MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

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206 Bibliography [106] J. A. Flint, “A Biomimetic Antenna in the Shape of a Bat’s Ear”, IEEE Antennas and Wireless Propagation Letters, Vol. 5, Issue 1 (Dec. 2006), pp. 145-147. [107] D. H. Fowler, The Mathematics of Plato’s Academy: A New Reconstruction, Oxford University Press, Oxford, 1987. [108] J. B. Fraleigh, A First Course in Abstract Algebra, Addison-Wesley, Reading, MA, 1967. [109] G. N. Frederickson, Dissections: Plane & Fancy, Cambridge University Press, Cambridge, 1997. [110] E. Friedman, Erich’s Packing Center, http://www2.stetson.edu/ ˜efriedma/packing.html, 2010. [111] H. Fukagawa and D. Pedoe, Japanese Temple Geometry Problems, Charles Babbage Research Center, Winnipeg, 1989. [112] H. Fukagawa and T. Rothman, Sacred Mathematics: Japanese Temple Geometry, Princeton University Press, Princeton, NJ, 2008. [113] R. B. Fuller, Synergetics: Explorations in the Geometry of Thinking, Macmillan, New York, NY, 1975. [114] Z. Füredi and J. E. Wetzel, “The Smallest Convex Cover for Triangles of Perimeter Two”, Geometriae Dedicata, Vol. 81, No. 3 (July 2000), pp. 285-293. [115] D. Furlong, The Keys to the Temple, Piatkus, London, 1997. [116] W. Gallatly, The Modern Geometry of the Triangle, Second Edition, Hodgson, London, 1929. [117] A. F. Garcia Marin, G. Heinzel and K. Danzmann, “Interferometry for LISA and LISA Pathfinder”, Journal of Physics: Conference Series, Vol. 66, No. 012052 (2007), pp. 1-5. [118] M. Gardner, “Mathematical Games: How to solve puzzles by graphing the rebounds of a bouncing ball”, Scientific American, Vol. 209, No. 3 (September 1963), pp. 248-266. [119] M. Gardner, Hexagons, Probability Paradoxes, and the Tower of Hanoi, Cambridge University Press, New York, NY, 2008. [120] M. Gardner, Origami, Eleusis, and the Soma Cube, Cambridge University Press, New York, NY, 2008.
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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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Page 170 and 171: 162 Biographical Vignettes Swiss 10
Page 172 and 173: 164 Biographical Vignettes sität B
Page 174 and 175: 166 Biographical Vignettes for Eucl
Page 176 and 177: 168 Biographical Vignettes ellipse
Page 178 and 179: 170 Biographical Vignettes Schwarz
Page 180 and 181: 172 Biographical Vignettes the numb
Page 182 and 183: 174 Biographical Vignettes a conseq
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 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 244 and 245: 236 Index Tartaglian Measuring Puzz
Page 246: 238 Index Weber, Wilhelm 164 Weiers
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