MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

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208 Bibliography [138] M. Gardner, Gardner’s Workout: Training the Mind and Entertaining the Spirit, A K Peters, Natick, MA, 2001. [139] M. J. Gazalé, Gnomon: From Pharaohs to Fractals, Princeton University Press, Princeton, NJ, 1999. [140] P. Gerdes, Geometry from Africa: Mathematical and Educational Explorations, Mathematical Association of America, Washington, DC, 1999. [141] M. Gessen, Perfect Rigor, Houghton Mifflin Harcourt, New York, NY, 2009. [142] M. Ghyka, The Geometry of Art and Life, Dover, New York, NY, 1977. [143] J. Gies and F. Gies, Leonard of Pisa and the New Mathematics of the Middle Ages, Crowell, New York, NY, 1969. [144] C. C. Gillispie, Biographical Dictionary of Mathematicians, Volumes 1-4, Charles Scribners’ Sons, New York, NY, 1970-1991. [145] J. W. von Goethe, Theory of Colours, MIT, Cambridge, MA, 1970. [146] S. W. Golomb, “Replicating Figures in the Plane” in The Changing Shape of Geometry, C. Pritchard (Editor), Cambridge University Press, Cambridge, 2003, pp. 367-370. [147] J. M. Gordon, A. M. Goldman, J. Maps, D. Costello, R. Tiberio, and B. Whitehead, “Superconducting-Normal Phase Boundary of a Fractal Network in a Magnetic Field”, Physical Review Letters, Vol. 56, No. 21 (1986), pp. 2280-2283. [148] P. Gorman, Pythagoras: A Life, Routledge & Kegan Paul, London, 1979. [149] R. L. Graham, “On Partitions of an Equilateral Triangle”, Canadian Journal of Mathematics, Vol. XIX, No. 2 (1967), pp. 394-409. [150] R. L. Graham and B. D. Lubachevsky, “Dense Packings of Equal Disks in an Equilateral Triangle: From 22 to 34 and Beyond”, Electronic Journal of Combinatorics, Vol. 2, No. 1, A1 (1995), pp. 1-39. [151] I. Grattan-Guinness, Convolutions in French Mathematics, 1800-1840, Birkhäuser Verlag, Basel, 1990. [152] J. E. Graver, Counting on Frameworks: Mathematics to Aid the Design of Rigid Structures, Mathematical Association of America, Washington, DC, 2001.
Bibliography 209 [153] C. Green, Triangular Philatelics: A Guide for Beginning to Advanced Collectors, Krause Publications, Iola, WI, 1998. [154] A. D. Greenberg, Chemical History Tour, Picturing Chemistry from Alchemy to Modern Molecular Science, Wiley-Interscience, New York, NY, 2000. [155] S. L. Greitzer, International Mathematical Olympiads 1959-1977, Mathematical Association of America, Washington, DC, 1978. [156] B. Grünbaum and G. C. Shephard, Tilings and Patterns, W. H. Freeman and Co., New York, NY, 1987. [157] O. Gupta, Encyclopaedia of India, Pakistan and Bangladesh, Gyan Publishing House, New Delhi, 2006. [158] E. Gutkin, “Two Applications of Calculus to Triangular Billiards”, American Mathematical Monthly, Vol. 104, No. 7 (August-September 1997), pp. 618-622. [159] R. K. Guy, Unsolved Problems in Number Theory, Second Edition, Springer-Verlag, New York, NY, 1994. [160] T. Hall, Carl Friedrich Gauss: A Biography, MIT, Cambridge, MA, 1970. [161] P. R. Halmos, Problems for Mathematicians, Young and Old, Mathematical Association of America, Washington, DC, 1991. [162] P. Hamlyn and E. Friedman, “Partridge Numbers”, Geombinatorics, Vol. XIII, No. 1 (2003), pp. 10-18. [163] M. Hargittai and I. Hargittai, Visual Symmetry, World Scientific, Singapore, 2009. [164] T. L. Heath, The Thirteen Books of Euclid’s Elements, Second Unabridged Edition, Dover, New York, NY, 1956. [165] T. L. Heath, A History of Greek Mathematics, Volume I: From Thales to Euclid, Dover, New York, NY, 1981. [166] T. L. Heath, A History of Greek Mathematics, Volume II: From Aristarchus to Diophantus, Dover, New York, NY, 1981. [167] T. L. Heath, Apollonius of Perga, W. Heffer & Sons, Cambridge, 1961. [168] T. L. Heath, The Works of Archimedes, Dover, Mineola, NY, 2002.
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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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Page 174 and 175: 166 Biographical Vignettes for Eucl
Page 176 and 177: 168 Biographical Vignettes ellipse
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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 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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