202 Bibliography [42] R. Calinger, Classics of Mathematics, Prentice Hall, Upper Saddle River, NJ, 1982. [43] L. Campbell and W. Garnett, The Life of James Clerk Maxwell, Macmillan, London, 1884. [44] F. Capra, The Science of Leonardo, Doubleday, New York, NY, 2007. [45] E. P. Carter, C. P. Richter and C. H. Greene, “A Graphic Application of the Principle of the Equilateral Triangle for Determining the Direction of the Electrical Axis of the Heart in the Human Electrocardiogram”, Bulletin of the Johns Hopkins Hospital, Vol. XXX, No. 340 (June 1919), pp. 162- 167. [46] J. Casey, A Treatise on the Analytical Geometry of the Point, Line, Circle, and Conic Sections, Dublin University Press, Dublin, 1893. [47] G. Chang and T. W. Sederberg, Over and Over Again, Mathematical Association of America, Washington, DC, 1997. [48] Z. Chen and T. Liang, “The Converse of Viviani’s Theorem”, College Mathematics Journal, Vol. 37, No. 5 (2006), pp. 390-391. [49] P. Christian, The History and Practice of Magic, Citadel Press, Secaucus, NJ, 1963. [50] T. Churton, The Invisible History of the Rosicrucians: The World’s Most Mysterious Secret Society, Inner Traditions, Rochester, VT, 2009. [51] R. W. Clark, The Life of Bertrand Russell, Knopf, New York, NY, 1975. [52] M. N. Cohen, Lewis Carroll: A Biography, Vintage, New York, NY, 1995. [53] G. M. Cole, “The Beginnings of Satellite Geodesy”, Professional Surveyor Magazine, Vol. 30, No. 1 (January 2010), History Corner. [54] S. Colman, Harmonic Proportion and Form in Nature, Art and Architecture, Dover, Mineola, NY, 2003. [55] J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus, New York, NY, 1996. [56] J. L. Coolidge, The Mathematics of Great Amateurs, Dover, New York, NY, 1963. [57] R. Courant and H. Robbins, What Is Mathematics?, Oxford University Press, New York, NY, 1941.
Bibliography 203 [58] H. S. M. Coxeter, Introduction to Geometry, Second Edition, Wiley, New York, NY, 1969. [59] H. S. M. Coxeter, “Virus Macromolecules and Geodesic Domes”, in A Spectrum of Mathematics (Essays Presented to H. G. Forder), J. C. Butcher (Editor), Auckland University Press, Auckland, 1971, pp. 98-107. [60] H. S. M. Coxeter, Regular Polytopes, Third Edition, Dover, New York, NY, 1973. [61] H. S. M. Coxeter, “Symmetrical Combinations of Three or Four Hollow Triangles”, Mathematical Intelligencer, Vol. 16, No. 3 (1994), pp. 25-30. [62] H. S. M. Coxeter and S. L. Greitzer, Geometry Revisited, Mathematical Association of America, Washington, DC, 1967. [63] T. Crilly, 50 Mathematical Ideas You Really Need to Know, Quercus, London, 2007. [64] H. T. Croft, K. J. Falconer and R. K. Guy, Unsolved Problems in Geometry, Springer-Verlag, New York, NY, 1991. [65] J. F. Crow and M. Kimura, An Introduction to Population Genetics Theory, Blackburn, Caldwell, NJ, 1970. [66] H. M. Cundy and A. P. Rollett, Mathematical Models, Oxford University Press, Oxford, 1951. [67] T. Dantzig, Henri Poincaré, Scribners, New York, NY, 1954. [68] D. Darling, The Universal Book of Mathematics: From Abracadabra to Zeno’s Paradoxes, Castle, Edison, NJ, 2007. [69] P. J. Davis, The Schwarz Function and Its Applications, Mathematical Association of America, Washington, DC, 1974. [70] P. J. Davis, “The Rise, Fall, and Possible Transfiguration of Triangle Geometry: A Mini-History”, American Mathematical Monthly, Vol. 102, No. 3 (1995), pp. 204-214. [71] P. J. Davis, Mathematical Encounters of the Second Kind, Birkhäuser, Boston, MA, 1997. [72] R. O. E. Davis and H. H. Bennett, “Grouping of Soils on the Basis of Mechanical Analysis”, USDA Departmental Circulation, No. 419 (1927). [73] D. Dekov, “Equilateral Triangles”, Journal of Computer-Generated Euclidean Geometry, Vol. 2007, No. 41 (December 2007), pp. 1-9.
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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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- Page 208 and 209: 200 Bibliography [12] J. Aubrey, Br
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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
- Page 232 and 233: 224 Index Cruise, Tom 24 Crusades 2
- Page 234 and 235: 226 Index ture 157 Fermat’s Princ
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- Page 238 and 239: 230 Index MacMahon, Percy Alexander
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- Page 242 and 243: 234 Index Riemann Surfaces 51, 167
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