218 Bibliography [290] S. K. Stein, Mathematics: The Man-Made Universe, Third Edition, Dover, Mineola, NY, 1999. [291] H. Steinhaus, Mathematical Snapshots, Third American Edition, Oxford University Press, Oxford, 1969. [292] H. Steinhaus, One Hundred Problems in Elementary Mathematics, Dover, New York, NY, 1979. [293] I. Stewart, “Tales of Neglected Number”, Scientific American, Vol. 274 (June 1996), pp. 102-103. [294] I. Stewart, “Feedback”, Scientific American (July 1997), p.96; August 1998, p. 97; March 1999, p. 106. [295] I. Stewart, Professor Stewart’s Cabinet of Mathematical Curiosities, Basic Books, New York, NY, 2008. [296] I. Stewart, Professor Stewart’s Hoard of Mathematical Treasures, Basic Books, New York, NY, 2009. [297] D. J. Struik, A Source Book in Mathematics, 1200-1800, Princeton University Press, Princeton, NJ, 1986. [298] J. W. N. Sullivan, Isaac Newton: 1642-1727, Macmillan, New York, NY, 1938. [299] F. Suzuki, “Tumugu Sakuma’s Problem”, Mathematical Gazette, Vol. 85, No. 503 (July 2001), pp. 233-238. [300] F. Suzuki, “An Equilateral Triangle with Sides through the Vertices of an Isosceles Triangle”, Mathematics Magazine, Vol. 74, No. 4 (October 2001), pp. 304-310. [301] G. G. Szpiro, Kepler’s Conjecture, Wiley, New York, NY, 2003. [302] D. Taimina, Crocheting Adventures with Hyperbolic Planes, A K Peters, Wellesley, MA, 2009. [303] D. Taimina and D. W. Henderson, “Reuleaux Triangle”, Kinematic Models for Design Digital Library, http://kmoddl.library.cornell.edu/ tutorials/02/, Accessed 08 February 2010. [304] R. Thiele, “Mathematics in Göttingen (1737-1866)”, Mathematical Intelligencer, Vol. 16, No. 4 (1994), pp. 50-60.
Bibliography 219 [305] H. Tietze, Famous Problems in Mathematics: Solved and Unsolved Mathematical Problems from Antiquity to Modern Times, Graylock, Baltimore, MD, 1965. [306] R. Todev, Geometry Problems from Mathematical Olympiads, CreateSpace, Scotts Valley, CA, 2010. [307] I. Tolstoy, James Clerk Maxwell: A Biography, Cannongate, Edinburgh, 1981. [308] M. Trenkler, “Magic Stars”, ΠME Journal, Vol. 11, No. 10 (2004), pp. 549-554. [309] W. T. Tutte, “The Dissection of Equilateral Triangles into Equilateral Triangles”, Proceedings of the Cambridge Philosophical Society, Mathematical and Physical Sciences, Vol. 44 (1948), pp. 463-482. [310] W. T. Tutte, “Dissections into Equilateral Triangles” in Mathematical Recreations: A Collection in Honor of Martin Gardner, D. A. Klarner (Editor), Dover, Mineola, NY, 1998, pp. 346-382. [311] M. C. K. Tweedie, “A Graphical Method for Solving Tartaglian Measuring Puzzles”, Mathematical Gazette, Vol. 23 (July 1939), pp. 278-282. [312] J. Von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, Princeton, NJ, 1953. [313] M. Wainwright, “Prize Specimens”, Plus, Issue 13 (January 2001), http://plus.maths.org/issue13/features/eternity/index.html. [314] H. Walser, The Golden Section, Mathematical Association of America, Washington, DC, 2001. [315] H. Walser, Fibonacci in the Triangular Lattice, http://www.math. unibas.ch/˜walser/Miniaturen/F/Fibonacci Triangle/Fibonacci Triangle.htm, 2009. [316] J. J. Watkins, Across the Board: The Mathematics of Chessboard Problems, Princeton University Press, Princeton, NJ, 2004. [317] Weather Station, Wind Speed and Direction (Ultrasonic Anemometer 2D), Essendon Bushwalking Club, Victoria, Australia, http://trekker.customer.netspace.net.au/wind.htm. [318] J. R. Weeks, The Shape of Space, Second Edition, Marcel Dekker, New York, 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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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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164 Biographical Vignettes sität B
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166 Biographical Vignettes for Eucl
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- Page 208 and 209: 200 Bibliography [12] J. Aubrey, Br
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- 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 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
- Page 244 and 245: 236 Index Tartaglian Measuring Puzz
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