MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

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236 Index Tartaglian Measuring Puzzles 120- 121 tattvas 5 Tatzenkreuz 20 Technical University of Berlin 169 Technical University of Braunschweig 125 Technische Hochschule (Graz) 175 telegraph 164 Telesto 83 Tenebrae 9 Tercentenary Euler Celebration 162 ternary diagram 33-34, 88, 90, 121 Terra 9 tertiary color 86 tessellations to fractals 62-63 Tethys 83 tetracaidecadeltahedron 15 Tetragrammaton 10 tetrahedral geodesics 64-65 tetrahedron 9, 11, 15, 117 tetraktys 9-10 Tetris 178 TeX 180 Thales 149 Theaetetus 149-150 Theobald, Gavin 107 Theodorus 149 Theorema Egregium 164 Theoria motus corporum coelestium 164 Theory of Forms 149-150 Thirty Years’ War 156 three-body problem 83, 163 three jug problem 120-121, 154 Three Pagodas 6-7 Thurston model 75 Timaeus 11, 150 Torricelli, Evangelista 35, 157-158, 184 Torricelli’s Equation 158 Torricelli’s Law / Theorem 158 Torricelli’s Trumpet (Gabriel’s Horn) 158 torsional rigidity 100 Traffic Jam Game 123 Traité du triangle arithmétique 58, 159 Trattato della Pittura 153 Trattato generale di numeri e misure 154 Travolta, John 24 Treatise on Electricity and Magnetism 168-169 triangle 9 Triangle and Square Puzzle 105 Triangle Book 180 triangle geometry v Triangle Inequality 52 triangle in rectangle 41 triangle in square 41-42 triangles with integer sides 122-123 Triangle-to-Triangle Dissection 106 Triangle Waist Co. 198 triangular bounds 100-101 dipyramid 15 honeycomb 125-126 numbers 10, 32-33, 59 triangulation triangles 38-39 trihexaflexagon 108-109 trilinear coordinates 33 Triluminary 27-28 Trinity 4, 18 Trinity College, Cambridge 160, 173 Tripurasundari 5 trisection thru bisection 32 Trojan asteroid 83 truncated cube 13 dodecahedron 13 octahedron 13 tetrahedron 13 Tschirnhaus, E. W. von 159
Index 237 Tuckerman, Bryant 109 Tukey, John W. 109 tulip (triangular) 189 Turkish Mathematical Olympiad 141 Tutte, W. T. 70 Tweedie, M. C. K. 120 two-color map 110 UFO (triangular) 190 Uhura, Lieutenant 27 Ulam, Stanislaw 177 Umble, R. 120 University of Alaska 178 University of Basel 161 University of Berlin 165-166, 169 University of Bonn 172, 175 University of Breifswald 175 University of Caen 170 University of California-Berkeley 94, 178 University of California-San Diego 179 University of Chicago 178, 182 University of Ferrara 162 University of Göttingen 164, 166, 169, 172, 175 University of Halle 169 University of Hamburg 175 University of Helmstedt 164 University of Königsberg 172, 175 University of Lvov 175 University of Orleans 157 University of Paris 170 University of Pisa 175 University of Poitiers 156 University of Prague 175 University of Southern California 178 University of Toronto 176 University of Tübingen 155, 175 University of Vienna 175 University of Warsaw 175 upper explosive limit (UEL) 86 USA Mathematical Olympiad 129, 136-137 U. S. Chess Hall of Fame 181 U. S. Coast and Geodetic Survey 80 USDA Soil Texture Triangle 88-89 Valen 27-28 Van der Waerden, B. L. 15 ventricular hypertrophy 81 vesica piscis 22 vibration theory 102 Victoria cross 20 da Vinci, Leonardo 11, 13, 17-18, 153, 183 Virgin Mary 22 viruses 99 Vishnavite 16 Vishnu 5, 16 Vitruvius 18 Viviani’s Theorem 33-34 Viviani, Vincenzo 157-158, 184 Viviani Window 159 Von Neumann, John 90 Voronoi diagram 62 Voronoi, G. F. 175 voting paradox 91 theory vi, 91 Voyager spacecrafts 168 Wackhenfels, Baron von 155 Wagner, Richard 25 Wagner, Rudolf 165 Wainwright, R. T. 71 Wallenstein, General 155 Wallis, John 76, 148 Wanderer Fantasy 25 Wankel engine 96 Warren truss 85-86 Wasan 7 Washington, George 21 Watts drill 96
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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)
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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 242 and 243: 234 Index Riemann Surfaces 51, 167
Page 246: 238 Index Weber, Wilhelm 164 Weiers
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MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

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