Ф symbol, 103
Abu Kamil Shuja ibn Aslam, 39
The Adoration of the Magi (Botticelli), 77
African spiral aloe plant, 149
Agnew, H. C., 96
Alhambra palace, 193
Alma-Tadema, Lawrence, 106
Altarpiece of Saint Mark (Botticelli), 80
animals
cats, 164
chameleons, 161
conch shells, 162
five-fold symmetry, 152
primates, 165
screw shell, 162
seahorses, 161
Annunciation (Leonardo da Vinci), 66
Annunciation (Sandro Botticelli), 77, 78, 79, 80
apples, 152
Archimedean spiral, 156
Archimedean truncated icosahedron, 61
Archimedes, 195
Art Forms in Nature (Ernst Haeckel), 153
Aston Martin automobiles, 138
Athena Parthenos (Phidias), 104
The Baptism of Christ (Piero della Francesca), 62, 63
Barr, Mark, 103
Basel Minster, 156
Bathers in Asnières (Georges Seurat), 120
Bernoulli, Jacob, 156
Birds and Nature, 145
The Birth of Venus (Sandro Botticelli), 75, 77
blue passionflower, 151
Bonnet, Charles, 145
Book of Algebra (Abu Kamil Shuja ibn Aslam), 39
BP logo, 137
Brady, Oliver, 13
Bridge of Courbevoie (Georges Seurat), 124
Bronnikov, Fyodor, 16
Brunelleschi, Filippo, 115
Caldwall, James, 145
Cambio, Arnolfo di, 115
caricatures, 177
Cathedral of Saint Mary of the Flower, 115, 116
cats, 164
Cattedrale di Santa Maria del Fiore, 115, 116
The Cestello Annunciation (Botticelli), 78
chameleons, 161
The Channel of Gravelines, Petit Fort Philippe (Georges Seurat), 124
Chartres Cathedral, 111, 112, 113, 114, 203
Christ as Savior of the World (Leonardo da Vinci), 72
Chrystal, George, 9
Cité radieuse (Radiant City), 127
Clark, Carmel, 13
Clark, Kenneth, 62
Codea, Radu, 196
Coltellini, Michele, 74
The Compendious Book on Calculation by Completion and Balancing (Muhammad ibn Musa al-Khwarizmi), 38
conch shells, 162
Cook, Theodore Andrea, 103
Corbusierhaus, 127
cosmos
Moon, 183
Sun, 185
Venus, 185
Coxeter plane projections, 196, 197
The Creation of Adam (Michelangelo), 84, 85
The Creation of Eve (Michelangelo), 86
Cruz, Norman, 189
Curl, Robert, 195
The Curves of Life (Sir Theodore Andrea Cook), 103
Dambrun, Jean, 16
Darb-i Imam shrine, 193
Dash, Glen, 99
Davies, Paul, 189
The Da Vinci Code (Dan Brown), 66
da Vinci, Leonardo, 12, 59, 60, 61, 66, 68, 69, 74, 149, 150
De Architectura (Vitruvius), 108
DeBruine, Lisa, 167
De Divina Proportione (Luca Pacioli), 59, 61, 62, 66, 74
Dell, Susan, 140
De Prospectiva Pingendi (Piero della Francesca), 62
discovery, 16
Disney logo, 137
DNA, 170
dodecahedron, 17, 25, 31, 32, 33, 58, 61, 182, 183, 195
Dow Jones Industrial Average, 200
The Drunkenness of Noah (Michelangelo), 87
Dürer, Albrecht, 58
E8 Coxeter plane projections, 196, 197
Echeveria succulent plants, 148
Einstein, Albert, 22
Elements (Euclid)
Arabic translation of, 20
Book II, Proposition 5, 8
Book III, Propositions 8, 19
Book VI, Proposition 11, 22
Book VI, Proposition 30, 22
Book XIII, Proposition 1, 23
Book XIII, Proposition 2, 23
Book XIII, Proposition 3, 23
Book XIII, Proposition 4, 24
Book XIII, Proposition 5, 24
Book XIII, Proposition 6, 24
Book XIII, Proposition 8, 24, 26
Book XIII, Proposition 9, 25
Book XIII, Proposition 17, 25
circulation of, 58
description of Ф, 10
Encyclopedia Britannica, 9
Epitome Astronomiae Copernicanae (Johannes Kepler), 30
ethnicity, 175
“Euclid Alone Has Looked on Beauty Bare” (Edna St. Vincent Millay), 19
extreme and mean ratio, 8, 17, 22, 24
faces, 164, 165, 167, 173, 179
The Fall and Expulsion from the Garden of Eden (Michelangelo), 85
“Famous Men” series (Justus of Ghent), 19
The Fashion Code, 140
fashion design, 140
Fibonacci heap, 199
Fibonacci, Leonardo, 39, 42, 103
Fibonacci numbers, 146, 166, 169
Fibonacci search technique, 199
Fibonacci sequence, 43, 47, 48, 199
Fibonacci spiral. See golden spiral.
Fibonacci system, 199
Fibonacci triangle, 48
financial markets, 199
fingers, 166
Finklestein, David, 189
five-petaled violets, 149, 150
The Flagellation of Christ (Piero della Francesca), 62, 65
forearm, 166
fractal patterns, 186, 199, 205
fractals, 154
Francesca, Piero della, 62, 74
fruit, 152
Fuller, Buckminster, 195
galaxies, 161
Galileo Galilei, 37
gambling, 199
gauge calipers, 57
German yellowjackets, 163
Ghyika, Matila, 120
giant silk moths, 163
Giza site, 93
golden gnomon, 29
golden ratio
calculating, 51
constructing, 26
discovery, 16
golden rectangle, 31, 99, 100, 107, 130, 131, 132
golden spiral, 13, 46, 47, 68, 146, 154, 157, 160
Google logo, 136
Gosset, Thorold, 196
Great Pyramid of Giza, 93, 99, 184
Great Sphinx, 102
Greek letters, 9
Gutenberg, Johannes, 19
Haeckel, Ernst, 153
hand, 166
Harmonices Mundi (Johannes Kepler), 30, 182
Herodotus, 96
Hertzsprung–Russell diagram, 187
Heyday of Greece (August Ahlborn), 106
Hollar, Wenceslaus, 74
Ho-Mg-Zn quasicrystal, 192, 193
House of Wisdom (Baghdad), 38
The Human Face documentary, 173
human body
caricatures, 177
DNA, 170
ethnicity, 175
fashion, 140
forearm, 166
hand, 166
head, 168
index finger, 166
teeth, 178
icosahedrite, 192
index finger, 166
insects, 163
Introduction to Algebra (George Chrystal), 9
Jahan, Shah, 118
John the Baptist (Leonardo da Vinci), 12
Jones, Ben, 167
Julia Titi Flavia, 174
Justus of Ghent, 19
Kepler, Johannes, 15, 17, 27, 30, 53, 95, 181, 182
Khafre Pyramid, 99
al-Khwarizmi, Muhammad ibn Musa, 38, 39
Koch snowflake, 154
Kroto, Harry, 195
Kunstformen der Natur (Ernst Haeckel), 153
al-Khwarizmi, 38
Lagrange, Joseph Louis, 50
Lahori, Ustad Ahmad, 118
The Last Supper (Leonardo da Vinci), 69
Lefebvre, Vladimir A., 200
Levy, Ruth, 140
Levy, Sara, 140
Liber Abaci (Leonardo Fibonacci), 39, 42, 45
The Lighthouse at Honfleur (Georges Seurat), 121
Limburg Cathedral, 114
Lindner, John, 186
logarithmic spiral, 156
lotus flowers, 148
Lucas, Edouard, 45
Luminet, Jean-Pierre, 183
lute of Pythagoras, 154
Madonna della Misericordia (Piero della Francesca), 64
Maestlin, Michael, 51
Mahal, Mumtaz, 118
Marquardt Beauty Mask, 173
Marquardt, Stephen R., 143, 169, 173
Martingale progression, 199
Mästlin, Michael, 28
Matsys, Quentin, 177
Menkaure Pyramid, 99
Michelangelo (Daniele da Volterra), 84
Millet, Aimé, 104
Modestini, Dianne Dwyer, 72
Modular design system, 126, 127, 128, 132
molecular structures
quasicrystals, 191
Mona Lisa (Leonardo da Vinci), 68
Moon, 183
morning glory, 151
moths, 163
Mysterium Cosmographicum (Kepler), 17, 30, 31
National Geographic logo, 137
nautilus shell, 157
The Navvies (Georges Seurat), 122
Nefertiti, 174
nest fern, 161
Neue Lehre von den Proportionen des menschlichen Körpers (Adolph Ziesing), 144
A New Illustration of the Sexual System of Carolus von Linnaeus (Robert John Thornton), 145
New Doctrine of the Proportions of the Human Body (Adolph Ziesing), 144
Nieto, J. A., 189
Nissan logo, 137
Notre-Dame Cathedral, 109, 110, 111, 196, 197
numeric reduction, 49
Occam’s razor, 166
Ohm, Martin, 9
okra, 152
Olivares, Marco, 189
On Perspective for Painting (Piero della Francesca), 62
orchids, 161
origami triangle, 29
Ostwald, Michael J., 126
Oxyrhynchus papyri, 8
Pacioli, Luca, 55, 58, 59, 74, 195, 205
Padovan, Richard, 130
Paganucci, Giovanni, 43
papaya, 152
Parthenon, 103, 104, 105, 106, 107
Pascal, Blaise, 44
Pascal’s triangle, 44
Peasant with a Hoe (Georges Seurat), 122
Penrose, Sir Roger, 34
Pentagon construction, 26, 193
people. See human body.
periwinkle, 151
“The Phi Collection” (Susan Dell), 140
PhiMatrix software, 11, 57, 62, 82, 162, 168, 174
phyllotaxis, 145
plants
African spiral aloe plant, 149
apples, 152
blue passionflower, 151
Echeveria succulent, 148
five-fold symmetry, 152
fractals, 154
fruit, 152
golden angle, 147
lotus flower, 148
morning glory, 151
nautilus shell, 157
nest fern, 161
okra, 152
orchids, 161
papaya, 152
periwinkle, 151
pine cones, 146
Plumeria, 151
Romanesco broccoli, 154
sacred datura, 151
starfruit, 152
Theobroma cocoa plant, 152
Pliny the Elder, 145
Plumeria flower, 151
polyhedrons, 61
Polyptych of the Misericordia (Piero della Francesca), 62, 65
primates, 165
The Procession of the Youngest King (Benozzo Gozzoli), 76
Proportion: Science, Philosophy, Architecture (Richard Padovan), 130
A Psychological Theory of Bipolarity and Reflexivity (Vladimir A. Lefebvre), 200
PsychoMorph software, 167
The Pure Elementary Mathematics (Martin Ohm), 9
Pyramids of Queens, 101
Pythagorean 3–4–5 triangle, 28
quasicrystals, 191
quasi-periodicity, 194
Radiant City, 127
Raphael, 82
Recherches sur l’usage des feuilles dans les plantes (Charles Bonnet), 145
Die Reine Elementar-Mathematik (Martin Ohm), 9
Remarks on Rural Scenery (John Thomas Smith), 134
Research on the Use of Leaves in Plants (Charles Bonnet), 145
Rhind Mathematical Papyrus, 97
Roddenberry, Gene, 138
Romanesco broccoli, 154
RR Lyrae-class stars, 186, 187
rule of thirds, 134
sacred datura plant, 151
Sacred Golden Ratio (Oliver Brady and Carmel Clark), 13
Sainte Marie de la Tourette convent, 127
Salvator Mundi (Leonardo da Vinci), 72, 73, 74
al-Saud, Bader bin Abdullah bin Mohammed bin Farhan, 72
scarab beetles, 163
The School of Athens (Raphael), 82
screw shell, 162
seahorses, 161
Secretariat building, 127
The Seine at La Grande Jatte (Georges Seurat), 125
seked measurements, 97
Self-portrait (Raphael), 82
Semper, Godfried, 108
The Separation of the Earth from the Waters (Michelangelo), 86
Shah-i-Zinda necropolis, 193
Short Book on (the) Five Regular Solids (Piero della Francesca), 62
Sierpinski triangle, 154
Simon, Robert, 72
Simson, Robert, 45
Sistine Chapel, 84, 85, 87, 88, 89
Smalley, Richard, 195
Smith, John Thomas, 134
Solomon’s Temple (Jerusalem), 61
Sphinx, 102
Square construction, 26
starfruit, 152
Star Trek television show, 138, 139
Stiftskirche (“Collegiate Church”), 114
stock markets, 199
Stradivarius violins, 136
St. Vincent Millay, Edna, 19
Sulley, James, 9
Sully, Maurice de, 111
Summary of Arithmetic (Luca Pacioli), 59
Sun, 185
A Sunday Afternoon on the Island of La Grande Jatte (Georges Seurat), 120, 121
Taj Mahal, 118
Talenti, Francesco, 115
Tedder, Chris, 99
teeth, 178
Temple of Zeus (Olympia), 103
Theobroma cocoa plant, 152
Thornton, Robert John, 145
Three Lines construction, 26
Tiddeman, Bernard, 167
Toyota, 137
Triangle construction, 26
truncated icosahedron, 195
Tuman Aka mausoleum, 193
al-Tusi, Nasir al-Din, 20
Typhoon Sonca, 160
The Ugly Duchess (Quentin Matsys), 177
Unité d’Habitation of Berlin. See Corbusierhaus.
UN Secretariat building, 128, 130
Venus, 185
Vernet, Horace, 56
Villanueva, J. R., 189
Vinci, Leonardo da, 134
Vitruvian Man (Leonardo da Vinci), 69, 72, 166
Vitruvius, 108
Vogel, Helmut, 146
Volterra, Daniele da, 84
volutes, 47
Whirlpool Galaxy, 161
William of Ockham, 166
WMAP radiation data, 183
Woman with Umbrella (Georges Seurat), 123
yellowjackets, 163
Ziesing, Adolf, 144