MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

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226 Index ture 157 Fermat’s Principle of Least Time 157 Fermat-Torricelli Problem 35, 158- 159 Feynman, Richard P. 109 Fibonacci numbers 67, 69, 153 Fibonacci sequence 67, 70 Fibonacci Triangle 67-68 Fields Medal 151 fighters (triangular) 189 figurate numbers 32 Finite Semifields and Projective Planes 180 Fisher, Irving 97-99 Flag of Israel 16 flag (triangular) 193 flammability diagram 86-87 flammability region 86 flexagon 108-109 Flexagon Committee 109 Flint, J. A. 81 Flint, Michigan 151 Florentine enigma 159 flower (triangular) 23 Fludd, Robert 9 fly (triangular) 23 Fontana, Niccolò (Tartaglia) 154, 120, 183 Foucault, Léon 158 four elements 9-11, 24 Four Squares Theorem 163 Fourth Dynasty 2 Four Triangle Sculpture 25 fractal dimension 58 Fraenkel, A. S. 123 Freemasonry 20-21 Free Will Theorem 169 French Mathematical Olympiad 140 Freudenthal, H. 15 Friedman, Erich 44-45 Frost, E. 15 fullerenes 176 Fuller, R. Buckminster 97-99, 176, 186 fundamental domain 67 fundamental mode 101 Fundamental Theorem of Algebra 164 fundamental triangle 90 Fundamenta Mathematica 175 Fürst, Paul 100 Galileo 157-158 Gallery of Equilateral Triangles vi, 26, 188-198 Game of Life 169 Gamesters of Triskelion 27 game theory vi, 90 game (triangular) 192 Gardner, Martin vi, 43, 119, 169, 179, 181-182, 187 Gardner’s Gaffe 119-120 Garfunkel-Bankoff inequality 53 Gateway Arch 26-27 Gaussian curvature 164 Gauss, Karl Friedrich 50, 163, 167, 185 Gauss Plane 50, 164 Gauss’ Theorem on Triangular Numbers 50, 164 Gazalé, M. J. 69 geese (triangular) 189 gem (triangular) 191 General Theory of Relativity 84, 167, 172 generating parallelogram 61 genetics vi, 90 genotype 90 geodesic dome 99, 176, 195 geometric spiral 69 Géométrie 156 Geometrie der Zahlen 172 Geometry v Gerbert of Aurillac v Gergonne point 39
Index 227 Global Positioning System 80 global warming 100 gnana 5 gnomon 70 Goethe color triangle 86-87 Goldberg, Michael 66, 107 golden mean 2 ratio 68-69 section 13, 58, 153 Golden Triangle Fractal 58 Golomb, Solomon Wolf 112, 178, 187 Gonville and Caius College, Cambridge 179 Gordon, J. M. 94 Gothic cathedral 18-19, 22 Gothic masons 20 GPS antenna 79-80 Graham, Ronald Lewis 73, 177-178, 187 Grand Architect of the Universe 21 Grand Duke Ferdinando II de’ Medici 157-158 Grandi, Luigi Guido 159 gravitational waves vi, 84 Great Pyramid (Giza) 2, 3 Greek Symbol Puzzle 103, 181 Greenhill, Alfred George 171 green pepper (triangular) 23 Green, Trevor 45 group of isometries 67 Grunsky, H. 77 Guinness Book of Records 178 Haberdasher’s Puzzle 104 Hales, Thomas 155 Halley, Edmond 162 Hall, Jr., Marshall 180 Halma 16 Hamada, N. 92 Hamlyn, P. 72 Hamming code 92 distance 92 hana gusari 7-9 handshake problem 32 Harboth, Heiko 125 Hardy-Weinberg frequency 90 Harmonice Mundi 15, 155 Harriot, Thomas 148 Harvard University 176, 178 Hasse, Helmut 175 hat (triangular) 193 Haverford College 171 Haydn, Franz Joseph 25 heat transfer 102 heccaidecadeltahedron 15 Hecke, Erich 175 Heiberg, J. L. 151 Helene 83 heliotrope 164 Hellenic Mathematics 150 Heraclitus 149 Heraldic Cross 20 Hermite, Charles 166, 170 Hertz, Heinrich 169 hexagon 10, 16, 107 hexagram 10, 16 hexiamonds 112, 112-114, 178 Hilbert, David 172 Hilbert’s Eighth Problem 167 Hilbert’s Problems 172 Hinduism v, 4, 5, 16 hinged dissection 104-105 Hioka, Y. 92 history (equilateral triangle) v, 1-28 hollow triangle 26 Holy Lands 20 Holy Spirit 18 homogeneous coordinates 33-34 honeydew melon (triangular) 23 Hooke, Robert 160 Hop Ching Checkers 16 Hopkins, A. A. 30
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MYSTERIES OF THE EQUILATERAL TRIANG
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Dedicated to our beloved Beta Katze
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Preface v PREFACE Welcome to Myster
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Contents Preface . . . . . . . . .
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2 History Lepenski Vir, located on
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4 History counter the sister-states
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6 History Figure 1.11: Chinese Wind
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8 History Wasan which was usually s
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10 History Figure 1.17: Pythagorean
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12 History Figure 1.24: Five Platon
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14 History Figure 1.26: Eight Conve
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16 History (a) (b) (c) Figure 1.31:
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18 History The equilateral triangle
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20 History Figure 1.36: Gothic Maso
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22 History Figure 1.40: Vesica Pisc
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24 History Figure 1.43: Alchemical
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26 History Modern sculpture has not
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28 History (a) (b) Figure 1.49: Tri
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30 Mathematical Properties The rela
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32 Mathematical Properties Figure 2
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38 Mathematical Properties 2.14(b)
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40 Mathematical Properties - Combin
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44 Mathematical Properties be the s
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56 Mathematical Properties (a) (b)
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58 Mathematical Properties Property
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72 Mathematical Properties The best
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74 Mathematical Properties in colum
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Chapter 3 Applications of the Equil
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80 Applications Application 2 (Sate
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82 Applications The ei are the proj
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84 Applications (a) Figure 3.9: (a)
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86 Applications Figure 3.11: Warren
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88 Applications Figure 3.14: Maxwel
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90 Applications Figure 3.17: De Fin
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92 Applications (a) (b) Figure 3.20
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94 Applications (a) Figure 3.23: Lo
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96 Applications Application 25 (Squ
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98 Applications (a) Figure 3.28: Na
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100 Applications (a) (b) (c) (d) Fi
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102 Applications The eigenstructure
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104 Mathematical Recreations Figure
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108 Mathematical Recreations (a) (b
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112 Mathematical Recreations of pla
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120 Mathematical Recreations and n
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124 Mathematical Recreations (a) Fi
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128 Mathematical Recreations Recrea
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130 Mathematical Competitions Probl
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132 Mathematical Competitions Figur
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Chapter 6 Biographical Vignettes In
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150 Biographical Vignettes Forms wh
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152 Biographical Vignettes Apolloni
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154 Biographical Vignettes He disco
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156 Biographical Vignettes He fell
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158 Biographical Vignettes give the
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160 Biographical Vignettes Vignette
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162 Biographical Vignettes Swiss 10
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164 Biographical Vignettes sität B
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166 Biographical Vignettes for Eucl
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168 Biographical Vignettes ellipse
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170 Biographical Vignettes Schwarz
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172 Biographical Vignettes the numb
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174 Biographical Vignettes a conseq
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Page 188 and 189: 180 Biographical Vignettes and Recr
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Page 192 and 193: 184 Biographical Vignettes Figure 6
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Page 196 and 197: Appendix A Gallery of Equilateral T
Page 198 and 199: 190 Gallery Figure A.8: ET Wing Fig
Page 200 and 201: 192 Gallery Figure A.18: ET Bowling
Page 202 and 203: 194 Gallery Figure A.28: ET Escher
Page 204 and 205: 196 Gallery Figure A.36: ET Street
Page 206 and 207: 198 Gallery Figure A.44: ET Tragedy
Page 208 and 209: 200 Bibliography [12] J. Aubrey, Br
Page 210 and 211: 202 Bibliography [42] R. Calinger,
Page 212 and 213: 204 Bibliography [74] J.-P. Delahay
Page 214 and 215: 206 Bibliography [106] J. A. Flint,
Page 216 and 217: 208 Bibliography [138] M. Gardner,
Page 218 and 219: 210 Bibliography [169] H. Hellman,
Page 220 and 221: 212 Bibliography [199] M. Kraitchik
Page 222 and 223: 214 Bibliography [229] T. H. O’Be
Page 224 and 225: 216 Bibliography [260] B. Russell,
Page 226 and 227: 218 Bibliography [290] S. K. Stein,
Page 228 and 229: 220 Bibliography [319] A. Weil, Num
Page 230 and 231: 222 Index Barbier’s Theorem 56 ba
Page 232 and 233: 224 Index Cruise, Tom 24 Crusades 2
Page 236 and 237: 228 Index house (triangular) 197 Hu
Page 238 and 239: 230 Index MacMahon, Percy Alexander
Page 240 and 241: 232 Index oriented triangles 70 ori
Page 242 and 243: 234 Index Riemann Surfaces 51, 167
Page 244 and 245: 236 Index Tartaglian Measuring Puzz
Page 246: 238 Index Weber, Wilhelm 164 Weiers
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MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

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