138, 145, 150, 175, 176, 195, 202
586587omnitriangulation 141
588589square cross-section of IVM 141
590591VE and IVM 2
592593IVM 2
594 J
595596Jitterbug
597598complex of jitterbugs 181, 182
599600flexible VE model 170, 180
601602transformation 171, 180, 182, 183, 184, 226, 231, 304
603 K
604605Kenner, Hugh 75
606607kissing point 214
608609Klug, Aaron 253
610 L
611612Least common denominator (LCD) 208, 209, 212, 227, 239, 248, 257
613614Lesser circle 219
615616Tropic of Cancer 219
617618Leverage 14, 15, 61
619620Life 2
621622Life-support advantage 26, 284
623624Line 2
625626chord 279
627628chord as 252
629630Euclidean 220
631632vector as replacement for 9, 41, 74
633634Local holding patterns 236, 242
635636Loeb, 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
637 M
638639MacCready, Paul
640641Gossamer Albatross 261
642643Malthus, Thomas, Malthusian thinking 5, 284
644645Massachusetts Institute of Technology (MIT) 5, 6, 64, 71
646647Mathematics
648649defined as science of structure and pattern 64, 71, 75
650651Mercator projection 279, 280
652653Metaphysical phenomena
654655mind, life, thought, equilibrium, generalized principles, pattern integrities 4, 8, 13, 26, 35, 63, 89, 106, 107, 205, 304
656657Mite 209, 210, 212, 213, 215, 304
658659Mite
660661cubes and 211, 213
662663mirror symmetry of 211, 215
664665rearrangement of 215, 216
666667rhombic dodecahedron and 212, 213
668669More with less (ephemeralization) 261, 284, 285, 303
670671Mozart 63
672673Multiplication by division 152, 158, 168, 174, 189, 205, 225
674 N
675676Natural is what nature permits 11
677678Nature’s coordinate system 3, 4, 10, 11, 12, 18, 19, 26, 37, 74, 91, 110, 206, 304
679680Navy 2
681682Nests 2, 304
683684Net, polyhedral 83, 86, 206, 304
685686Neutral axis 261
687688Nuclear spheres 2, 109, 112, 119, 214, 215
689690Nuclear spheres
691692defined 119
693694removal of 170, 175
695696tetrahedron and nuclei 121, 129
697698VE and nuclei 170
699 O
700701Octahedron 2, 41, 42, 45, 47, 80, 148
702703closepacked spheres and 114, 115
704705jitterbug and 172
706707octahedral cavities 99, 137, 141, 165, 181, 190, 196
708709octahedral core 159, 176
710711structural system 145
712713symmetry of 80, 222
714715truncated 2
716717Octant 145, 160, 161, 162, 163, 204, 213
718719Octet symmetry 2
720721Octet Truss 3, 68, 70, 137, 149, 150, 190, 211
722723Operational mathematics 7, 8, 26, 32, 33, 152, 154, 155, 232, 250
724725Operational mathematics
726727operational procedure 10, 11, 20, 158, 187, 191, 206
728 P
729730Patents 2
731732Pattern integrity 59, 61, 104, 305
733734Pattern integrity
735736knot 62, 63
737738life 10, 63
739740wave 62, 63, 183
741742Pentagonal dodecahedron 2
743744Phase changes 2
745746Philosophy (of Buckminster Fuller) 2, 6, 10, 25, 34, 35, 105, 276, 277, 284
747748Philosophy (of Buckminster Fuller)
749750philosophy 274
751752philosophy and geometry 35, 133, 168, 266
753754Planes of symmetry 114
755756Platonic polyhedra 2
757758Poles of spinnability 47, 49, 124, 221
759760Polyhedra 2
761762geodesic (triangulated) 31, 266, 294
763764irregular 67, 84, 85, 131, 266
765766regular 31, 45, 46, 57, 97, 141, 220, 266, 294, 305
767768regular-Platonic ’solids’ 37, 40, 49, 51, 268, 269
769770semiregular 31, 54, 56, 57, 97, 141, 195, 200, 220, 266, 294
771772Precession 2, 59, 130, 183, 305
773774Principle of angular topology 2
775 Q
776777Quantum 2, 31, 133, 305
778779Quantum
780781discrete quanta 153, 218, 252
782783edges (six) as one 31, 68, 84, 133
784785physics 190
786787units 178
788 R
789790Regular polyhedra 2
791792Rhombic dodecahedron 2, 31, 54, 55, 56, 146, 147, 154, 163, 164, 179, 231
793794duality of 193
795796icosahedron and 146, 179, 180
797798space-filling property 193, 194, 195, 197
799800space-filling property 195
801802spheric 147, 148, 195, 212, 213, 217, 305
803804volume 163
805806Rhombic triacontahedron 28, 230, 239
807808Rhombicuboctahedron 165
809810Rhombohedron 143, 191, 197
811 S
812813S-module 178, 179, 231
814815Sadao, Shoji 268, 279
816817Saint Peter’s Cathedral Dome 258, 260
818819Schlaefli’s formula 48
820821Science
822823definition of 8, 36, 158
824825Science of spatial complexity 2
826827Shell, or single-layer, systems 2, 65, 126, 175, 216, 241, 252, 253
828829Sixness
830831cosmic 238
832833six positive-negative linear directions 100, 123, 283
834835Slenderness ratio 260
836837Snelson, Kenneth 266
838839Sodium chloride 36
840841Solar system as tensegrity 263
842843Solids 2
844845geometric 2, 8, 19, 37, 164
846847phase changes in chemistry 174, 184, 185
848849Solway, Carl
850851Carl Solway Gallery 182
852853Southeast Asian basketry 247
854855Space
856857science of spatial complexity 4, 10, 15, 25, 283, 285
858859self-organization/order inherent in space 10, 11, 25, 30, 64, 91, 93, 101, 114, 127, 163, 168, 179, 187, 201, 244
860861shape 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
862863spatial constraints 10, 11, 39, 44, 45, 63, 75, 77, 91, 109, 116, 127, 128, 140, 141, 189, 222, 253, 256, 271, 273
864865Space Structures 11, 51
866867Space-filling 2
868869all-space filling 187, 195, 209, 213
870871complementarity 2, 181
872873complex 185, 187, 209, 243
874875cubes 192
876877domain of sphere 147
878879filling space with closepacked spheres 116, 242
880881formula for space filling 192, 197
882883IVM and 2, 148, 149, 192, 202
884885octet symmetry 190, 212, 217
886887rhombohedron 143, 191
888889space fillers 187, 189, 197, 200, 209, 213, 215, 217
890891space fillers, other 191
892893teams 192
894895truncated octahedron 2, 195, 217
896897Spaceship Earth 6, 22, 66, 274, 276, 277, 305
898899Special case 72, 275, 305
900901Special case
902903special case system 167
904905special-case experience 14, 31
906907Sphere 2
908909defined 108
910911frame of reference for polyhedral systems 221
912913omnisymmetrical form 122, 221, 242
914915surface area of 19, 236, 250, 278
916917Spheric 2
918919Spherical polyhedra 220, 221, 222, 223, 225, 227, 228, 234, 237, 247, 279
920921Spherical triangles 32, 223, 227, 229, 238, 240, 305
922923Spherical trigonometry 86, 257, 258
924925Spin/spinnability 2
926927Star tetrahedron 223, 238
928929Stellation
930931definition of 51
932933degenerate 55
934935degenerate stellation 52, 56, 145, 148, 193, 230
936937Straight line 2
938939Structural stability 2
940941necklace 59
942943prime structural systems 125
944945stability and jitterbug 170
946947stability formula 65
948949triangulation 64, 127, 149, 202, 240, 247, 249, 250, 256, 272
950951Structure
952953definition of 66
954955Sunrise/Sunset
956957Sunsight/Sunclipse, suggested modern-era terms 22
958959persistent misnomers evidencing misperceptions 3, 5, 22
960961Symmetry 2
962963defined 57, 109, 202
964965mirror symmetry 57, 203
966967octet symmetry 216
968969omnisymmetry 2, 95, 96, 99, 122, 148, 149, 242
970971planar symmetry 92
972973polyhedra as symmetry patterns 75, 192
974975rotational symmetry 121, 176, 181, 189, 211, 221, 223
976977seven unique axes of symmetry 114, 226, 244
978979spatial symmetry 2
980981Synergetics accounting 139
982983cosmic accounting 205
984985Synergetics\
986987Explorations 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
988989Explorations in the Geometry of Thinking
990991topology combined with vectorial geometry 74
992993Loeb’s ’Contribution to Synergetics’ 40, 157, 168, 178, 180, 191, 192, 210
994995Synergetics2\
996997Further Explorations in the Geometry of Thinking xiii, xviii, xx, xxiii
998999Loeb’s ’Addendum’ 178
10001001Synergy 15, 28, 36, 151, 306
10021003Synergy
10041005alloys 36
10061007and synergetics, synergetic-energetic-geometry 37
10081009defined 36
10101011in tensegrity 269
10121013System
10141015definition of 28, 29, 46, 48, 306
1016 T
10171018Takeout 2
10191020Technology
10211022as pure principle in action 274
10231024nature’s self-organization as high technology 15
10251026Tensegrity 4, xv, 258, 260, 263, 306
10271028Tensegrity
10291030interplay of tension and compression in Universe 258, 265, 271, 272
10311032models 266
10331034pneumatics 271, 272
10351036tensile strength 37, 261, 268, 269
10371038tension materials 106, 261, 263, 269, 282
10391040use of tension in construction 263, 265
10411042Tessellations 41, 188, 250
10431044Tetrahedron 41, 42, 45, 47, 250
10451046Tetrahedron
10471048basic unit in Synergetics 31, 41, 156, 158, 159, 184
10491050central angle of 145, 146
10511052cheese 155
10531054inside-out 173
10551056isotropic vector matrix and 140
10571058jitterbug and 173
10591060minimum system of Universe 29, 30, 34, 35, 81, 104, 140, 149, 156, 168, 173, 203, 215, 236
10611062perpendicular symmetry of 130, 164, 165
10631064rigidity of 150
10651066sphere-cluster tetrahedra 2
10671068subdivision of tetrahedron 2, 159, 160, 163, 164, 202, 203
10691070surface angles of 62, 84
10711072tetrahedroning 23, 24, 199
10731074truncation of 51, 143
10751076unit of volume 153, 156, 162, 168, 174, 215
10771078Tetrakaidecahedron (truncated octahedron) 52, 143, 195, 196
10791080Three-way grid 2, 247, 256, 272
10811082Titanium shell experiment 253
10831084Triangles 2
10851086equilateral triangles in vector equilibrium 98
10871088similar 155, 157
10891090stability of 2, 28, 61, 172, 258, 278
10911092triangular numbers 117
10931094’triangling’ instead of squaring 22, 23, 24
10951096Tropic of Cancer 2
10971098Truncation 50, 196
10991100Truncation
11011102definition of 51
11031104degenerate 55, 98, 165
11051106isotropic vector matrix and 143, 148, 195
11071108Truss 2
11091110Tune-in-ability 33, 34, 35, 271, 306
11111112Twelve degrees of freedom 2
1113 U
11141115Unempirical constructs 2
11161117United States Patents
111811192,682,235 (1954) 258
112011214,377,114 (1983) 282
112211232,393,676 (1946) 281
11241125Universe 2, 12, 306
11261127Universe
11281129as ’incredible technology’ 274
11301131defined by Fuller 13
11321133differences in Universe as modulation of angle and frequency 73
11341135product of interaction between principles and energy 14, 40, 66, 173, 274
11361137’scenario Universe’ 12, 13, 26, 36, 61, 149, 158
11381139’single-frame’ Universe 12, 13
11401141’trans-Universe’ vs ’locally operative’ 175
1142 V
11431144Valency 51, 176, 183, 306
11451146Valency
11471148definition of 32
11491150in duality 55, 147, 148
11511152’quadrivalent’ 173
11531154Valving 206, 211, 306
11551156Vector 2
11571158and energy events 74, 91, 135, 306
11591160and forces 94, 252
11611162and interactions 90, 91, 93
11631164as replacement for line 2
11651166sphere packing and 2
11671168topology and 74
11691170Vector equilibrium (VE) 2, 306
11711172Vector equilibrium (VE)
11731174closepacked spheres and 108, 114, 175
11751176conceptual vs actual equilibrium 174, 176
11771178cuboctahedron as 97
11791180equilibrium defined 89
11811182equilibrium in nature 263
11831184hexagons and equilibrium 95, 96, 97, 101, 108, 111, 112, 114, 180
11851186hidden VE inside octahedron 165, 166
11871188model of 94
11891190space filling and 136, 139, 181, 192, 197
11911192tetrahedron and 162
11931194time and equilibrium 107
11951196Video 2
11971198Virus 10, 11, 127, 128, 175, 252, 253, 307, 308
11991200Visual literacy 25
12011202Volume ratios 152, 153, 158, 159, 167, 174
12031204use of volume constant 156, 157
12051206volume-to-surface-area ratio 67, 127, 128, 150, 278
1207 W
12081209Wealth 284, 306
12101211Wealth
12121213generalized principles as humanity’s 14, 82
12141215redefined 284
12161217Whole numbers 166, 168, 306
12181219Whole numbers
12201221whole-number relationship 19, 20, 31, 153, 154, 162, 163, 174, 175, 293
12221223Whole 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
1224 Y
12251226Yale University 272
12271228Yang, Chen Ning 191
1229 Z
12301231Zung, Thomas T.K. 268
1232 -
12331234-ness (conceptionings of space/systems) 2
1235123690-degreeness 81
12371238betweenness 29
12391240fourness 55, 81
12411242handedness 191
12431244insideness/outsideness 29, 35, 104, 215, 293
12451246oneness 33
12471248somethingness of space 12
12491250thingness 13
12511252twelveness 241
1253 ’
12541255’Dare to be naïve’ 27, 39
12561257’Fake bubbles’ 17
12581259’Hands-on’ mathematics 3, 26, 119, 217
12601261’Impossible’ achievements
12621263human flight 261
12641265spans exceeding 150 ft. 259
12661267’Unity is plural’ 33, 168, 173, 191, 302, 303