MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

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222 Index Barbier’s Theorem 56 barrel sharing problems 121-123 Barrow, Isaac 160 barycentric coordinates 33 Basel Problem 161 basic properties 29-30 Bath College 171 Baxter, A. M. 120 Beeckman, Isaac 156 Beeson, M. J. 61 Beethoven, Ludwig van 25 Belarusan Mathematical Olympiad 140 Bell Telephone Laboratories 178 Bent Pyramid (Dashur) 2 Berlin Academy 161 Bernoulli, Daniel 161 Bernoulli, Johann 161 Bertrand, Joseph 166, 185 Bertrand’s Paradox 109, 166 Bessel, F. W. 164 Biefeld-Brown effect 84 billiard ball packing 94 billiard ball problem 118 bination 69 binomial coefficients 59 binomial theorem 160 Biographical Dictionary of Mathematicians vi biographical vignettes vi, 148-187 biomimetic antenna (“Bat’s Ear”) 80-81 black hole 84 Blaschke, Josef 175 Blaschke-Lebesgue Theorem 56, 174, 176 Blaschke’s Theorem 45, 176 Blaschke, Wilhelm 45, 175, 186 Blundon’s inequality v, 53 Bodleian Library 150 bombers (triangular) 189 The Book 177 Borda voting 91 Borel, Émile 174 Borelli, Giovanni Alfonso 158 Borromean rings 26 bowling pins (triangular) 192 Brahe, Tycho 155 Brahma 5 Brahms, Johannes 25 Brief Lives 148 Briggs, Henry 148 Brotherhood of the Rosy Cross 21 Brown, T. T. 84 Brunnian link 5 Buchman, E. 70 buckminsterfullerene 176 buckyball 176 Budapest University of Art and Design 128 Buddha 6 Buddhism v building (triangular) 197 Bulgarian Mathematical Olympiad 139-140 Burgiel, H. 26 butterfly (triangular) 23, 98 Butterfly Map 97-98 Caesariano, Caesare 18-19 Cahill, B. J. S. 97-98 California Institute of Technology 178, 180 Calypso 83 Cambridge University 168, 176, 180 camera obscura 155 Canterbury Puzzles 181 Cantrell, David 45 Cardano, Girolamo 154 cardiac vector 81-82 Carpenter’s Plane 112 cartography vi, 97-98 Case Institute of Technology 180 Castelli, Benedetto 157
Index 223 cat iii, 189 Catholic Church 20 Cauchy, Augustin-Louis 50 Cauchy-Schwarz inequality 169 Cavalieri, Bonaventura 157-158 Cavendish Laboratory 168 CBS Evening News 180 cellular automata 179 Center for New Music and Audio Technologies (CNMAT) 94 centroid 30, 46 Ceres 164 cevian triangle 38 chainmail (triangular) 7-8 chair (triangular) 195 Chaos Game 59-60 Chartres Cathedral 22 Chebyshev, Pafnuty 165 Chekov, Ensign 27 Chennai Temple 5 Cheops (Khufu) 2 Chess Strategy 181 Chinese Checkers 16 Chinese Remainder Theorem 153 Chinese window lattices 6 Chongsheng Monastery 6 chord progressions 25 Chou Dynasty 6 Christian art 18 Christianity v, 22 Christian mysticism 22 Christ of Saint John of the Cross 17-18 chromaticity 88 Chung, Fan 179 church (triangular) 197 church window (triangular) 196 Chu shih-chieh 59 Ciampoli, Giovanni 157 Cipra, B. 43 circle-of-fifths 25 circumcenter 30, 46 circumcevian triangle 39 circumcircle 30, 52, 69, 76 circumscribing rectangle 47 City College of New York 174 Clark, Andrew 148 classification of cubic curves 160 Cloak of Invisibility 28 closed light paths 54-55 Collège de France 166, 174 College of Invisibles 21 College of San Francesco Saverio 162 Collegio della Sapienza 157 Collegium Carolinum (TU Braunschweig) 163-164 Coltrane, John 25 Combinatory Analysis 171 Companion (Gothic) 20 Computational Confectionery 100 Computer-Generated Encyclopedia of Euclidean Geometry 38 Condorcet voting 91 Conics 151 constructions v, 30 convex tilings 71 Conway, John Horton 43, 123, 179, 187, 180 Conway’s Soldiers 179 Copernicus 155 Corea, Chick 24 corner triangles 38-39 covering properties 45 coverings v, 45 Coxeter groups 176 Coxeter, H. S. M. 25, 69, 176, 187 Coxeter polytopes 176 CO2 emissions 100 Cratylus 149 Crelle, August 165 Crelle’s Journal 165 crochet model (hyperbolic plane) 75 Cronkite, Walter 180 cross formée 20
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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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Page 184 and 185: 176 Biographical Vignettes topologi
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Page 188 and 189: 180 Biographical Vignettes and Recr
Page 190 and 191: 182 Biographical Vignettes meeting)
Page 192 and 193: 184 Biographical Vignettes Figure 6
Page 194 and 195: 186 Biographical Vignettes Figure 6
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 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 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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