MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

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234 Index Riemann Surfaces 51, 167 Riemann zeta function 167 Riordan, Oliver 124-125 Ripley’s Believe It or Not 179 Roberval, G. P. de 159 Robin boundary condition 102 Robinson, John 25-26 Robinson, J. T. R. 96 rock formation (triangular) 191 Romanian IMO Selection Test 140 Romanian Mathematical Olympiad 140 root movement 25 Rosicrucian cross 21 Rosicrucians 21, 156 Royal Artillery School (Turin) 162 Royal Institute of Technology (Stockholm) 173 Royal Military Academy (Woolwich) 171 Royal Society 105 Rubik, Ernö 128 Rubik’s Cube 128 Rudolphine Tables 155 Russell, Bertrand 1, 169, 173, 186 Russell’s Paradox 173 Russian Mathematical Olympiad 140 rusty compass construction 30-31, 153 Saari, D. G. 91 Sacred Geometry 22, 69 sacred paintings 18 Saint John of the Cross 18 sakthis 5 Sakuma, Tumugu 8 salt 9 Sangaku Geometry 8, 126 Santa Clara University 117 Santa Maria delle Grazie 18 satellite geodesy 79-80 saturation 88 Saturn 83 Saturn’s rings 168 Saviour 18 Schellbach, K. H. 66 Schoenberg, I. J. 77, 105 Schubert, Franz 25 Schwarz alternating method 169 Schwarz-Christoffel formula 169 Schwarz, Hermann Amandus 54, 169, 185 Schwarzian derivative 169 Schwarz minimal surface 169 Schwarz reflection principle / procedure 54, 119, 169 Schwarz’s Lemma 169 Scientific American 119, 178, 181- 182 Scientology v, 24 Scott, C. 80 secondary color 86 Second Punic War 151 Selberg, Atle 177 Selby, Alex 124-125 semiregular tilings 15, 156 Seversky, A. P. de 84 Sforza, Ludovico (Duke of Milan) 11 shawl (triangular) 194 Sheridan, Captain 27 Sherlock Holmes 181 Shield of David 16 shift register sequences 178 Shinto 126 Shiva 5 shogun 126 shortest bisecting path 53 Sicherman, George 117 siege of Syracuse 151 Sierpinski carpet 175 Sierpinski curve 175 Sierpinski Gasket 58-59, 175 Sierpinski number 175 Sierpinski Problem 175
Index 235 Sierpinski, Waclaw 174, 186 Sikorska, J. 75 Silver Age of Greek Mathematics 152 similarity transformation 75 Simmons, G. J. 111 simplex plot 34 Sinclair, Commander 27-28 Singmaster, David 122-123 six triangles 48-49 smallest enclosing circle 52 inscribed triangle 54 small rhombicosidodecahedron 13 small rhombicuboctahedron 13 Smith’s Prize 168 Snail 112 Snefru 2 Snell’s Law 156-157 snow crystal (triangular) 98 snub cube 13 snub dodecahedron 13 Society of Apostles 168, 173 Socrates 149 Socratic dialogues 149 so gusari 8 Soma cube 179 Son 18 Sorbonne 174 Southern Illinois University 176 Spaceship Earth 176 space-time continuum 172 Special Theory of Relativity 172 spherical equilateral triangles 74 Sphinx 112 spidrons vi, 127-128 Square and Triangle Puzzle 105-106 square hole drill vi, 95-96 stamp (triangular) 192 Stanford University 180 Star of David 16 Star Trek 27 Steiner ellipses 166 Steiner, Jakob 66, 165, 167, 175, 185 Steiner surface 165 Steiner Theorem 165 Steiner triple-system 91, 166 Steinhaus, Hugo 43, 105 Stephen the Clerk 150 Stern-Halma 16 Stertenbrink, Günter 124-125 St. John’s College, Cambridge 168 Stockholm University 173 Stone Age 2 Stone, Arthur H. 109 stone (triangular) 191 St. Petersburg Academy of Sciences 161 Strand Magazine 181 Straus, E. G. 111 street signs (triangular) 196 strictly convex position 55 Sun 83-84 superconducting (Sierpinski) gasket vi, 94-95 Supper at Emmaus 17, 18 Supreme Fascist 177 surreal numbers 179-180 sushumna 5 Suzuki, Fukuzo 8 sweets (triangular) 193 Symbolic Logic 169 symmetry group 25, 66 tiling 67 Synagoge (Collection) 152 Synergetics 176 syzygies 42-43 Szostok, T. 75 Tahiti Triangle 190 Tang Dynasty 6 Tangencies 151 tantra 5 Tarot 10
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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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176 Biographical Vignettes topologi
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178 Biographical Vignettes Vignette
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180 Biographical Vignettes and Recr
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182 Biographical Vignettes meeting)
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 234 and 235: 226 Index ture 157 Fermat’s Princ
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 244 and 245: 236 Index Tartaglian Measuring Puzz
Page 246: 238 Index Weber, Wilhelm 164 Weiers
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