200 Bibliography [12] J. Aubrey, Brief Lives and Other Selected Writings, Scribners, New York, NY, 1949. [13] R. Avizienis, A. Freed, P. Kassakian, and D. Wessel, “A Compact 120 Independent Element Spherical Loudspeaker Array with Programmable Radiation Patterns”, Audio Engineering Society 120th Convention, Paris, France (2006), Paper No. 6783. [14] W. W. R. Ball, Mathematical Recreations & Essays, Eleventh Edition, Macmillan, New York, NY, 1944. [15] M. Barber, The New Knighthood: A History of the Order of the Temple, Cambridge University Press, Cambridge, 1994. [16] A. M. Baxter and R. Umble, “Periodic Orbits for Billiards on an Equilateral Triangle”, American Mathematical Monthly, Vol. 115, No. 6 (June-July 2008), pp. 479-491. [17] M. J. Beeson, “Triangles with Vertices on Lattice Points”, American Mathematical Monthly, Vol. 99, No. 3 (March 1992), pp. 243-252. [18] S.-M. Belcastro and C. Yackel, Making Mathematics with Needlework, A. K. Peters, Wellesly, MA, 2008. [19] E. T. Bell, The Last Problem, Simon and Schuster, New York, NY, 1961. [20] C. D. Bennett, B. Mellor, and P. D. Shanahan, “Drawing a Triangle on the Thurston Model of Hyperbolic Space”, Mathematics Magazine, Vol. 83, No. 2 (2010), pp. 83-99. [21] D. Bergamini, Mathematics (Life Science Library), Time, New York, NY, 1963. [22] G. Berzsenyi and S. B. Maurer, The Contest Problem Book V: 1983-1988, Mathematical Association of America, Washington, DC, 1997. [23] G. Birkhoff, A Source Book in Classical Analysis, Harvard University Press, Cambridge, MA, 1973. [24] G. D. Birkhoff, Dynamical Systems, American Mathematical Society Colloquium Publications, Volume IX, Providence, RI, 1927. [25] M. Bishop, Pascal: The Life of Genius, Bell, London, 1937. [26] W. J. Blundon, “Inequalities Associated with the Triangle”, Canadian Mathematical Bulletin, Vol. 8 (1965), pp. 615-626.
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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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34 Mathematical Properties Figure 2
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36 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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42 Mathematical Properties Figure 2
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44 Mathematical Properties be the s
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46 Mathematical Properties Figure 2
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48 Mathematical Properties Figure 2
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50 Mathematical Properties Figure 2
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52 Mathematical Properties Figure 2
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54 Mathematical Properties Figure 2
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56 Mathematical Properties (a) (b)
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58 Mathematical Properties Property
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60 Mathematical Properties Figure 2
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62 Mathematical Properties Figure 2
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64 Mathematical Properties (a) (b)
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66 Mathematical Properties Figure 2
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68 Mathematical Properties Figure 2
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70 Mathematical Properties (a) (b)
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72 Mathematical Properties The best
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74 Mathematical Properties in colum
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76 Mathematical Properties Figure 2
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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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106 Mathematical Recreations Figure
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108 Mathematical Recreations (a) (b
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110 Mathematical Recreations Figure
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112 Mathematical Recreations of pla
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114 Mathematical Recreations Figure
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116 Mathematical Recreations Figure
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118 Mathematical Recreations Figure
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120 Mathematical Recreations and n
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122 Mathematical Recreations Figure
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124 Mathematical Recreations (a) Fi
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126 Mathematical Recreations Figure
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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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134 Mathematical Competitions Figur
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136 Mathematical Competitions Probl
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138 Mathematical Competitions Probl
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140 Mathematical Competitions Probl
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142 Mathematical Competitions Figur
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144 Mathematical Competitions Figur
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146 Mathematical Competitions Figur
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Chapter 6 Biographical Vignettes In
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- Page 210 and 211: 202 Bibliography [42] R. Calinger,
- Page 212 and 213: 204 Bibliography [74] J.-P. Delahay
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- 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
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- 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
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- Page 234 and 235: 226 Index ture 157 Fermat’s Princ
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- 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
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