210 Bibliography [169] H. Hellman, Great Feuds in Mathematics, Wiley, Hoboken, NJ, 2006. [170] P. Hemenway, Divine Proportion: Φ In Art, Nature, and Science, Sterling, New York, NY, 2005. [171] D. Hestenes, New Foundations for Classical Mechanics, D. Reidel, Dordrecht, 1987. [172] D. Hilbert and S. Cohn-Vossen, Geometry and the Imagination, Chelsea, New York, NY, 1952. [173] Y. Hioka and N. Hamada, “A Tracking Algorithm of Speaker Direction Using Microphones Located at Vertices of Equilateral-Triangle”, European Signal Processing Conference, Vienna, Austria (2004), pp. 1983-1986. [174] C. Hodapp, Freemasons for Dummies, Wiley, Hoboken, NJ, 2005. [175] P. Hoffman, The Man Who Loved Only Numbers: The Story of Paul Erdös and the Search for Mathematical Truth, Hyperion, New York, NY, 1998. [176] L. Hogben, Mathematics for the Million, Norton, New York, NY, 1983. [177] R. Honsberger, Ingenuity in Mathematics, Mathematical Association of America, Washington, DC, 1970. [178] R. Honsberger, Mathematical Gems, Mathematical Association of America, Washington, DC, 1973. [179] R. Honsberger, Mathematical Morsels, Mathematical Association of America, Washington, DC, 1978. [180] R. Honsberger, Mathematical Plums, Mathematical Association of America, Washington, DC, 1979. [181] R. Honsberger, Mathematical Gems III, Mathematical Association of America, Washington, DC, 1985. [182] R. Honsberger, In Pólya’s Footsteps, Mathematical Association of America, Washington, DC, 1997. [183] R. Honsberger, Mathematical Chestnuts from Around the World, Mathematical Association of America, Washington, DC, 2001. [184] R. Honsberger, Mathematical Delights, Mathematical Association of America, Washington, DC, 2004.
Bibliography 211 [185] A. A. Hopkins, Scientific American Handy Book of Facts and Formulas, Munn & Co., New York, NY, 1918. [186] E. How, How to Read an Anemometer, http://www.ehow.com/ how_2074392_read-anemometer.html. [187] L. R. Hubbard, Dianetics: The Modern Science of Mental Health, Hermitage House, New York, NY, 1950. [188] R. P. Jerrard and J. E. Wetzel, “Equilateral Triangles and Triangles”, American Mathematical Monthly, Vol. 109, No. 10 (December 2002), pp. 909-915. [189] R. A. Johnson, Advanced Euclidean Geometry, Dover, Mineola, NY, 2007. [190] J. Kappraff, Connections: The Geometric Bridge Between Art and Science, McGraw-Hill, New York, NY, 1991. [191] N. D. Kazarinoff, Geometric Inequalities, Mathematical Association of America, Washington, DC, 1961. [192] L. M. Kelly, “Equilateral Feeble Four-Point Property” in The Geometry of Metric and Linear Spaces, L. M. Kelly (Editor), Springer-Verlag, New York, NY, 1975, pp. 14-16. [193] M. Khanna, Yantra: The Tantric Symbol of Cosmic Unity, Inner Traditions, Rochester, VT, 2003. [194] J. Kingston and J. L. Synge, “The Sequence of Pedal Triangles”, American Mathematical Monthly, Vol. 95, No. 7 (August-September 1988), pp. 609-620. [195] M. S. Klamkin, International Mathematical Olympiads 1979-1985 and Forty Supplementary Problems, Mathematical Association of America, Washington, DC, 1986. [196] M. S. Klamkin, USA Mathematical Olympiads 1972-1986, Mathematical Association of America, Washington, DC, 1988. [197] M. Kline, Mathematics in Western Culture, Oxford University Press, New York, NY, 1953. [198] D. E. Knuth, “Billiard Balls in an Equilateral Triangle”, Recreational Mathematics Magazine, Vol. 14 (January-February 1964), pp. 20-23.
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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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- Page 196 and 197: Appendix A Gallery of Equilateral T
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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 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
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