214 Bibliography [229] T. H. O’Beirne, Puzzles and Paradoxes, Oxford University Press, New York, NY, 1965. [230] J. J. O’Connor and E. F. Robertson, The MacTutor History of Mathematics, http://www-history.mcs.st-andrews.ac.uk/Biographies/, 2010. [231] C. S. Ogilvy, Excursions in Geometry, Dover, Mineola, NY, 1990. [232] A. Okabe, B. Boots and K. Sugihara, Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, Wiley, Chichester, 1992. [233] D. J. O’Meara, Pythagoras Revived: Mathematics and Philosophy in Late Antiquity, Oxford University Press, Oxford, 1989. [234] T. Orton, “From Tessellations to Fractals” in The Changing Shape of Geometry, C. Pritchard (Editor), Cambridge University Press, Cambridge, 2003, pp. 401-405. [235] J. Pach and R. Pinchasi, “How Many Unit Equilateral Triangles Can Be Generated by N Points in Convex Position?”, American Mathematical Monthly, Vol. 110, No. 5 (May 2003), pp. 400-406. [236] D. Parlett, The Oxford History of Board Games, Oxford University Press, Oxford, 1999. [237] D. Pedoe, Circles: A Mathematical View, 2nd Edition, Mathematical Association of America, Washington, DC, 1995. [238] E. Pegg, “The Eternity Puzzle”, Math Puzzle: The Puzzling Weblog of Recreational Mathematics, http://mathpuzzle.com/eternity.html. [239] H.-O. Peitgen, H. Jürgens and D. Saupe, Chaos and Fractals: New Frontiers in Science, Springer-Verlag, New York, NY, 1992. [240] I. Peterson, Fragments of Infinity: A Kaleidoscope of Math and Art, Wiley, New York, NY, 2001. [241] I. Peterson, Mathematical Treks: From Surreal Numbers to Magic Circles, Mathematical Association of America, Washington, DC, 2002. [242] C. A. Pickover, The Mαth βook, Sterling, New York, NY, 2009. [243] G. Pólya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Princeton University Press, Princeton, NJ, 1951. [244] L. Pook, Flexagons Inside Out, Cambridge University Press, Cambridge, 2003.
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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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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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- 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 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
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