Index of Synergetics Sections Cited
1(’b’ designates Synergetics-2)
2
45A-module 2, 178, 203, 213, 221, 227, 228, 302
67A-module
89defining new framework 205, 216
1011energy characteristics 205, 211
1213net 207, 208
1415volume 215
1617Alloys 5, 36, 261, 284
1819Alloys
2021chrome-nickel-steel 37
2223Angle types, definition of
2425axial, central, dihedral, surface 87
2627Angular topology 71, 302
2829Angular topology
3031720ř excess 84
3233principle of 82
3435takeout 82, 280, 293
3637Architecture 20, 88, 149, 253, 258, 259
3839housing 277
4041Avogadro, Amadeo 134, 135, 152
4243B-module 2, 178, 204, 302
4445B-module
4647energy characteristics 205, 215
4849Bamboo 256
5051Bicycle wheel 102, 103, 264, 283
5253Black Mountain College 266
5455Bohr, Niels
5657complementarity principle (1928) 191
5859Boltzmann, Ludwig 92
6061Bookshelf 2
6263Bowties 2
6465Brain-Mind distinction 14, 275, 284
6667Brooklyn Bridge (1883) 261
6869Buckminster Fuller Institute (BFI) xxii, 270, 281, 309
7071C60 carbon molecule xx
7273Carbon atoms
7475carbon fiber 261
7677diamond vs graphite 31, 150
7879general bonding of 185
8081Cell
8283as topological element 48, 135, 144, 148, 150, 160, 164, 182, 192, 196, 198, 199
8485Chinese physicists, Tsung-Dao Lee and Ning Yang 191
8687Chord 19
8889chord factors 85
9091chordal and radial equivalence in VE 180
9293chordal forces 96
9495chordal rates of convergence and divergence 180
9697great-circle arcs 220
9899great-circle chords 256, 257, 271
100101Closepacked spheres, sphere packing 2, 10, 20, 108, 111, 135, 140, 141, 147, 164, 187, 189, 194, 202, 214
102103Closepacked spheres, sphere packing
104105cubic vs hexagonal 112, 113, 114
106107formula for total numbers of spheres 123, 125, 126
108109icosahedron and sphere packing 2, 125, 127, 170
110111mathematical challenge 110, 116
112113nests 111, 119, 128, 130
114115planes of symmetry 114
116117tetrahedral clusters 116, 118, 128
118119vector equilibrium and sphere packing 109, 122
120121Complementarity 140, 168, 190, 191, 302
122123Complementarity
124125complementary quanta
126127A- and B-modules 205, 208
128129concave-convex, tension-compression, and other pairs 32, 143, 191, 259
130131fundamental complementarity in physics 190, 205
132133inherent complementarity of Universe 141, 168, 189, 190
134135of octahedron and tetrahedron 140, 149, 191
136137Compression 2
138139Consciousness
140141defined by Fuller 12, 13
142143Constant relative abundance 2
1441452 faces, 3 edges per vertex (less poles) in triangulated polyhedra 49
146147faces=2 times number of vertices minus 2 in triangulated systems 48
148149of ’dimensions’ (topological elements) 81
150151Cookies 93, 138
152153Coordinate system 71, 104, 218, 254
154155Coordinate system
156157Cartesian 77, 78, 79, 95, 139, 145, 149, 164, 168, 222, 225
158159origin 36, 71, 149
160161origins, historical 15
162163spherical 78
164165Copernicus 77
166167Cosmic hierarchy 10, 152, 167, 175, 176, 177, 229, 293
168169Cosmic Railroad Tracks 2
170171Coupler 2, 213, 214, 215, 302
172173Cube 2, 43, 44, 45, 47, 50, 224
174175Cube
176177employment as basic unit of mathematics 8, 9, 15, 22, 23, 77, 80, 168, 190, 202
178179ghost 9, 75, 153
180181inherent tetrahedron in 50, 64, 65, 145, 146, 154, 190, 197
182183instability of 64, 65, 115, 133, 143, 145, 149, 154, 155, 190
184185tetrahedral volume of 162
186187used as unit of volume 153, 154, 162, 168
188189weightless 75
190191Cuboctahedron 2, 37, 53, 54, 55, 56, 97, 99
192193Cuboctahedron
194195duality of 56
196197twist 97
198199Degrees of freedom 2, 101, 123, 241, 283, 302
200201Degrees of freedom
202203conventional treatment 103
204205freedom of motion in sphere packing 118
206207in space 102, 105
208209planar analogy 101
210211tetrahedron and 103
212213Democritus 63
214215Descartes, René 82
216217Design
218219defined 274
220221Design science 2, 14, xv, 127, 150, 151, 274, 281, 283
222223comprehensive thinking 275
224225design-science revolution 284
226227Design Science Collection xv, xvi
228229Dictionary as inventory of experiences 21
230231Dimension xvi, 44, 71, 76, 302
232233Dimension
234235as direction 81
236237definition of 76
238239four-dimensional 82, 100, 180, 181, 183
240241multi-dimensional 76, 136, 138
242243other applications of 81, 82
244245three-dimensional 81, 138
246247Dodecahedron 2
248249Dodecahedron, pentagonal 44, 45, 47, 49, 53, 180, 189, 192, 227, 230
250251Dodecahedron, pentagonal
252253symmetry of 54, 180, 229
254255Dodecahedron, rhombic 2
256257Domain 227
258259Domain
260261and closepacked spheres 147, 214
262263and duality 147, 194
264265defined 147
266267Duality 2, 53, 192, 224
268269dual operations 56, 148
270271dual polyhedra 49, 54, 180, 225
272273IVM and 144, 146, 148, 193
274275Dymaxion 37, 303
276277Dymaxion
278279Map 70, 279, 281
280281Eddington, Arthur 8, 36, 158
282283Edmondson, Amy C. 6, xvi, 267
284285Einstein 12, 72
286287Einstein
288289E= mc š 14
290291Empire State Building 9
292293Energy-event
294295descriptive term to replace ’solid’ 8, 9, 30, 207, 303
296297discrete energy events 2, 19, 20, 205, 235, 236, 242, 271
298299’energy-event Universe’ 16, 55, 72, 235, 240, 242
300301Engineering 150, 183, 252, 269, 270
302303Entropy xiii, 92
304305Environment control 278
306307Equilibrium 2
308309Euler, Leonhard 46
310311Euler’s Law 2, 46, 49, 74, 84, 124, 244, 245
312313Everything I Know video 9, 12, 13, 33, 34, 36, 74, 91, 150, 253, 307
314315Extinction 275
316317Finite accounting system 2, 20, 133, 178, 221, 303
318319Flat-Earth thinking 15, 21, 22, 77, 153, 169, 279
320321Food system 276, 277, 278, 311
322323Four planes of symmetry 100, 114, 138, 141, 149, 180
324325Frequency 120, 241, 303
326327Frequency
328329and size 72
330331and time 73
332333angle and 73, 78, 90, 98
334335defined 120
336337formula to relate frequency and number of spheres 134, 253
338339higher-frequency polyhedra 143, 157, 164, 196, 198, 249, 252, 254, 271
340341sphere-packing and 120, 123
342343vs continuum 73, 250
344345Fuller Institute 2
346347Fuller, R. Buckminster (’Bucky’)
348349Anne Hewlett Fuller 1, xvi
350351Harvard University 10
352353Milton MA 2, xvi
354355United States Navy experience 18, 90, 275
356357’careers’ as inventor, architect, engineer, philosopher 2
358359General Dynamics, titanium shell experiment 253
360361Generalized principle 2, 3, 14, 36, 38, 117, 254, 303, 304
362363design science as application of 14
364365eternal not special-case 275
366367exceptionless 14
368369God
370371as unknowable totality of 15
372373humanity’s wealth 306
374375invention as novel application of 14, 254, 278
376377key to humanity’s success 274
378379of 12 degrees of freedom 283
380381of 720ř angular takeout 84
382383of duality 55
384385of formula of nuclear sphere packings 125
386387of icosahedron as best sphere approximation 279
388389of oct-tet space-filling ratio 192, 201
390391of synergy 15
392393of triangular-number formula 117
394395of varying rates of geometric expansion 278
396397omni-interaccommodative 15, 40, 305
398399principle of angular topology 2
400401synergetics as the search for 14
402403Universe as total web of all 15
404405Geodesics 2, 241, 245, 246, 250, 251
406407defined 246
408409Expo67 U.S. pavilion dome 1
410411four-frequency icosahedron 86, 251, 255
412413geodesic breakdowns 255
414415geodesic dome 2, 3, 6, 68, 70, 250, 252, 254, 270, 274, 278
416417geodesic dome and frequency 248
418419geodesic mathematics 4, 246
420421geodesic polyhedra 84, 242, 245, 250, 254, 271
422423great-circle chords 250, 256, 278
424425God, not ’the God’ 12
426427as ’greater intellectual integrity of eternally regenerative universe’ 63, 274, 304
428429as ’unknowable totality of generalized principles’ 15
430431as non-anthropomorphic all-encompassing greater intelligence 274
432433Golden section 20, 178
434435Gravity
436437Fuller anecdotes 3, 263
438439mass interattraction 14, 36, 218, 259, 263, 283
440441Great circles 29, 219, 303
442443Great circles
444445bowties 232, 242, 244
446447cosmic railroad tracks 243, 245
448449definition of 219
450451Energy paths 240
452453great-circle arc 220, 235, 247
454455great-circle patterns 222
456457icosahedral 226, 238, 244, 248, 249, 271
458459minimum models 236
460461shortest path 219, 220, 240, 242, 246
462463icosahedron as local shunting circuit 243
464465Greece, ancient 2
466467geometry of 8, 18, 39, 40, 81, 190, 260
468469Greek, use in nomenclature 17, 28, 29, 30, 37, 42, 44
470471Hanging bookshelf 282
472473Harvard University 10, xvi, xxii, 40, 273
474475Harvard University
476477Sever Hall 4
478479Heisenberg, indeterminism 191
480481Hexahedron 2, 154, 156
482483Icosahedron 2, 29, 42, 43, 47, 53
484485and geodesics 250
486487jitterbug and 172, 174
488489net 83
490491structural system 66
492493symmetry of 81, 127, 175, 176, 226, 247, 252, 253, 278, 279
494495volume of 174, 175
496497’dimpling’ 68, 69, 303
498499’out-of-phase’ role 175, 176, 178, 182, 189, 192, 229, 231
500501Icosidodecahedron 53, 54
502503Impossibles (unempirical constructs) 8
504505circle, perfect continuous 19
506507continuum 133
508509equilibrium, perfect static 173
510511line, imaginary infinite straight 5, 7, 8, 9, 17, 91
512513plane, continuous infinite 9, 75
514515point, sizeless 9, 75
516517solid-things thinking 8, 66, 196, 260, 263, 265, 283
518519solid, continuous-surface 8, 12, 18, 30, 133, 183
520521sphere, continuous-surface 19, 86, 108, 250, 252
522523surface, zero-thickness 25
524525vs ’demonstrables’ 8, 9, 18, 20, 25, 72, 75, 109, 188
526527’oneness’ 33
528529In-Out vs Up-Down 12
530531Infinity 2, 25
532533and irrational numbers 18
534535circle as many-sided polygon 19
536537sphere as multifaceted polyhedron 19
538539vertices on sphere surface 86
540541Ingber, Donald 5, 272
542543Interprecessing 2, 130, 131, 132
544545Intertransformabilities 50, 54, 55, 149, 152, 167, 202, 205, 217, 222, 223, 228, 231, 304
546547Invention 2, 3, 15, xxi, 25, 26, 70, 149, 254, 258, 274
548549defined 14, 254
550551gestation rates 277
552553Invisibles
554555invisible reality 3, 14, 15, 37, 174, 183, 261, 263, 265, 271, 284
556557invisible Universe 173, 265
558559Isotropic vector matrix (IVM) 2, 12, 135, 170, 175, 202, 205, 208, 304
560561Isotropic vector matrix (IVM)
562563alternating octahedra and tetrahedra 135, 136, 145, 202
564565cube and IVM 145, 147, 148
566567equilibrium 138
568569frame of reference 148, 152, 153, 155, 164, 167, 175, 176, 178, 183, 187, 192, 193, 195, 197, 201, 217, 231, 243
570571IVM’ 148, 152, 160, 164, 192
572573omnisymmetry 137, 138, 145, 150, 175, 176, 195, 202
574575omnitriangulation 141
576577square cross-section of IVM 141
578579VE and IVM 2
580581IVM 2
582583Jitterbug
584585complex of jitterbugs 181, 182
586587flexible VE model 170, 180
588589transformation 171, 180, 182, 183, 184, 226, 231, 304
590591Kenner, Hugh 75
592593kissing point 214
594595Klug, Aaron 253
596597Least common denominator (LCD) 208, 209, 212, 227, 239, 248, 257
598599Lesser circle 219
600601Tropic of Cancer 219
602603Leverage 14, 15, 61
604605Life 2
606607Life-support advantage 26, 284
608609Line 2
610611chord 279
612613chord as 252
614615Euclidean 220
616617vector as replacement for 9, 41, 74
618619Local holding patterns 236, 242
620621Loeb, 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
622623MacCready, Paul
624625Gossamer Albatross 261
626627Malthus, Thomas, Malthusian thinking 5, 284
628629Massachusetts Institute of Technology (MIT) 5, 6, 64, 71
630631Mathematics
632633defined as science of structure and pattern 64, 71, 75
634635Mercator projection 279, 280
636637Metaphysical phenomena
638639mind, life, thought, equilibrium, generalized principles, pattern integrities 4, 8, 13, 26, 35, 63, 89, 106, 107, 205, 304
640641Mite 209, 210, 212, 213, 215, 304
642643Mite
644645cubes and 211, 213
646647mirror symmetry of 211, 215
648649rearrangement of 215, 216
650651rhombic dodecahedron and 212, 213
652653More with less (ephemeralization) 261, 284, 285, 303
654655Mozart 63
656657Multiplication by division 152, 158, 168, 174, 189, 205, 225
658659Natural is what nature permits 11
660661Nature’s coordinate system 3, 4, 10, 11, 12, 18, 19, 26, 37, 74, 91, 110, 206, 304
662663Navy 2
664665Nests 2, 304
666667Net, polyhedral 83, 86, 206, 304
668669Neutral axis 261
670671Nuclear spheres 2, 109, 112, 119, 214, 215
672673Nuclear spheres
674675defined 119
676677removal of 170, 175
678679tetrahedron and nuclei 121, 129
680681VE and nuclei 170
682683Octahedron 2, 41, 42, 45, 47, 80, 148
684685closepacked spheres and 114, 115
686687jitterbug and 172
688689octahedral cavities 99, 137, 141, 165, 181, 190, 196
690691octahedral core 159, 176
692693structural system 145
694695symmetry of 80, 222
696697truncated 2
698699Octant 145, 160, 161, 162, 163, 204, 213
700701Octet symmetry 2
702703Octet Truss 3, 68, 70, 137, 149, 150, 190, 211
704705Operational mathematics 7, 8, 26, 32, 33, 152, 154, 155, 232, 250
706707Operational mathematics
708709operational procedure 10, 11, 20, 158, 187, 191, 206
710711Patents 2
712713Pattern integrity 59, 61, 104, 305
714715Pattern integrity
716717knot 62, 63
718719life 10, 63
720721wave 62, 63, 183
722723Pentagonal dodecahedron 2
724725Phase changes 2
726727Philosophy (of Buckminster Fuller) 2, 6, 10, 25, 34, 35, 105, 276, 277, 284
728729Philosophy (of Buckminster Fuller)
730731philosophy 274
732733philosophy and geometry 35, 133, 168, 266
734735Planes of symmetry 114
736737Platonic polyhedra 2
738739Poles of spinnability 47, 49, 124, 221
740741Polyhedra 2
742743geodesic (triangulated) 31, 266, 294
744745irregular 67, 84, 85, 131, 266
746747regular 31, 45, 46, 57, 97, 141, 220, 266, 294, 305
748749regular-Platonic ’solids’ 37, 40, 49, 51, 268, 269
750751semiregular 31, 54, 56, 57, 97, 141, 195, 200, 220, 266, 294
752753Precession 2, 59, 130, 183, 305
754755Principle of angular topology 2
756757Quantum 2, 31, 133, 305
758759Quantum
760761discrete quanta 153, 218, 252
762763edges (six) as one 31, 68, 84, 133
764765physics 190
766767units 178
768769Regular polyhedra 2
770771Rhombic dodecahedron 2, 31, 54, 55, 56, 146, 147, 154, 163, 164, 179, 231
772773duality of 193
774775icosahedron and 146, 179, 180
776777space-filling property 193, 194, 195, 197
778779space-filling property 195
780781spheric 147, 148, 195, 212, 213, 217, 305
782783volume 163
784785Rhombic triacontahedron 28, 230, 239
786787Rhombicuboctahedron 165
788789Rhombohedron 143, 191, 197
790791S-module 178, 179, 231
792793Sadao, Shoji 268, 279
794795Saint Peter’s Cathedral Dome 258, 260
796797Schlaefli’s formula 48
798799Science
800801definition of 8, 36, 158
802803Science of spatial complexity 2
804805Shell, or single-layer, systems 2, 65, 126, 175, 216, 241, 252, 253
806807Sixness
808809cosmic 238
810811six positive-negative linear directions 100, 123, 283
812813Slenderness ratio 260
814815Snelson, Kenneth 266
816817Sodium chloride 36
818819Solar system as tensegrity 263
820821Solids 2
822823geometric 2, 8, 19, 37, 164
824825phase changes in chemistry 174, 184, 185
826827Solway, Carl
828829Carl Solway Gallery 182
830831Southeast Asian basketry 247
832833Space
834835science of spatial complexity 4, 10, 15, 25, 283, 285
836837self-organization/order inherent in space 10, 11, 25, 30, 64, 91, 93, 101, 114, 127, 163, 168, 179, 187, 201, 244
838839shape 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
840841spatial constraints 10, 11, 39, 44, 45, 63, 75, 77, 91, 109, 116, 127, 128, 140, 141, 189, 222, 253, 256, 271, 273
842843Space Structures 11, 51
844845Space-filling 2
846847all-space filling 187, 195, 209, 213
848849complementarity 2, 181
850851complex 185, 187, 209, 243
852853cubes 192
854855domain of sphere 147
856857filling space with closepacked spheres 116, 242
858859formula for space filling 192, 197
860861IVM and 2, 148, 149, 192, 202
862863octet symmetry 190, 212, 217
864865rhombohedron 143, 191
866867space fillers 187, 189, 197, 200, 209, 213, 215, 217
868869space fillers, other 191
870871teams 192
872873truncated octahedron 2, 195, 217
874875Spaceship Earth 6, 22, 66, 274, 276, 277, 305
876877Special case 72, 275, 305
878879Special case
880881special case system 167
882883special-case experience 14, 31
884885Sphere 2
886887defined 108
888889frame of reference for polyhedral systems 221
890891omnisymmetrical form 122, 221, 242
892893surface area of 19, 236, 250, 278
894895Spheric 2
896897Spherical polyhedra 220, 221, 222, 223, 225, 227, 228, 234, 237, 247, 279
898899Spherical triangles 32, 223, 227, 229, 238, 240, 305
900901Spherical trigonometry 86, 257, 258
902903Spin/spinnability 2
904905Star tetrahedron 223, 238
906907Stellation
908909definition of 51
910911degenerate 55
912913degenerate stellation 52, 56, 145, 148, 193, 230
914915Straight line 2
916917Structural stability 2
918919necklace 59
920921prime structural systems 125
922923stability and jitterbug 170
924925stability formula 65
926927triangulation 64, 127, 149, 202, 240, 247, 249, 250, 256, 272
928929Structure
930931definition of 66
932933Sunrise/Sunset
934935Sunsight/Sunclipse, suggested modern-era terms 22
936937persistent misnomers evidencing misperceptions 3, 5, 22
938939Symmetry 2
940941defined 57, 109, 202
942943mirror symmetry 57, 203
944945octet symmetry 216
946947omnisymmetry 2, 95, 96, 99, 122, 148, 149, 242
948949planar symmetry 92
950951polyhedra as symmetry patterns 75, 192
952953rotational symmetry 121, 176, 181, 189, 211, 221, 223
954955seven unique axes of symmetry 114, 226, 244
956957spatial symmetry 2
958959Synergetics accounting 139
960961cosmic accounting 205
962963Synergetics\
964965Explorations 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
966967Explorations in the Geometry of Thinking
968969topology combined with vectorial geometry 74
970971Loeb’s ’Contribution to Synergetics’ 40, 157, 168, 178, 180, 191, 192, 210
972973Synergetics2\
974975Further Explorations in the Geometry of Thinking xiii, xviii, xx, xxiii
976977Loeb’s ’Addendum’ 178
978979Synergy 15, 28, 36, 151, 306
980981Synergy
982983alloys 36
984985and synergetics, synergetic-energetic-geometry 37
986987defined 36
988989in tensegrity 269
990991System
992993definition of 28, 29, 46, 48, 306
994995Takeout 2
996997Technology
998999as pure principle in action 274
10001001nature’s self-organization as high technology 15
10021003Tensegrity 4, xv, 258, 260, 263, 306
10041005Tensegrity
10061007interplay of tension and compression in Universe 258, 265, 271, 272
10081009models 266
10101011pneumatics 271, 272
10121013tensile strength 37, 261, 268, 269
10141015tension materials 106, 261, 263, 269, 282
10161017use of tension in construction 263, 265
10181019Tessellations 41, 188, 250
10201021Tetrahedron 41, 42, 45, 47, 250
10221023Tetrahedron
10241025basic unit in Synergetics 31, 41, 156, 158, 159, 184
10261027central angle of 145, 146
10281029cheese 155
10301031inside-out 173
10321033isotropic vector matrix and 140
10341035jitterbug and 173
10361037minimum system of Universe 29, 30, 34, 35, 81, 104, 140, 149, 156, 168, 173, 203, 215, 236
10381039perpendicular symmetry of 130, 164, 165
10401041rigidity of 150
10421043sphere-cluster tetrahedra 2
10441045subdivision of tetrahedron 2, 159, 160, 163, 164, 202, 203
10461047surface angles of 62, 84
10481049tetrahedroning 23, 24, 199
10501051truncation of 51, 143
10521053unit of volume 153, 156, 162, 168, 174, 215
10541055Tetrakaidecahedron (truncated octahedron) 52, 143, 195, 196
10561057Three-way grid 2, 247, 256, 272
10581059Titanium shell experiment 253
10601061Triangles 2
10621063equilateral triangles in vector equilibrium 98
10641065similar 155, 157
10661067stability of 2, 28, 61, 172, 258, 278
10681069triangular numbers 117
10701071’triangling’ instead of squaring 22, 23, 24
10721073Tropic of Cancer 2
10741075Truncation 50, 196
10761077Truncation
10781079definition of 51
10801081degenerate 55, 98, 165
10821083isotropic vector matrix and 143, 148, 195
10841085Truss 2
10861087Tune-in-ability 33, 34, 35, 271, 306
10881089Twelve degrees of freedom 2
10901091Unempirical constructs 2
10921093United States Patents
109410952,682,235 (1954) 258
109610974,377,114 (1983) 282
109810992,393,676 (1946) 281
11001101Universe 2, 12, 306
11021103Universe
11041105as ’incredible technology’ 274
11061107defined by Fuller 13
11081109differences in Universe as modulation of angle and frequency 73
11101111product of interaction between principles and energy 14, 40, 66, 173, 274
11121113’scenario Universe’ 12, 13, 26, 36, 61, 149, 158
11141115’single-frame’ Universe 12, 13
11161117’trans-Universe’ vs ’locally operative’ 175
11181119Valency 51, 176, 183, 306
11201121Valency
11221123definition of 32
11241125in duality 55, 147, 148
11261127’quadrivalent’ 173
11281129Valving 206, 211, 306
11301131Vector 2
11321133and energy events 74, 91, 135, 306
11341135and forces 94, 252
11361137and interactions 90, 91, 93
11381139as replacement for line 2
11401141sphere packing and 2
11421143topology and 74
11441145Vector equilibrium (VE) 2, 306
11461147Vector equilibrium (VE)
11481149closepacked spheres and 108, 114, 175
11501151conceptual vs actual equilibrium 174, 176
11521153cuboctahedron as 97
11541155equilibrium defined 89
11561157equilibrium in nature 263
11581159hexagons and equilibrium 95, 96, 97, 101, 108, 111, 112, 114, 180
11601161hidden VE inside octahedron 165, 166
11621163model of 94
11641165space filling and 136, 139, 181, 192, 197
11661167tetrahedron and 162
11681169time and equilibrium 107
11701171Video 2
11721173Virus 10, 11, 127, 128, 175, 252, 253, 307, 308
11741175Visual literacy 25
11761177Volume ratios 152, 153, 158, 159, 167, 174
11781179use of volume constant 156, 157
11801181volume-to-surface-area ratio 67, 127, 128, 150, 278
11821183Wealth 284, 306
11841185Wealth
11861187generalized principles as humanity’s 14, 82
11881189redefined 284
11901191Whole numbers 166, 168, 306
11921193Whole numbers
11941195whole-number relationship 19, 20, 31, 153, 154, 162, 163, 174, 175, 293
11961197Whole 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
11981199Yale University 272
12001201Yang, Chen Ning 191
12021203Zung, Thomas T.K. 268
12041205-ness (conceptionings of space/systems) 2
1206120790-degreeness 81
12081209betweenness 29
12101211fourness 55, 81
12121213handedness 191
12141215insideness/outsideness 29, 35, 104, 215, 293
12161217oneness 33
12181219somethingness of space 12
12201221thingness 13
12221223twelveness 241
12241225’Dare to be naïve’ 27, 39
12261227’Fake bubbles’ 17
12281229’Hands-on’ mathematics 3, 26, 119, 217
12301231’Impossible’ achievements
12321233human flight 261
12341235spans exceeding 150 ft. 259
12361237’Unity is plural’ 33, 168, 173, 191, 302, 303